Advances in Brillouin–Mandelstam light-scattering spectroscopy

<!DOCTYPE html> <html lang="en" class="grade-c"> <head> <title>Advances in Brillouin–Mandelstam light-scattering spectroscopy | Nature Photonics</title> <link rel="alternate" type="application/rss+xml" href="https://www.nature.com/nphoton.rss"/> <script id="save-data-connection-testing"> function hasConnection() { return navigator.connection || navigator.mozConnection || navigator.webkitConnection || navigator.msConnection; } function createLink(src) { var preloadLink = document.createElement("link"); preloadLink.rel = "preload"; preloadLink.href = src; preloadLink.as = "font"; preloadLink.type = "font/woff2"; preloadLink.crossOrigin = ""; document.head.insertBefore(preloadLink, document.head.firstChild); } var connectionDetail = { saveDataEnabled: false, slowConnection: false }; var connection = hasConnection(); if (connection) { connectionDetail.saveDataEnabled = connection.saveData; if (/\slow-2g|2g/.test(connection.effectiveType)) { connectionDetail.slowConnection = true; } } if (!(connectionDetail.saveDataEnabled || connectionDetail.slowConnection)) { createLink("/static/fonts/HardingText-Regular-Web-cecd90984f.woff2"); } else { document.documentElement.classList.add('save-data'); } </script> <link rel="preconnect" href="https://cmp.nature.com" crossorigin> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="applicable-device" content="pc,mobile"> <meta name="viewport" content="width=device-width,initial-scale=1.0,maximum-scale=5,user-scalable=yes"> <meta name="360-site-verification" content="5a2dc4ab3fcb9b0393241ffbbb490480" /> <script data-test="dataLayer"> window.dataLayer = [{"content":{"category":{"contentType":"review article","legacy":{"webtrendsPrimaryArticleType":"reviews","webtrendsSubjectTerms":"raman-spectroscopy","webtrendsContentCategory":null,"webtrendsContentCollection":null,"webtrendsContentGroup":"Nature Photonics","webtrendsContentGroupType":null,"webtrendsContentSubGroup":"Review Article","status":null}},"article":{"doi":"10.1038/s41566-021-00836-5"},"attributes":{"cms":null,"deliveryPlatform":"oscar","copyright":{"open":false,"legacy":{"webtrendsLicenceType":null}}},"contentInfo":{"authors":["Fariborz Kargar","Alexander A. Balandin"],"publishedAt":1626912000,"publishedAtString":"2021-07-22","title":"Advances in Brillouin–Mandelstam light-scattering spectroscopy","legacy":null,"publishedAtTime":null,"documentType":"aplusplus","subjects":"Raman spectroscopy"},"journal":{"pcode":"nphoton","title":"nature photonics","volume":"15","issue":"10","id":41566,"publishingModel":"Hybrid Access"},"authorization":{"status":false},"features":[{"name":"furtherReadingSection","present":true}],"collection":null},"page":{"category":{"pageType":"article"},"attributes":{"template":"mosaic","featureFlags":[{"name":"nature-onwards-journey","active":false}],"testGroup":null},"search":null},"privacy":{},"version":"1.0.0","product":null,"session":null,"user":null,"backHalfContent":true,"country":"HK","hasBody":true,"uneditedManuscript":false,"twitterId":["o3xnx","o43y9","o3ef7"],"baiduId":"d38bce82bcb44717ccc29a90c4b781ea","japan":false}]; window.dataLayer.push({ ga4MeasurementId: 'G-ERRNTNZ807', ga360TrackingId: 'UA-71668177-1', twitterId: ['3xnx', 'o43y9', 'o3ef7'], baiduId: 'd38bce82bcb44717ccc29a90c4b781ea', ga4ServerUrl: 'https://collect.nature.com', imprint: 'nature' }); </script> <script> (function(w, d) { w.config = w.config || {}; w.config.mustardcut = false; if (w.matchMedia && w.matchMedia('only print, only all and (prefers-color-scheme: no-preference), only all and (prefers-color-scheme: light), only all and (prefers-color-scheme: dark)').matches) { w.config.mustardcut = true; d.classList.add('js'); d.classList.remove('grade-c'); d.classList.remove('no-js'); } })(window, document.documentElement); </script> <style>@media only print, only all and (prefers-color-scheme: no-preference), only all and (prefers-color-scheme: light), only all and (prefers-color-scheme: dark) { .c-article-editorial-summary__container .c-article-editorial-summary__article-title,.c-card--major .c-card__title,.c-card__title,.u-h2,.u-h3,h2,h3{-webkit-font-smoothing:antialiased;font-family:Harding,Palatino,serif;font-weight:700;letter-spacing:-.0117156rem}.c-article-editorial-summary__container .c-article-editorial-summary__article-title,.c-card__title,.u-h3,h3{font-size:1.25rem;line-height:1.4rem}.c-reading-companion__figure-title,.u-h4,h4{-webkit-font-smoothing:antialiased;font-weight:700;line-height:1.4rem}html{text-size-adjust:100%;box-sizing:border-box;font-size:100%;height:100%;line-height:1.15;overflow-y:scroll}body{background:#eee;color:#222;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1.125rem;line-height:1.76;margin:0;min-height:100%}details,main{display:block}h1{font-size:2em;margin:.67em 0}a,sup{vertical-align:baseline}a{background-color:transparent;color:#069;overflow-wrap:break-word;text-decoration:underline;text-decoration-skip-ink:auto;word-break:break-word}b{font-weight:bolder}sup{font-size:75%;line-height:0;position:relative;top:-.5em}img{border:0;height:auto;max-width:100%;vertical-align:middle}button,input,select{font-family:inherit;font-size:100%;line-height:1.15;margin:0}button,input{overflow:visible}button,select{text-transform:none}[type=submit],button{-webkit-appearance:button}[type=checkbox]{box-sizing:border-box;padding:0}summary{display:list-item}[hidden]{display:none}button{border-radius:0;cursor:pointer;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif}h1{-webkit-font-smoothing:antialiased;font-family:Harding,Palatino,serif;font-size:2rem;font-weight:700;letter-spacing:-.0390625rem;line-height:2.25rem}.c-card--major .c-card__title,.u-h2,.u-h3,h2{font-family:Harding,Palatino,serif;letter-spacing:-.0117156rem}.c-card--major .c-card__title,.u-h2,h2{-webkit-font-smoothing:antialiased;font-size:1.5rem;font-weight:700;line-height:1.6rem}.u-h3{font-size:1.25rem}.c-card__title,.c-reading-companion__figure-title,.u-h3,.u-h4,h4,h5,h6{-webkit-font-smoothing:antialiased;font-weight:700;line-height:1.4rem}.c-article-editorial-summary__container .c-article-editorial-summary__article-title,.c-card__title,h3{font-family:Harding,Palatino,serif;font-size:1.25rem}.c-article-editorial-summary__container .c-article-editorial-summary__article-title,h3{-webkit-font-smoothing:antialiased;font-weight:700;letter-spacing:-.0117156rem;line-height:1.4rem}.c-reading-companion__figure-title,.u-h4,h4{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1.125rem;letter-spacing:-.0117156rem}button:focus{outline:3px solid #fece3e;will-change:transform}input+label{padding-left:.5em}nav ol,nav ul{list-style:none none}p:empty{display:none}.sans-serif{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif}.article-page{background:#fff}.c-article-header{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;margin-bottom:40px}.c-article-identifiers{color:#6f6f6f;display:flex;flex-wrap:wrap;font-size:1rem;line-height:1.3;list-style:none;margin:0 0 8px;padding:0}.c-article-identifiers__item{border-right:1px solid #6f6f6f;list-style:none;margin-right:8px;padding-right:8px}.c-article-identifiers__item:last-child{border-right:0;margin-right:0;padding-right:0}.c-article-title{font-size:1.5rem;line-height:1.25;margin:0 0 16px}@media only screen and (min-width:768px){.c-article-title{font-size:1.875rem;line-height:1.2}}.c-article-author-list{display:inline;font-size:1rem;list-style:none;margin:0 8px 0 0;padding:0;width:100%}.c-article-author-list__item{display:inline;padding-right:0}.c-article-author-list svg{margin-left:4px}.c-article-author-list__show-more{display:none;margin-right:4px}.c-article-author-list__button,.js .c-article-author-list__item--hide,.js .c-article-author-list__show-more{display:none}.js .c-article-author-list--long .c-article-author-list__show-more,.js .c-article-author-list--long+.c-article-author-list__button{display:inline}@media only screen and (max-width:539px){.js .c-article-author-list__item--hide-small-screen{display:none}.js .c-article-author-list--short .c-article-author-list__show-more,.js .c-article-author-list--short+.c-article-author-list__button{display:inline}}#uptodate-client,.js .c-article-author-list--expanded .c-article-author-list__show-more{display:none!important}.js .c-article-author-list--expanded .c-article-author-list__item--hide-small-screen{display:inline!important}.c-article-author-list__button,.c-button-author-list{background:#ebf1f5;border:4px solid #ebf1f5;border-radius:20px;color:#666;font-size:.875rem;line-height:1.4;padding:2px 11px 2px 8px;text-decoration:none}.c-article-author-list__button svg,.c-button-author-list svg{margin:1px 4px 0 0}.c-article-author-list__button:hover,.c-button-author-list:hover{background:#069;border-color:transparent;color:#fff}.c-article-info-details{font-size:1rem;margin-bottom:8px;margin-top:16px}.c-article-info-details__cite-as{border-left:1px solid #6f6f6f;margin-left:8px;padding-left:8px}.c-article-metrics-bar{display:flex;flex-wrap:wrap;font-size:1rem;line-height:1.3}.c-article-metrics-bar__wrapper{margin:16px 0}.c-article-metrics-bar__item{align-items:baseline;border-right:1px solid #6f6f6f;margin-right:8px}.c-article-metrics-bar__item:last-child{border-right:0}.c-article-metrics-bar__count{font-weight:700;margin:0}.c-article-metrics-bar__label{color:#626262;font-style:normal;font-weight:400;margin:0 10px 0 5px}.c-article-metrics-bar__details{margin:0}.c-article-main-column{font-family:Harding,Palatino,serif;margin-right:8.6%;width:60.2%}@media only screen and (max-width:1023px){.c-article-main-column{margin-right:0;width:100%}}.c-article-extras{float:left;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;width:31.2%}@media only screen and (max-width:1023px){.c-article-extras{display:none}}.c-article-associated-content__container .c-article-associated-content__title,.c-article-section__title{border-bottom:2px solid #d5d5d5;font-size:1.25rem;margin:0;padding-bottom:8px}@media only screen and (min-width:768px){.c-article-associated-content__container .c-article-associated-content__title,.c-article-section__title{font-size:1.5rem;line-height:1.24}}.c-article-associated-content__container .c-article-associated-content__title{margin-bottom:8px}.c-article-body p{margin-bottom:24px;margin-top:0}.c-article-section{clear:both}.c-article-section__content{margin-bottom:40px;padding-top:8px}@media only screen and (max-width:1023px){.c-article-section__content{padding-left:0}}.c-article-authors-search{margin-bottom:24px;margin-top:0}.c-article-authors-search__item,.c-article-authors-search__title{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif}.c-article-authors-search__title{color:#626262;font-size:1.05rem;font-weight:700;margin:0;padding:0}.c-article-authors-search__item{font-size:1rem}.c-article-authors-search__text{margin:0}.c-article-license__badge,c-card__section{margin-top:8px}.c-code-block{border:1px solid #eee;font-family:monospace;margin:0 0 24px;padding:20px}.c-code-block__heading{font-weight:400;margin-bottom:16px}.c-code-block__line{display:block;overflow-wrap:break-word;white-space:pre-wrap}.c-article-share-box__no-sharelink-info{font-size:.813rem;font-weight:700;margin-bottom:24px;padding-top:4px}.c-article-share-box__only-read-input{border:1px solid #d5d5d5;box-sizing:content-box;display:inline-block;font-size:.875rem;font-weight:700;height:24px;margin-bottom:8px;padding:8px 10px}.c-article-share-box__button--link-like{background-color:transparent;border:0;color:#069;cursor:pointer;font-size:.875rem;margin-bottom:8px;margin-left:10px}.c-article-editorial-summary__container{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1rem}.c-article-editorial-summary__container .c-article-editorial-summary__content p:last-child{margin-bottom:0}.c-article-editorial-summary__container .c-article-editorial-summary__content--less{max-height:9.5rem;overflow:hidden}.c-article-editorial-summary__container .c-article-editorial-summary__button{background-color:#fff;border:0;color:#069;font-size:.875rem;margin-bottom:16px}.c-article-editorial-summary__container .c-article-editorial-summary__button.active,.c-article-editorial-summary__container .c-article-editorial-summary__button.hover,.c-article-editorial-summary__container .c-article-editorial-summary__button:active,.c-article-editorial-summary__container .c-article-editorial-summary__button:hover{text-decoration:underline;text-decoration-skip-ink:auto}.c-article-associated-content__container .c-article-associated-content__collection-label{font-size:.875rem;line-height:1.4}.c-article-associated-content__container .c-article-associated-content__collection-title{line-height:1.3}.c-context-bar{box-shadow:0 0 10px 0 rgba(51,51,51,.2);position:relative;width:100%}.c-context-bar__title{display:none}.c-reading-companion{clear:both;min-height:389px}.c-reading-companion__sticky{max-width:389px}.c-reading-companion__scroll-pane{margin:0;min-height:200px;overflow:hidden auto}.c-reading-companion__tabs{display:flex;flex-flow:row nowrap;font-size:1rem;list-style:none;margin:0 0 8px;padding:0}.c-reading-companion__tabs>li{flex-grow:1}.c-reading-companion__tab{background-color:#eee;border:1px solid #d5d5d5;border-image:initial;border-left-width:0;color:#069;font-size:1rem;padding:8px 8px 8px 15px;text-align:left;width:100%}.c-reading-companion__tabs li:first-child .c-reading-companion__tab{border-left-width:1px}.c-reading-companion__tab--active{background-color:#fff;border-bottom:1px solid #fff;color:#222;font-weight:700}.c-reading-companion__sections-list{list-style:none;padding:0}.c-reading-companion__figures-list,.c-reading-companion__references-list{list-style:none;min-height:389px;padding:0}.c-reading-companion__references-list--numeric{list-style:decimal inside}.c-reading-companion__sections-list{margin:0 0 8px;min-height:50px}.c-reading-companion__section-item{font-size:1rem;padding:0}.c-reading-companion__section-item a{display:block;line-height:1.5;overflow:hidden;padding:8px 0 8px 16px;text-overflow:ellipsis;white-space:nowrap}.c-reading-companion__figure-item{border-top:1px solid #d5d5d5;font-size:1rem;padding:16px 8px 16px 0}.c-reading-companion__figure-item:first-child{border-top:none;padding-top:8px}.c-reading-companion__reference-item{border-top:1px solid #d5d5d5;font-size:1rem;padding:8px 8px 8px 16px}.c-reading-companion__reference-item:first-child{border-top:none}.c-reading-companion__reference-item a{word-break:break-word}.c-reading-companion__reference-citation{display:inline}.c-reading-companion__reference-links{font-size:.813rem;font-weight:700;list-style:none;margin:8px 0 0;padding:0;text-align:right}.c-reading-companion__reference-links>a{display:inline-block;padding-left:8px}.c-reading-companion__reference-links>a:first-child{display:inline-block;padding-left:0}.c-reading-companion__figure-title{display:block;margin:0 0 8px}.c-reading-companion__figure-links{display:flex;justify-content:space-between;margin:8px 0 0}.c-reading-companion__figure-links>a{align-items:center;display:flex}.c-reading-companion__figure-full-link svg{height:.8em;margin-left:2px}.c-reading-companion__panel{border-top:none;display:none;margin-top:0;padding-top:0}.c-cod,.c-reading-companion__panel--active{display:block}.c-cod{font-size:1rem;width:100%}.c-cod__form{background:#ebf0f3}.c-cod__prompt{font-size:1.125rem;line-height:1.3;margin:0 0 24px}.c-cod__label{display:block;margin:0 0 4px}.c-cod__row{display:flex;margin:0 0 16px}.c-cod__row:last-child{margin:0}.c-cod__input{border:1px solid #d5d5d5;border-radius:2px;flex-basis:75%;flex-shrink:0;margin:0;padding:13px}.c-cod__input--submit{background-color:#069;border:1px solid #069;color:#fff;flex-shrink:1;margin-left:8px;transition:background-color .2s ease-out 0s,color .2s ease-out 0s}.c-cod__input--submit-single{flex-basis:100%;flex-shrink:0;margin:0}.c-cod__input--submit:focus,.c-cod__input--submit:hover{background-color:#fff;color:#069}.c-pdf-download__link .u-icon{padding-top:2px}.c-pdf-download{display:flex;margin-bottom:16px;max-height:48px}@media only screen and (min-width:540px){.c-pdf-download{max-height:none}}@media only screen and (min-width:1024px){.c-pdf-download{max-height:48px}}.c-pdf-download__link{display:flex;flex:1 1 0%}.c-pdf-download__link:hover{text-decoration:none}.c-pdf-download__text{padding-right:4px}@media only screen and (max-width:539px){.c-pdf-download__text{text-transform:capitalize}}@media only screen and (min-width:540px){.c-pdf-download__text{padding-right:8px}}.c-context-bar--sticky .c-pdf-download{display:block;margin-bottom:0;white-space:nowrap}@media only screen and (max-width:539px){.c-pdf-download .u-sticky-visually-hidden{clip:rect(0,0,0,0);border:0;height:1px;margin:-100%;overflow:hidden;padding:0;position:absolute!important;width:1px}}.c-pdf-container{display:flex;justify-content:flex-end}@media only screen and (max-width:539px){.c-pdf-container .c-pdf-download{display:flex;flex-basis:100%}}.c-pdf-container .c-pdf-download+.c-pdf-download{margin-left:16px}.c-article-extras .c-pdf-container .c-pdf-download{width:100%}.c-article-extras .c-pdf-container .c-pdf-download+.c-pdf-download{margin-left:0}@media only screen and (min-width:540px){.c-context-bar--sticky .c-pdf-download__link{align-items:center;flex:1 1 183px}}@media only screen and (max-width:320px){.c-context-bar--sticky .c-pdf-download__link{padding:16px}}.article-page--commercial .c-article-main-column .c-pdf-button__container .c-pdf-download{display:none}@media only screen and (max-width:1023px){.article-page--commercial .c-article-main-column .c-pdf-button__container .c-pdf-download{display:block}}.c-status-message--success{border-bottom:2px solid #00b8b0;justify-content:center;margin-bottom:16px;padding-bottom:8px}.c-recommendations-list__item .c-card{flex-basis:100%}.c-recommendations-list__item .c-card__image{align-items:baseline;flex:1 1 40%;margin:0 0 0 16px;max-width:150px}.c-recommendations-list__item .c-card__image img{border:1px solid #cedbe0;height:auto;min-height:0;position:static}@media only screen and (max-width:1023px){.c-recommendations-list__item .c-card__image{display:none}}.c-card__layout{display:flex;flex:1 1 auto;justify-content:space-between}.c-card__title-recommendation{-webkit-box-orient:vertical;-webkit-line-clamp:4;display:-webkit-box;font-size:1rem;font-weight:700;line-height:1.4;margin:0 0 8px;max-height:5.6em;overflow:hidden!important;text-overflow:ellipsis}.c-card__title-recommendation .c-card__link{color:inherit}.c-card__title-recommendation .c-card__link:hover{text-decoration:underline}.c-card__title-recommendation .MathJax_Display{display:inline!important}.c-card__link:not(.c-card__link--no-block-link):before{z-index:1}.c-article-metrics__heading a,.c-article-metrics__posts .c-card__title a,.c-article-recommendations-card__link{color:inherit}.c-recommendations-column-switch .c-meta{margin-top:auto}.c-article-recommendations-card__meta-type,.c-meta .c-meta__item:first-child{font-weight:700}.c-article-body .c-article-recommendations-card__authors{display:none;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:.875rem;line-height:1.5;margin:0 0 8px}@media only screen and (max-width:539px){.c-article-body .c-article-recommendations-card__authors{display:block;margin:0}}.c-article-metrics__posts .c-card__title{font-size:1.05rem}.c-article-metrics__posts .c-card__title+span{color:#6f6f6f;font-size:1rem}p{overflow-wrap:break-word;word-break:break-word}.c-ad{text-align:center}@media only screen and (min-width:320px){.c-ad{padding:8px}}.c-ad--728x90{background-color:#ccc;display:none}.c-ad--728x90 .c-ad__inner{min-height:calc(1.5em + 94px)}@media only screen and (min-width:768px){.js .c-ad--728x90{display:none}}.c-ad__label{color:#333;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:.875rem;font-weight:400;line-height:1.5;margin-bottom:4px}.c-author-list{color:#6f6f6f;font-family:inherit;font-size:1rem;line-height:inherit;list-style:none;margin:0;padding:0}.c-author-list>li,.c-breadcrumbs>li,.c-footer__links>li,.js .c-author-list,.u-list-comma-separated>li,.u-list-inline>li{display:inline}.c-author-list>li:not(:first-child):not(:last-child):before{content:", "}.c-author-list>li:not(:only-child):last-child:before{content:" & "}.c-author-list--compact{font-size:.875rem;line-height:1.4}.c-author-list--truncated>li:not(:only-child):last-child:before{content:" ... "}.js .c-author-list__hide{display:none;visibility:hidden}.js .c-author-list__hide:first-child+*{margin-block-start:0}.c-meta{color:inherit;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:.875rem;line-height:1.4;list-style:none;margin:0;padding:0}.c-meta--large{font-size:1rem}.c-meta--large .c-meta__item{margin-bottom:8px}.c-meta__item{display:inline-block;margin-bottom:4px}.c-meta__item:not(:last-child){border-right:1px solid #d5d5d5;margin-right:4px;padding-right:4px}@media only screen and (max-width:539px){.c-meta__item--block-sm-max{display:block}.c-meta__item--block-sm-max:not(:last-child){border-right:none;margin-right:0;padding-right:0}}@media only screen and (min-width:1024px){.c-meta__item--block-at-lg{display:block}.c-meta__item--block-at-lg:not(:last-child){border-right:none;margin-right:0;padding-right:0}}.c-meta__type{font-weight:700;text-transform:none}.c-skip-link{background:#069;bottom:auto;color:#fff;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:.875rem;padding:8px;position:absolute;text-align:center;transform:translateY(-100%);z-index:9999}@media (prefers-reduced-motion:reduce){.c-skip-link{transition:top .3s ease-in-out 0s}}@media print{.c-skip-link{display:none}}.c-skip-link:link{color:#fff}.c-status-message{align-items:center;box-sizing:border-box;display:flex;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1rem;position:relative;width:100%}.c-card__summary>p:last-child,.c-status-message :last-child{margin-bottom:0}.c-status-message--boxed{background-color:#fff;border:1px solid #eee;border-radius:2px;line-height:1.4;padding:16px}.c-status-message__heading{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1rem;font-weight:700}.c-status-message__icon{fill:currentcolor;display:inline-block;flex:0 0 auto;height:1.5em;margin-right:8px;transform:translate(0);vertical-align:text-top;width:1.5em}.c-status-message__icon--top{align-self:flex-start}.c-status-message--info .c-status-message__icon{color:#003f8d}.c-status-message--boxed.c-status-message--info{border-bottom:4px solid #003f8d}.c-status-message--error .c-status-message__icon{color:#c40606}.c-status-message--boxed.c-status-message--error{border-bottom:4px solid #c40606}.c-status-message--success .c-status-message__icon{color:#00b8b0}.c-status-message--boxed.c-status-message--success{border-bottom:4px solid #00b8b0}.c-status-message--warning .c-status-message__icon{color:#edbc53}.c-status-message--boxed.c-status-message--warning{border-bottom:4px solid #edbc53}.c-breadcrumbs{color:#000;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1rem;list-style:none;margin:0;padding:0}.c-breadcrumbs__link{color:#666}svg.c-breadcrumbs__chevron{fill:#888;height:10px;margin:4px 4px 0;width:10px}@media only screen and (max-width:539px){.c-breadcrumbs .c-breadcrumbs__item{display:none}.c-breadcrumbs .c-breadcrumbs__item:last-child,.c-breadcrumbs .c-breadcrumbs__item:nth-last-child(2){display:inline}}.c-card{background-color:transparent;border:0;box-shadow:none;display:flex;flex-direction:column;font-size:14px;min-width:0;overflow:hidden;padding:0;position:relative}.c-card--no-shape{background:0 0;border:0;box-shadow:none}.c-card__image{display:flex;justify-content:center;overflow:hidden;padding-bottom:56.25%;position:relative}@supports (aspect-ratio:1/1){.c-card__image{padding-bottom:0}}.c-card__image img{left:0;min-height:100%;min-width:100%;position:absolute}@supports ((-o-object-fit:cover) or (object-fit:cover)){.c-card__image img{height:100%;object-fit:cover;width:100%}}.c-card__body{flex:1 1 auto;padding:16px}.c-card--no-shape .c-card__body{padding:0}.c-card--no-shape .c-card__body:not(:first-child){padding-top:16px}.c-card__title{letter-spacing:-.01875rem;margin-bottom:8px;margin-top:0}[lang=de] .c-card__title{hyphens:auto}.c-card__summary{line-height:1.4}.c-card__summary>p{margin-bottom:5px}.c-card__summary a{text-decoration:underline}.c-card__link:not(.c-card__link--no-block-link):before{bottom:0;content:"";left:0;position:absolute;right:0;top:0}.c-card--flush .c-card__body{padding:0}.c-card--major{font-size:1rem}.c-card--dark{background-color:#29303c;border-width:0;color:#e3e4e5}.c-card--dark .c-card__title{color:#fff}.c-card--dark .c-card__link,.c-card--dark .c-card__summary a{color:inherit}.c-header{background-color:#fff;border-bottom:5px solid #000;font-size:1rem;line-height:1.4;margin-bottom:16px}.c-header__row{padding:0;position:relative}.c-header__row:not(:last-child){border-bottom:1px solid #eee}.c-header__split{align-items:center;display:flex;justify-content:space-between}.c-header__logo-container{flex:1 1 0px;line-height:0;margin:8px 24px 8px 0}.c-header__logo{transform:translateZ(0)}.c-header__logo img{max-height:32px}.c-header__container{margin:0 auto;max-width:1280px}.c-header__menu{align-items:center;display:flex;flex:0 1 auto;flex-wrap:wrap;font-weight:700;gap:8px 8px;line-height:1.4;list-style:none;margin:0 -8px;padding:0}@media print{.c-header__menu{display:none}}@media only screen and (max-width:1023px){.c-header__menu--hide-lg-max{display:none;visibility:hidden}}.c-header__menu--global{font-weight:400;justify-content:flex-end}.c-header__menu--global svg{display:none;visibility:hidden}.c-header__menu--global svg:first-child+*{margin-block-start:0}@media only screen and (min-width:540px){.c-header__menu--global svg{display:block;visibility:visible}}.c-header__menu--journal{font-size:.875rem;margin:8px 0 8px -8px}@media only screen and (min-width:540px){.c-header__menu--journal{flex-wrap:nowrap;font-size:1rem}}.c-header__item{padding-bottom:0;padding-top:0;position:static}.c-header__item--pipe{border-left:2px solid #eee;padding-left:8px}.c-header__item--padding{padding-bottom:8px;padding-top:8px}@media only screen and (min-width:540px){.c-header__item--dropdown-menu{position:relative}}@media only screen and (min-width:1024px){.c-header__item--hide-lg{display:none;visibility:hidden}}@media only screen and (max-width:767px){.c-header__item--hide-md-max{display:none;visibility:hidden}.c-header__item--hide-md-max:first-child+*{margin-block-start:0}}.c-header__link{align-items:center;color:inherit;display:inline-flex;gap:4px 4px;padding:8px;white-space:nowrap}.c-header__link svg{transition-duration:.2s}.c-header__show-text{display:none;visibility:hidden}.has-tethered .c-header__heading--js-hide:first-child+*{margin-block-start:0}@media only screen and (min-width:540px){.c-header__show-text{display:inline;visibility:visible}}.c-header__dropdown{background-color:#000;border-bottom:1px solid #2f2f2f;color:#eee;font-size:.875rem;line-height:1.2;padding:16px 0}@media print{.c-header__dropdown{display:none}}.c-header__heading{display:inline-block;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1.25rem;font-weight:400;line-height:1.4;margin-bottom:8px}.c-header__heading--keyline{border-top:1px solid;border-color:#2f2f2f;margin-top:16px;padding-top:16px;width:100%}.c-header__list{display:flex;flex-wrap:wrap;gap:0 16px;list-style:none;margin:0 -8px}.c-header__flush{margin:0 -8px}.c-header__visually-hidden{clip:rect(0,0,0,0);border:0;height:1px;margin:-100%;overflow:hidden;padding:0;position:absolute!important;width:1px}.c-header__search-form{margin-bottom:8px}.c-header__search-layout{display:flex;flex-wrap:wrap;gap:16px 16px}.c-header__search-layout>:first-child{flex:999 1 auto}.c-header__search-layout>*{flex:1 1 auto}.c-header__search-layout--max-width{max-width:720px}.c-header__search-button{align-items:center;background-color:transparent;background-image:none;border:1px solid #fff;border-radius:2px;color:#fff;cursor:pointer;display:flex;font-family:sans-serif;font-size:1rem;justify-content:center;line-height:1.15;margin:0;padding:8px 16px;position:relative;text-decoration:none;transition:all .25s ease 0s,color .25s ease 0s,border-color .25s ease 0s;width:100%}.u-button svg,.u-button--primary svg{fill:currentcolor}.c-header__input,.c-header__select{border:1px solid;border-radius:3px;box-sizing:border-box;font-size:1rem;padding:8px 16px;width:100%}.c-header__select{-webkit-appearance:none;background-image:url("data:image/svg+xml,%3Csvg height='16' viewBox='0 0 16 16' width='16' xmlns='http://www.w3.org/2000/svg'%3E%3Cpath d='m5.58578644 3-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z' fill='%23333' fill-rule='evenodd' transform='matrix(0 1 -1 0 11 3)'/%3E%3C/svg%3E");background-position:right .7em top 50%;background-repeat:no-repeat;background-size:1em;box-shadow:0 1px 0 1px rgba(0,0,0,.04);display:block;margin:0;max-width:100%;min-width:150px}@media only screen and (min-width:540px){.c-header__menu--journal .c-header__item--dropdown-menu:last-child .c-header__dropdown.has-tethered{left:auto;right:0}}@media only screen and (min-width:768px){.c-header__menu--journal .c-header__item--dropdown-menu:last-child .c-header__dropdown.has-tethered{left:0;right:auto}}.c-header__dropdown.has-tethered{border-bottom:0;border-radius:0 0 2px 2px;left:0;position:absolute;top:100%;transform:translateY(5px);width:100%;z-index:1}@media only screen and (min-width:540px){.c-header__dropdown.has-tethered{transform:translateY(8px);width:auto}}@media only screen and (min-width:768px){.c-header__dropdown.has-tethered{min-width:225px}}.c-header__dropdown--full-width.has-tethered{padding:32px 0 24px;transform:none;width:100%}.has-tethered .c-header__heading--js-hide{display:none;visibility:hidden}.has-tethered .c-header__list--js-stack{flex-direction:column}.has-tethered .c-header__item--keyline,.has-tethered .c-header__list~.c-header__list .c-header__item:first-child{border-top:1px solid #d5d5d5;margin-top:8px;padding-top:8px}.c-header__item--snid-account-widget{display:flex}.c-header__container{padding:0 4px}.c-header__list{padding:0 12px}.c-header__menu .c-header__link{font-size:14px}.c-header__item--snid-account-widget .c-header__link{padding:8px}.c-header__menu--journal{margin-left:0}@media only screen and (min-width:540px){.c-header__container{padding:0 16px}.c-header__menu--journal{margin-left:-8px}.c-header__menu .c-header__link{font-size:16px}.c-header__link--search{gap:13px 13px}}.u-button{align-items:center;background-color:transparent;background-image:none;border:1px solid #069;border-radius:2px;color:#069;cursor:pointer;display:inline-flex;font-family:sans-serif;font-size:1rem;justify-content:center;line-height:1.3;margin:0;padding:8px;position:relative;text-decoration:none;transition:all .25s ease 0s,color .25s ease 0s,border-color .25s ease 0s;width:auto}.u-button--primary{background-color:#069;background-image:none;border:1px solid #069;color:#fff}.u-button--full-width{display:flex;width:100%}.u-display-none{display:none}.js .u-js-hide,.u-hide{display:none;visibility:hidden}.u-hide:first-child+*{margin-block-start:0}.u-visually-hidden{clip:rect(0,0,0,0);border:0;height:1px;margin:-100%;overflow:hidden;padding:0;position:absolute!important;width:1px}@media print{.u-hide-print{display:none}}@media only screen and (min-width:1024px){.u-hide-at-lg{display:none;visibility:hidden}.u-hide-at-lg:first-child+*{margin-block-start:0}}.u-clearfix:after,.u-clearfix:before{content:"";display:table}.u-clearfix:after{clear:both}.u-color-open-access{color:#b74616}.u-float-left{float:left}.u-icon{fill:currentcolor;display:inline-block;height:1em;transform:translate(0);vertical-align:text-top;width:1em}.u-full-height{height:100%}.u-list-reset{list-style:none;margin:0;padding:0}.u-sans-serif{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif}.u-container{margin:0 auto;max-width:1280px;padding:0 16px}.u-justify-content-space-between{justify-content:space-between}.u-mt-32{margin-top:32px}.u-mb-8{margin-bottom:8px}.u-mb-16{margin-bottom:16px}.u-mb-24{margin-bottom:24px}.u-mb-32{margin-bottom:32px}.c-nature-box svg+.c-article__button-text,.u-ml-8{margin-left:8px}.u-pa-16{padding:16px}html *,html :after,html :before{box-sizing:inherit}.c-article-section__title,.c-article-title{font-weight:700}.c-card__title{line-height:1.4em}.c-article__button{background-color:#069;border:1px solid #069;border-radius:2px;color:#fff;display:flex;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:.875rem;line-height:1.4;margin-bottom:16px;padding:13px;transition:background-color .2s ease-out 0s,color .2s ease-out 0s}.c-article__button,.c-article__button:hover{text-decoration:none}.c-article__button--inverted,.c-article__button:hover{background-color:#fff;color:#069}.c-article__button--inverted:hover{background-color:#069;color:#fff}.c-header__link{text-decoration:inherit}.grade-c-hide{display:block}.u-lazy-ad-wrapper{background-color:#ccc;display:none;min-height:137px}@media only screen and (min-width:768px){.u-lazy-ad-wrapper{display:block}}.c-nature-box{background-color:#fff;border:1px solid #d5d5d5;border-radius:2px;box-shadow:0 0 5px 0 rgba(51,51,51,.1);line-height:1.3;margin-bottom:24px;padding:16px 16px 3px}.c-nature-box__text{font-size:1rem;margin-bottom:16px}.c-nature-box .c-pdf-download{margin-bottom:16px!important}.c-nature-box--version{background-color:#eee}.c-nature-box__wrapper{transform:translateZ(0)}.c-nature-box__wrapper--placeholder{min-height:165px}.c-pdf-download__link{padding:13px 24px} } </style> <link data-test="critical-css-handler" data-inline-css-source="critical-css" rel="stylesheet" href="/static/css/enhanced-article-nature-branded-68c4876c28.css" media="print" onload="this.media='only print, only all and (prefers-color-scheme: no-preference), only all and (prefers-color-scheme: light), only all and (prefers-color-scheme: dark)';this.onload=null"> <noscript> <link rel="stylesheet" type="text/css" href="/static/css/enhanced-article-nature-branded-68c4876c28.css" media="only print, only all and (prefers-color-scheme: no-preference), only all and (prefers-color-scheme: light), only all and (prefers-color-scheme: dark)"> </noscript> <link rel="stylesheet" type="text/css" href="/static/css/article-print-122346e276.css" media="print"> <link rel="apple-touch-icon" sizes="180x180" href=/static/images/favicons/nature/apple-touch-icon-f39cb19454.png> <link rel="icon" type="image/png" sizes="48x48" href=/static/images/favicons/nature/favicon-48x48-b52890008c.png> <link rel="icon" type="image/png" sizes="32x32" href=/static/images/favicons/nature/favicon-32x32-3fe59ece92.png> <link rel="icon" type="image/png" sizes="16x16" href=/static/images/favicons/nature/favicon-16x16-951651ab72.png> <link rel="manifest" href=/static/manifest.json crossorigin="use-credentials"> <link rel="mask-icon" href=/static/images/favicons/nature/safari-pinned-tab-69bff48fe6.svg color="#000000"> <link rel="shortcut icon" href=/static/images/favicons/nature/favicon.ico> <meta name="msapplication-TileColor" content="#000000"> <meta name="msapplication-config" content=/static/browserconfig.xml> <meta name="theme-color" content="#000000"> <meta name="application-name" content="Nature"> <script> (function () { if ( typeof window.CustomEvent === "function" ) return false; function CustomEvent ( event, params ) { params = params || { bubbles: false, cancelable: false, detail: null }; var evt = document.createEvent( 'CustomEvent' ); evt.initCustomEvent( event, params.bubbles, params.cancelable, params.detail ); return evt; } CustomEvent.prototype = window.Event.prototype; window.CustomEvent = CustomEvent; })(); </script>  <script data-test="gtm-head"> window.initGTM = function() { if (window.config.mustardcut) { (function (w, d, s, l, i) { w[l] = w[l] || []; w[l].push({'gtm.start': new Date().getTime(), event: 'gtm.js'}); var f = d.getElementsByTagName(s)[0], j = d.createElement(s), dl = l != 'dataLayer' ? '&l=' + l : ''; j.async = true; j.src = 'https://www.googletagmanager.com/gtm.js?id=' + i + dl; f.parentNode.insertBefore(j, f); })(window, document, 'script', 'dataLayer', 'GTM-MRVXSHQ'); } } </script>  <script> (function(w,d,t) { function cc() { var h = w.location.hostname; if (h.indexOf('preview-www.nature.com') > -1) return; var e = d.createElement(t), s = d.getElementsByTagName(t)[0]; if (h.indexOf('nature.com') > -1) { if (h.indexOf('test-www.nature.com') > -1) { e.src = 'https://cmp.nature.com/production_live/en/consent-bundle-8-68.js'; e.setAttribute('onload', "initGTM(window,document,'script','dataLayer','GTM-MRVXSHQ')"); } else { e.src = 'https://cmp.nature.com/production_live/en/consent-bundle-8-68.js'; e.setAttribute('onload', "initGTM(window,document,'script','dataLayer','GTM-MRVXSHQ')"); } } else { e.src = '/static/js/cookie-consent-es5-bundle-cb57c2c98a.js'; e.setAttribute('data-consent', h); } s.insertAdjacentElement('afterend', e); } cc(); })(window,document,'script'); </script> <script id="js-position0"> (function(w, d) { w.idpVerifyPrefix = 'https://verify.nature.com'; w.ra21Host = 'https://wayf.springernature.com'; var moduleSupport = (function() { return 'noModule' in d.createElement('script'); })(); if (w.config.mustardcut === true) { w.loader = { index: 0, registered: [], scripts: [ {src: '/static/js/global-article-es6-bundle-c8a573ca90.js', test: 'global-article-js', module: true}, {src: '/static/js/global-article-es5-bundle-d17603b9e9.js', test: 'global-article-js', nomodule: true}, {src: '/static/js/shared-es6-bundle-606cb67187.js', test: 'shared-js', module: true}, {src: '/static/js/shared-es5-bundle-e919764a53.js', test: 'shared-js', nomodule: true}, {src: '/static/js/header-150-es6-bundle-5bb959eaa1.js', test: 'header-150-js', module: true}, {src: '/static/js/header-150-es5-bundle-994fde5b1d.js', test: 'header-150-js', nomodule: true} ].filter(function (s) { if (s.src === null) return false; if (moduleSupport && s.nomodule) return false; return !(!moduleSupport && s.module); }), register: function (value) { this.registered.push(value); }, ready: function () { if (this.registered.length === this.scripts.length) { this.registered.forEach(function (fn) { if (typeof fn === 'function') { setTimeout(fn, 0); } }); this.ready = function () {}; } }, insert: function (s) { var t = d.getElementById('js-position' + this.index); if (t && t.insertAdjacentElement) { t.insertAdjacentElement('afterend', s); } else { d.head.appendChild(s); } ++this.index; }, createScript: function (script, beforeLoad) { var s = d.createElement('script'); s.id = 'js-position' + (this.index + 1); s.setAttribute('data-test', script.test); if (beforeLoad) { s.defer = 'defer'; s.onload = function () { if (script.noinit) { loader.register(true); } if (d.readyState === 'interactive' || d.readyState === 'complete') { loader.ready(); } }; } else { s.async = 'async'; } s.src = script.src; return s; }, init: function () { this.scripts.forEach(function (s) { loader.insert(loader.createScript(s, true)); }); d.addEventListener('DOMContentLoaded', function () { loader.ready(); var conditionalScripts; conditionalScripts = [ {match: 'div[data-pan-container]', src: '/static/js/pan-zoom-es6-bundle-464a2af269.js', test: 'pan-zoom-js', module: true }, {match: 'div[data-pan-container]', src: '/static/js/pan-zoom-es5-bundle-98fb9b653b.js', test: 'pan-zoom-js', nomodule: true }, {match: 'math,span.mathjax-tex', src: '/static/js/math-es6-bundle-23597ae350.js', test: 'math-js', module: true}, {match: 'math,span.mathjax-tex', src: '/static/js/math-es5-bundle-6532c6f78b.js', test: 'math-js', nomodule: true} ]; if (conditionalScripts) { conditionalScripts.filter(function (script) { return !!document.querySelector(script.match) && !((moduleSupport && script.nomodule) || (!moduleSupport && script.module)); }).forEach(function (script) { loader.insert(loader.createScript(script)); }); } }, false); } }; loader.init(); } })(window, document); </script> <meta name="robots" content="noarchive"> <meta name="access" content="No"> <link rel="search" href="https://www.nature.com/search"> <link rel="search" href="https://www.nature.com/opensearch/opensearch.xml" type="application/opensearchdescription+xml" title="nature.com"> <link rel="search" href="https://www.nature.com/opensearch/request" type="application/sru+xml" title="nature.com"> <script type="application/ld+json">{"mainEntity":{"headline":"Advances in Brillouin–Mandelstam light-scattering spectroscopy","description":"Recent years have witnessed a much broader use of Brillouin inelastic light-scattering spectroscopy for the investigation of phonons and magnons in novel materials, nanostructures and devices. Driven by the developments in instrumentation and the strong need for accurate knowledge on the energies of elemental excitations, Brillouin–Mandelstam spectroscopy is rapidly becoming an essential technique that is complementary to Raman inelastic light-scattering spectroscopy. We provide an overview of recent progress in the Brillouin light-scattering technique, focusing on the use of this photonic method for the investigation of confined acoustic phonons, phononic metamaterials and magnon propagation and scattering. This Review emphasizes the emerging applications of Brillouin–Mandelstam spectroscopy for phonon-engineered structures and spintronic devices, and concludes with a perspective on future directions. Nearly 100 years after the prediction of Brillouin light-scattering spectroscopy, or Brillouin–Mandelstam light-scattering spectroscopy, the effect has proved itself a powerful tool for decades. Now its application to probing confined acoustic phonons, phononic metamaterials and magnons is reviewed.","datePublished":"2021-07-22T00:00:00Z","dateModified":"2021-07-22T00:00:00Z","pageStart":"720","pageEnd":"731","sameAs":"https://doi.org/10.1038/s41566-021-00836-5","keywords":["Raman spectroscopy","Physics","general","Applied and Technical Physics","Quantum Physics"],"image":["https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig1_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig2_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig3_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig4_HTML.png"],"isPartOf":{"name":"Nature Photonics","issn":["1749-4893","1749-4885"],"volumeNumber":"15","@type":["Periodical","PublicationVolume"]},"publisher":{"name":"Nature Publishing Group UK","logo":{"url":"https://www.springernature.com/app-sn/public/images/logo-springernature.png","@type":"ImageObject"},"@type":"Organization"},"author":[{"name":"Fariborz Kargar","url":"http://orcid.org/0000-0003-2192-2023","affiliation":[{"name":"Nano-Device Laboratory (NDL) and Phonon Optimized Engineered Materials (POEM) Center, Department of Electrical and Computer Engineering, University of California, Riverside","address":{"name":"Nano-Device Laboratory (NDL) and Phonon Optimized Engineered Materials (POEM) Center, Department of Electrical and Computer Engineering, University of California, Riverside, Riverside, USA","@type":"PostalAddress"},"@type":"Organization"}],"email":"fkargar@ece.ucr.edu","@type":"Person"},{"name":"Alexander A. Balandin","affiliation":[{"name":"Nano-Device Laboratory (NDL) and Phonon Optimized Engineered Materials (POEM) Center, Department of Electrical and Computer Engineering, University of California, Riverside","address":{"name":"Nano-Device Laboratory (NDL) and Phonon Optimized Engineered Materials (POEM) Center, Department of Electrical and Computer Engineering, University of California, Riverside, Riverside, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"}],"isAccessibleForFree":false,"hasPart":{"isAccessibleForFree":false,"cssSelector":".main-content","@type":"WebPageElement"},"@type":"ScholarlyArticle"},"@context":"https://schema.org","@type":"WebPage"}</script> <link rel="canonical" href="https://www.nature.com/articles/s41566-021-00836-5"> <meta name="journal_id" content="41566"/> <meta name="dc.title" content="Advances in Brillouin–Mandelstam light-scattering spectroscopy"/> <meta name="dc.source" content="Nature Photonics 2021 15:10"/> <meta name="dc.format" content="text/html"/> <meta name="dc.publisher" content="Nature Publishing Group"/> <meta name="dc.date" content="2021-07-22"/> <meta name="dc.type" content="ReviewPaper"/> <meta name="dc.language" content="En"/> <meta name="dc.copyright" content="2021 Springer Nature Limited"/> <meta name="dc.rights" content="2021 Springer Nature Limited"/> <meta name="dc.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="dc.description" content="Recent years have witnessed a much broader use of Brillouin inelastic light-scattering spectroscopy for the investigation of phonons and magnons in novel materials, nanostructures and devices. Driven by the developments in instrumentation and the strong need for accurate knowledge on the energies of elemental excitations, Brillouin–Mandelstam spectroscopy is rapidly becoming an essential technique that is complementary to Raman inelastic light-scattering spectroscopy. We provide an overview of recent progress in the Brillouin light-scattering technique, focusing on the use of this photonic method for the investigation of confined acoustic phonons, phononic metamaterials and magnon propagation and scattering. This Review emphasizes the emerging applications of Brillouin–Mandelstam spectroscopy for phonon-engineered structures and spintronic devices, and concludes with a perspective on future directions. Nearly 100 years after the prediction of Brillouin light-scattering spectroscopy, or Brillouin–Mandelstam light-scattering spectroscopy, the effect has proved itself a powerful tool for decades. Now its application to probing confined acoustic phonons, phononic metamaterials and magnons is reviewed."/> <meta name="prism.issn" content="1749-4893"/> <meta name="prism.publicationName" content="Nature Photonics"/> <meta name="prism.publicationDate" content="2021-07-22"/> <meta name="prism.volume" content="15"/> <meta name="prism.number" content="10"/> <meta name="prism.section" content="ReviewPaper"/> <meta name="prism.startingPage" content="720"/> <meta name="prism.endingPage" content="731"/> <meta name="prism.copyright" content="2021 Springer Nature Limited"/> <meta name="prism.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="prism.url" content="https://www.nature.com/articles/s41566-021-00836-5"/> <meta name="prism.doi" content="doi:10.1038/s41566-021-00836-5"/> <meta name="citation_pdf_url" content="https://www.nature.com/articles/s41566-021-00836-5.pdf"/> <meta name="citation_fulltext_html_url" content="https://www.nature.com/articles/s41566-021-00836-5"/> <meta name="citation_journal_title" content="Nature Photonics"/> <meta name="citation_journal_abbrev" content="Nat. Photon."/> <meta name="citation_publisher" content="Nature Publishing Group"/> <meta name="citation_issn" content="1749-4893"/> <meta name="citation_title" content="Advances in Brillouin–Mandelstam light-scattering spectroscopy"/> <meta name="citation_volume" content="15"/> <meta name="citation_issue" content="10"/> <meta name="citation_publication_date" content="2021/10"/> <meta name="citation_online_date" content="2021/07/22"/> <meta name="citation_firstpage" content="720"/> <meta name="citation_lastpage" content="731"/> <meta name="citation_article_type" content="Review Article"/> <meta name="citation_language" content="en"/> <meta name="dc.identifier" content="doi:10.1038/s41566-021-00836-5"/> <meta name="DOI" content="10.1038/s41566-021-00836-5"/> <meta name="size" content="258360"/> <meta name="citation_doi" content="10.1038/s41566-021-00836-5"/> <meta name="citation_springer_api_url" content="http://api.springer.com/xmldata/jats?q=doi:10.1038/s41566-021-00836-5&api_key="/> <meta name="description" content="Recent years have witnessed a much broader use of Brillouin inelastic light-scattering spectroscopy for the investigation of phonons and magnons in novel materials, nanostructures and devices. Driven by the developments in instrumentation and the strong need for accurate knowledge on the energies of elemental excitations, Brillouin–Mandelstam spectroscopy is rapidly becoming an essential technique that is complementary to Raman inelastic light-scattering spectroscopy. We provide an overview of recent progress in the Brillouin light-scattering technique, focusing on the use of this photonic method for the investigation of confined acoustic phonons, phononic metamaterials and magnon propagation and scattering. This Review emphasizes the emerging applications of Brillouin–Mandelstam spectroscopy for phonon-engineered structures and spintronic devices, and concludes with a perspective on future directions. Nearly 100 years after the prediction of Brillouin light-scattering spectroscopy, or Brillouin–Mandelstam light-scattering spectroscopy, the effect has proved itself a powerful tool for decades. Now its application to probing confined acoustic phonons, phononic metamaterials and magnons is reviewed."/> <meta name="dc.creator" content="Kargar, Fariborz"/> <meta name="dc.creator" content="Balandin, Alexander A."/> <meta name="dc.subject" content="Raman spectroscopy"/> <meta name="citation_reference" content="citation_journal_title=Ann. Phys.; citation_title=Diffusion de la lumière et des rayons X par un corps transparent homogène. Influence de l’agitation thermique; citation_author=L Brillouin; citation_volume=17; citation_publication_date=1922; citation_pages=88-122; citation_doi=10.1051/anphys/192209170088; citation_id=CR1"/> <meta name="citation_reference" content="citation_journal_title=Zh. Russ. Fiz. Khim. Ova.; citation_title=Light scattering by inhomogeneous media; citation_author=L Mandelstam; citation_volume=58; citation_publication_date=1926; citation_pages=381; citation_id=CR2"/> <meta name="citation_reference" content="citation_journal_title=Adv. Opt. Photonics; citation_title=Seeing cells in a new light: a renaissance of Brillouin spectroscopy; citation_author=Z Meng, AJ Traverso, CW Ballmann, MA Troyanova-Wood, VV Yakovlev; citation_volume=8; citation_publication_date=2016; citation_pages=300-327; citation_doi=10.1364/AOP.8.000300; citation_id=CR3"/> <meta name="citation_reference" content="citation_journal_title=Nature; citation_title=A new type of secondary radiation; citation_author=CV Raman, KS Krishnan; citation_volume=121; citation_publication_date=1928; citation_pages=501-502; citation_doi=10.1038/121501c0; citation_id=CR4"/> <meta name="citation_reference" content="Cardona, M. & Merlin, R. in Light Scattering in Solids IX Vol. 108 (eds Cardona, M. & Merlin, R.) Ch. 1 (Springer, 2006)."/> <meta name="citation_reference" content="citation_journal_title=Usp. Fiz. Nauk; citation_title=The prediction and discovery of Rayleigh line fine structure; citation_author=IL Fabelinskiĭ; citation_volume=170; citation_publication_date=2000; citation_pages=107-108; citation_doi=10.3367/UFNr.0170.200001f.0093; citation_id=CR6"/> <meta name="citation_reference" content="citation_journal_title=Phys. Usp.; citation_title=The discovery of combination scattering of light in Russia and India; citation_author=IL Fabelinskiĭ; citation_volume=46; citation_publication_date=2003; citation_pages=1105-1112; citation_doi=10.1070/PU2003v046n10ABEH001624; citation_id=CR7"/> <meta name="citation_reference" content="citation_journal_title=Nature; citation_title=Change of wave-length of light due to elastic waves at scattering in liquids; citation_author=E Gross; citation_volume=126; citation_publication_date=1930; citation_pages=201-202; citation_doi=10.1038/126201a0; citation_id=CR8"/> <meta name="citation_reference" content="citation_journal_title=Nature; citation_title=The splitting of spectral lines at scattering of light by liquids; citation_author=E Gross; citation_volume=126; citation_publication_date=1930; citation_pages=400; citation_doi=10.1038/126400a0; citation_id=CR9"/> <meta name="citation_reference" content="citation_journal_title=Z. Phys.; citation_title=über Änderung der WellenlÄnge bei Lichtzerstreuung in Kristallen; citation_author=E Gross; citation_volume=63; citation_publication_date=1930; citation_pages=685-687; citation_doi=10.1007/BF01340308; citation_id=CR10"/> <meta name="citation_reference" content="Sandercock, J. R. in Light Scattering in Solids III Vol. 51 (eds Cardona, M. & Güntherodt, G.) 173–206 (Springer, 1982)."/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. X; citation_title=High-performance versatile setup for simultaneous Brillouin–Raman microspectroscopy; citation_author=F Scarponi; citation_volume=7; citation_publication_date=2017; citation_pages=031015; citation_id=CR12"/> <meta name="citation_reference" content="citation_journal_title=Rev. Mineral. Geochem.; citation_title=Brillouin scattering and its application in geosciences; citation_author=S Speziale, H Marquardt, TS Duffy; citation_volume=78; citation_publication_date=2014; citation_pages=543-603; citation_doi=10.2138/rmg.2014.78.14; citation_id=CR13"/> <meta name="citation_reference" content="citation_journal_title=Nanotechnology; citation_title=Phononic and photonic properties of shape-engineered silicon nanoscale pillar arrays; citation_author=CYT Huang; citation_volume=31; citation_publication_date=2020; citation_pages=30LT01; citation_doi=10.1088/1361-6528/ab85ee; citation_id=CR14"/> <meta name="citation_reference" content="citation_journal_title=Adv. Funct. Mater.; citation_title=2D phononic crystals: progress and prospects in hypersound and thermal transport engineering; citation_author=M Sledzinska; citation_volume=30; citation_publication_date=2019; citation_pages=1904434; citation_doi=10.1002/adfm.201904434; citation_id=CR15"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. B; citation_title=Phonon dispersion in hypersonic two-dimensional phononic crystal membranes; citation_author=B Graczykowski; citation_volume=91; citation_publication_date=2015; citation_pages=075414; citation_doi=10.1103/PhysRevB.91.075414; citation_id=CR16"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. B; citation_title=Nanoscale pillar hypersonic surface phononic crystals; citation_author=D Yudistira; citation_volume=94; citation_publication_date=2016; citation_pages=094304; citation_doi=10.1103/PhysRevB.94.094304; citation_id=CR17"/> <meta name="citation_reference" content="citation_journal_title=Appl. Phys. Lett.; citation_title=Band structure of cavity-type hypersonic phononic crystals fabricated by femtosecond laser-induced two-photon polymerization; citation_author=AM Rakhymzhanov; citation_volume=108; citation_publication_date=2016; citation_pages=201901; citation_doi=10.1063/1.4949013; citation_id=CR18"/> <meta name="citation_reference" content="citation_journal_title=ACS Appl. Mater. Interfaces; citation_title=Phoxonic hybrid superlattice; citation_author=E Alonso-Redondo; citation_volume=7; citation_publication_date=2015; citation_pages=12488-12495; citation_doi=10.1021/acsami.5b01247; citation_id=CR19"/> <meta name="citation_reference" content="citation_journal_title=Nano Lett.; citation_title=One-dimensional hypersonic phononic crystals; citation_author=N Gomopoulos; citation_volume=10; citation_publication_date=2010; citation_pages=980-984; citation_doi=10.1021/nl903959r; citation_id=CR20"/> <meta name="citation_reference" content="citation_journal_title=Nano Lett.; citation_title=Engineering the hypersonic phononic band gap of hybrid Bragg stacks; citation_author=D Schneider; citation_volume=12; citation_publication_date=2012; citation_pages=3101-3108; citation_doi=10.1021/nl300982d; citation_id=CR21"/> <meta name="citation_reference" content="citation_journal_title=J. Appl. Phys.; citation_title=Off-axis phonon and photon propagation in porous silicon superlattices studied by Brillouin spectroscopy and optical reflectance; citation_author=LC Parsons, GT Andrews; citation_volume=116; citation_publication_date=2014; citation_pages=033510; citation_doi=10.1063/1.4890319; citation_id=CR22"/> <meta name="citation_reference" content="citation_journal_title=Appl. Phys. Lett.; citation_title=Acoustic phonon dispersion engineering in bulk crystals via incorporation of dopant atoms; citation_author=F Kargar; citation_volume=112; citation_publication_date=2018; citation_pages=191902; citation_doi=10.1063/1.5030558; citation_id=CR23"/> <meta name="citation_reference" content="citation_journal_title=Nat. Commun.; citation_title=Direct observation of confined acoustic phonon polarization branches in free-standing semiconductor nanowires; citation_author=F Kargar; citation_volume=7; citation_publication_date=2016; citation_doi=10.1038/ncomms13400; citation_id=CR24"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Brillouin study of the quantization of acoustic modes in nanospheres; citation_author=MH Kuok, HS Lim, SC Ng, NN Liu, ZK Wang; citation_volume=90; citation_publication_date=2003; citation_pages=255502; citation_doi=10.1103/PhysRevLett.90.255502; citation_id=CR25"/> <meta name="citation_reference" content="citation_journal_title=Nano Lett.; citation_title=Phonons in slow motion: dispersion relations in ultrathin Si membranes; citation_author=J Cuffe; citation_volume=12; citation_publication_date=2012; citation_pages=3569-3573; citation_doi=10.1021/nl301204u; citation_id=CR26"/> <meta name="citation_reference" content="citation_journal_title=Nano Lett.; citation_title=Elastic properties of few nanometers thick polycrystalline MoS2 membranes: a nondestructive study; citation_author=B Graczykowski; citation_volume=17; citation_publication_date=2017; citation_pages=7647-7651; citation_doi=10.1021/acs.nanolett.7b03669; citation_id=CR27"/> <meta name="citation_reference" content="citation_journal_title=Appl. Phys. Lett.; citation_title=Brillouin study of acoustic phonon confinement in GeO2 nanocubes; citation_author=Y Li; citation_volume=91; citation_publication_date=2007; citation_pages=093116; citation_doi=10.1063/1.2777174; citation_id=CR28"/> <meta name="citation_reference" content="citation_journal_title=Appl. Phys. Lett.; citation_title=Acoustic phonon spectrum and thermal transport in nanoporous alumina arrays; citation_author=F Kargar; citation_volume=107; citation_publication_date=2015; citation_pages=171904; citation_doi=10.1063/1.4934883; citation_id=CR29"/> <meta name="citation_reference" content="citation_journal_title=EPJ Web Conf.; citation_title=Inelastic and quasi-elastic neutron scattering. Application to soft-matter; citation_author=Q Berrod, K Lagrené, J Ollivier, J-M Zanotti; citation_volume=188; citation_publication_date=2018; citation_pages=05001; citation_doi=10.1051/epjconf/201818805001; citation_id=CR30"/> <meta name="citation_reference" content="citation_journal_title=Nature; citation_title=Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping; citation_author=SO Demokritov; citation_volume=443; citation_publication_date=2006; citation_pages=430-433; citation_doi=10.1038/nature05117; citation_id=CR31"/> <meta name="citation_reference" content="citation_journal_title=Nat. Commun.; citation_title=Excitation of coherent propagating spin waves by pure spin currents; citation_author=VE Demidov; citation_volume=7; citation_publication_date=2016; citation_doi=10.1038/ncomms10446; citation_id=CR32"/> <meta name="citation_reference" content="citation_journal_title=Nat. Phys.; citation_title=Detecting the phonon spin in magnon–phonon conversion experiments; citation_author=J Holanda, DS Maior, A Azevedo, SM Rezende; citation_volume=14; citation_publication_date=2018; citation_pages=500-506; citation_doi=10.1038/s41567-018-0079-y; citation_id=CR33"/> <meta name="citation_reference" content="Cho, J. et al. Thickness dependence of the interfacial Dzyaloshinskii–Moriya interaction in inversion symmetry broken systems. Nat. Commun. 6, 7635 (2015)."/> <meta name="citation_reference" content="citation_journal_title=AIP Adv.; citation_title=Brillouin–Mandelstam spectroscopy of standing spin waves in a ferrite waveguide; citation_author=M Balinskiy, F Kargar, H Chiang, AA Balandin, AG Khitun; citation_volume=8; citation_publication_date=2018; citation_pages=056017; citation_doi=10.1063/1.5007165; citation_id=CR35"/> <meta name="citation_reference" content="citation_journal_title=Appl. Phys. Lett.; citation_title=The discrete noise of magnons; citation_author=S Rumyantsev, M Balinskiy, F Kargar, A Khitun, AA Balandin; citation_volume=114; citation_publication_date=2019; citation_pages=090601; citation_doi=10.1063/1.5088651; citation_id=CR36"/> <meta name="citation_reference" content="citation_journal_title=Nat. Photonics; citation_title=Brillouin integrated photonics; citation_author=BJ Eggleton, CG Poulton, PT Rakich, MJ Steel, G Bahl; citation_volume=13; citation_publication_date=2019; citation_pages=664-677; citation_doi=10.1038/s41566-019-0498-z; citation_id=CR37"/> <meta name="citation_reference" content="citation_journal_title=Opt. Lett.; citation_title=Brillouin spectroscopy of a hybrid silicon-chalcogenide waveguide with geometrical variations; citation_author=A Zarifi; citation_volume=43; citation_publication_date=2018; citation_pages=3493-3496; citation_doi=10.1364/OL.43.003493; citation_id=CR38"/> <meta name="citation_reference" content="Boyd, R. W. Nonlinear Optics 4th edn (Elsevier, 2020)."/> <meta name="citation_reference" content="Hayes, W. & Loudon, R. Scattering of Light by Crystals (Wiley, 1978)."/> <meta name="citation_reference" content="Mutti, P. et al. in Advances in Acoustic Microscopy Vol. 1 (ed. Briggs, A.) 249–300 (Springer, 1995)."/> <meta name="citation_reference" content="citation_journal_title=Adv. Phys. X; citation_title=Brillouin scattering of phonons in complex materials; citation_author=CE Bottani, D Fioretto; citation_volume=3; citation_publication_date=2018; citation_pages=607-633; citation_id=CR42"/> <meta name="citation_reference" content="citation_journal_title=J. Phys. D; citation_title=Magnon and phonon thermometry with inelastic light scattering; citation_author=KS Olsson, K An, X Li; citation_volume=51; citation_publication_date=2018; citation_pages=133001; citation_doi=10.1088/1361-6463/aaadde; citation_id=CR43"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Theory of surface-ripple Brillouin scattering by solids; citation_author=R Loudon; citation_volume=40; citation_publication_date=1978; citation_pages=581-583; citation_doi=10.1103/PhysRevLett.40.581; citation_id=CR44"/> <meta name="citation_reference" content="citation_journal_title=Mater. Today; citation_title=Phononics in low-dimensional materials; citation_author=AA Balandin, DL Nika; citation_volume=15; citation_publication_date=2012; citation_pages=266-275; citation_doi=10.1016/S1369-7021(12)70117-7; citation_id=CR45"/> <meta name="citation_reference" content="citation_journal_title=ACS Nano; citation_title=Phononics of graphene and related materials; citation_author=AA Balandin; citation_volume=14; citation_publication_date=2020; citation_pages=5170-5178; citation_doi=10.1021/acsnano.0c02718; citation_id=CR46"/> <meta name="citation_reference" content="citation_journal_title=Nat. Mater.; citation_title=Thermal properties of graphene and nanostructured carbon materials; citation_author=AA Balandin; citation_volume=10; citation_publication_date=2011; citation_pages=569-581; citation_doi=10.1038/nmat3064; citation_id=CR47"/> <meta name="citation_reference" content="citation_journal_title=ES Mater. Manuf.; citation_title=Phonon transport within periodic porous structures—from classical phonon size effects to wave effects; citation_author=Y Xiao, Q Chen, D Ma, N Yang, Q Hao; citation_volume=5; citation_publication_date=2019; citation_pages=2-18; citation_id=CR48"/> <meta name="citation_reference" content="citation_journal_title=Adv. Funct. Mater.; citation_title=Thermal conductivity reduction in a nanophononic metamaterial versus a nanophononic crystal: a review and comparative analysis; citation_author=MI Hussein, C Tsai, H Honarvar; citation_volume=30; citation_publication_date=2020; citation_pages=1906718; citation_doi=10.1002/adfm.201906718; citation_id=CR49"/> <meta name="citation_reference" content="citation_journal_title=C. R. Phys.; citation_title=Phoxonic crystals and cavity optomechanics; citation_author=B Djafari-Rouhani, S El-Jallal, Y Pennec; citation_volume=17; citation_publication_date=2016; citation_pages=555-564; citation_doi=10.1016/j.crhy.2016.02.001; citation_id=CR50"/> <meta name="citation_reference" content="citation_journal_title=Nanotechnology; citation_title=Vibrational modes of GaN nanowires in the gigahertz range; citation_author=WL Johnson; citation_volume=23; citation_publication_date=2012; citation_pages=495709; citation_doi=10.1088/0957-4484/23/49/495709; citation_id=CR51"/> <meta name="citation_reference" content="citation_journal_title=Nano Lett.; citation_title=The ‘music’ of core–shell spheres and hollow capsules: influence of the architecture on the mechanical properties at the nanoscale; citation_author=T Still; citation_volume=8; citation_publication_date=2008; citation_pages=3194-3199; citation_doi=10.1021/nl801500n; citation_id=CR52"/> <meta name="citation_reference" content="citation_journal_title=ACS Nano; citation_title=Hypersonic vibrations of Ag@SiO2 (cubic core)–shell nanospheres; citation_author=JY Sun; citation_volume=4; citation_publication_date=2010; citation_pages=7692-7698; citation_doi=10.1021/nn102581g; citation_id=CR53"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. B; citation_title=Significant decrease of the lattice thermal conductivity due to phonon confinement in a free-standing semiconductor quantum well; citation_author=A Balandin, KL Wang; citation_volume=58; citation_publication_date=1998; citation_pages=1544-1549; citation_doi=10.1103/PhysRevB.58.1544; citation_id=CR54"/> <meta name="citation_reference" content="citation_journal_title=J. Appl. Phys.; citation_title=Confined electron-confined phonon scattering rates in wurtzite AlN/GaN/AlN heterostructures; citation_author=EP Pokatilov, DL Nika, AA Balandin; citation_volume=95; citation_publication_date=2004; citation_pages=5626-5632; citation_doi=10.1063/1.1710705; citation_id=CR55"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. B; citation_title=Far-infrared and Raman vibrational transitions of a solid sphere: selection rules; citation_author=E Duval; citation_volume=46; citation_publication_date=1992; citation_pages=5795-5797; citation_doi=10.1103/PhysRevB.46.5795; citation_id=CR56"/> <meta name="citation_reference" content="citation_journal_title=Nat. Phys.; citation_title=Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres; citation_author=P Dainese; citation_volume=2; citation_publication_date=2006; citation_pages=388-392; citation_doi=10.1038/nphys315; citation_id=CR57"/> <meta name="citation_reference" content="Pennec, Y. et al. Sensing light and sound velocities of fluids in 2D phoxonic crystal slab. In Proc. IEEE Sensors 355–357 (IEEE, 2014)."/> <meta name="citation_reference" content="citation_journal_title=Nature; citation_title=Optomechanical crystals; citation_author=M Eichenfield, J Chan, RM Camacho, KJ Vahala, O Painter; citation_volume=462; citation_publication_date=2009; citation_pages=78-82; citation_doi=10.1038/nature08524; citation_id=CR59"/> <meta name="citation_reference" content="citation_journal_title=Nanoscale; citation_title=Enabling silicon-on-silicon photonics with pedestalled Mie resonators; citation_author=M Garín, M Solà, A Julian, P Ortega; citation_volume=10; citation_publication_date=2018; citation_pages=14406-14413; citation_doi=10.1039/C8NR02259C; citation_id=CR60"/> <meta name="citation_reference" content="citation_journal_title=Front. Phys.; citation_title=Micro-focused Brillouin light scattering: imaging spin waves at the nanoscale; citation_author=T Sebastian, K Schultheiss, B Obry, B Hillebrands, H Schultheiss; citation_volume=3; citation_publication_date=2015; citation_doi=10.3389/fphy.2015.00035; citation_id=CR61"/> <meta name="citation_reference" content="citation_journal_title=Solid State Phys.; citation_title=Application of microfocused Brillouin light scattering to the study of spin waves in low-dimensional magnetic systems; citation_author=M Madami, G Gubbiotti, S Tacchi, G Carlotti, RL Stamps; citation_volume=63; citation_publication_date=2012; citation_pages=79-150; citation_doi=10.1016/B978-0-12-397028-2.00002-3; citation_id=CR62"/> <meta name="citation_reference" content="Cottam, M. G. & Lockwood, D. J. Light Scattering in Magnetic Solids (Wiley, 1986)."/> <meta name="citation_reference" content="Rezende, S. M. Fundamentals of Magnonics Vol. 969 (Springer, 2020)"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev.; citation_title=Scattering of light by one- and two-magnon excitations; citation_author=PA Fleury, R Loudon; citation_volume=166; citation_publication_date=1968; citation_pages=514-530; citation_doi=10.1103/PhysRev.166.514; citation_id=CR65"/> <meta name="citation_reference" content="citation_journal_title=IEEE Trans. Magn.; citation_title=Magnonic waveguides studied by microfocus brillouin light scattering; citation_author=VE Demidov, SO Demokritov; citation_volume=51; citation_publication_date=2015; citation_pages=0800215; citation_doi=10.1109/TMAG.2014.2388196; citation_id=CR66"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rep.; citation_title=Brillouin light scattering studies of confined spin waves: linear and nonlinear confinement; citation_author=SO Demokritov, B Hillebrands, AN Slavin; citation_volume=348; citation_publication_date=2001; citation_pages=441-489; citation_doi=10.1016/S0370-1573(00)00116-2; citation_id=CR67"/> <meta name="citation_reference" content="citation_journal_title=Appl. Phys. Lett.; citation_title=Phase-sensitive Brillouin light scattering spectroscopy from spin-wave packets; citation_author=AA Serga, T Schneider, B Hillebrands, SO Demokritov, MP Kostylev; citation_volume=89; citation_publication_date=2006; citation_pages=063506; citation_doi=10.1063/1.2335627; citation_id=CR68"/> <meta name="citation_reference" content="citation_journal_title=Appl. Phys. Lett.; citation_title=All-optical detection of phase fronts of propagating spin waves in a Ni81Fe19 microstripe; citation_author=K Vogt; citation_volume=95; citation_publication_date=2009; citation_pages=182508; citation_doi=10.1063/1.3262348; citation_id=CR69"/> <meta name="citation_reference" content="citation_journal_title=Phys. Status Solidi B; citation_title=Interference of coherent spin waves in micron-sized ferromagnetic waveguides; citation_author=P Pirro; citation_volume=248; citation_publication_date=2011; citation_pages=2404-2408; citation_doi=10.1002/pssb.201147093; citation_id=CR70"/> <meta name="citation_reference" content="citation_journal_title=Appl. Phys. Lett.; citation_title=Spin waves turning a corner; citation_author=K Vogt; citation_volume=101; citation_publication_date=2012; citation_pages=042410; citation_doi=10.1063/1.4738887; citation_id=CR71"/> <meta name="citation_reference" content="citation_journal_title=Nat. Commun.; citation_title=Realization of a spin-wave multiplexer; citation_author=K Vogt; citation_volume=5; citation_publication_date=2014; citation_doi=10.1038/ncomms4727; citation_id=CR72"/> <meta name="citation_reference" content="citation_journal_title=Nat. Commun.; citation_title=Direct evidence of spatial stability of Bose-Einstein condensate of magnons; citation_author=IV Borisenko; citation_volume=11; citation_publication_date=2020; citation_doi=10.1038/s41467-020-15468-6; citation_id=CR73"/> <meta name="citation_reference" content="citation_journal_title=Nat. Phys.; citation_title=Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii–Moriya interaction in metal films; citation_author=HT Nembach, JM Shaw, M Weiler, E Jué, TJ Silva; citation_volume=11; citation_publication_date=2015; citation_pages=825-829; citation_doi=10.1038/nphys3418; citation_id=CR74"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Interfacial Dzyaloshinskii-Moriya interaction: effect of 5d band filling and correlation with spin mixing conductance; citation_author=X Ma; citation_volume=120; citation_publication_date=2018; citation_pages=157204; citation_doi=10.1103/PhysRevLett.120.157204; citation_id=CR75"/> <meta name="citation_reference" content="citation_journal_title=J. Appl. Phys.; citation_title=Interfacial Dzyaloshinskii-Moriya interaction, interface-induced damping and perpendicular magnetic anisotropy in Pt/Co/W based multilayers; citation_author=I Benguettat-El Mokhtari; citation_volume=126; citation_publication_date=2019; citation_pages=133902; citation_doi=10.1063/1.5119193; citation_id=CR76"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. B; citation_title=Dzyaloshinskii-Moriya interaction induced asymmetry in dispersion of magnonic Bloch modes; citation_author=H Bouloussa; citation_volume=102; citation_publication_date=2020; citation_pages=014412; citation_doi=10.1103/PhysRevB.102.014412; citation_id=CR77"/> <meta name="citation_reference" content="citation_journal_title=J. Appl. Phys.; citation_title=High-intensity Brillouin light scattering by spin waves in a permalloy film under microwave resonance pumping; citation_author=AA Stashkevich, P Djemia, YK Fetisov, N Bizière, C Fermon; citation_volume=102; citation_publication_date=2007; citation_pages=103905; citation_doi=10.1063/1.2815673; citation_id=CR78"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. B; citation_title=Generation of the second harmonic by spin waves propagating in microscopic stripes; citation_author=VE Demidov; citation_volume=83; citation_publication_date=2011; citation_pages=054408; citation_doi=10.1103/PhysRevB.83.054408; citation_id=CR79"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Nonlinear propagation of spin waves in microscopic magnetic stripes; citation_author=VE Demidov; citation_volume=102; citation_publication_date=2009; citation_pages=177207; citation_doi=10.1103/PhysRevLett.102.177207; citation_id=CR80"/> <meta name="citation_reference" content="citation_journal_title=Appl. Phys. Lett.; citation_title=Mapping of localized spin-wave excitations by near-field Brillouin light scattering; citation_author=J Jersch; citation_volume=97; citation_publication_date=2010; citation_pages=152502; citation_doi=10.1063/1.3502599; citation_id=CR81"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. B; citation_title=Theory of coherence in Bose–Einstein condensation phenomena in a microwave-driven interacting magnon gas; citation_author=SM Rezende; citation_volume=79; citation_publication_date=2009; citation_pages=174411; citation_doi=10.1103/PhysRevB.79.174411; citation_id=CR82"/> <meta name="citation_reference" content="citation_journal_title=Nature; citation_title=Bose–Einstein condensation of the triplet states in the magnetic insulator TlCuCl3; citation_author=C Rüegg; citation_volume=423; citation_publication_date=2003; citation_pages=62-65; citation_doi=10.1038/nature01617; citation_id=CR83"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Observation of spontaneous coherence in Bose–Einstein condensate of magnons; citation_author=VE Demidov, O Dzyapko, SO Demokritov, GA Melkov, AN Slavin; citation_volume=100; citation_publication_date=2008; citation_pages=047205; citation_doi=10.1103/PhysRevLett.100.047205; citation_id=CR84"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Stability of Bose–Einstein condensates of hot magnons in yttrium iron garnet films; citation_author=IS Tupitsyn, PCE Stamp, AL Burin; citation_volume=100; citation_publication_date=2008; citation_pages=257202; citation_doi=10.1103/PhysRevLett.100.257202; citation_id=CR85"/> <meta name="citation_reference" content="citation_journal_title=J. Appl. Phys.; citation_title=Finite size effects in patterned magnetic permalloy films; citation_author=G Gubbiotti; citation_volume=87; citation_publication_date=2000; citation_pages=5633-5635; citation_doi=10.1063/1.372473; citation_id=CR86"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. B; citation_title=Experimental and theoretical study of quantized spin-wave modes in micrometer-size permalloy wires; citation_author=Y Roussigné, SM Chérif, C Dugautier, P Moch; citation_volume=63; citation_publication_date=2001; citation_pages=134429; citation_doi=10.1103/PhysRevB.63.134429; citation_id=CR87"/> <meta name="citation_reference" content="citation_journal_title=IEEE Trans. Magn.; citation_title=Finite-size effects in arrays of permalloy square dots; citation_author=SM Chérif, YE Roussigné, P Moch; citation_volume=38; citation_publication_date=2002; citation_pages=2529-2531; citation_doi=10.1109/TMAG.2002.801917; citation_id=CR88"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. B; citation_title=Magnetostatic interaction in arrays of nanometric permalloy wires: a magneto-optic Kerr effect and a Brillouin light scattering study; citation_author=G Gubbiotti; citation_volume=72; citation_publication_date=2005; citation_pages=224413; citation_doi=10.1103/PhysRevB.72.224413; citation_id=CR89"/> <meta name="citation_reference" content="citation_journal_title=J. Magn. Magn. Mater.; citation_title=Brillouin–Mandelstam spectroscopy of stress-modulated spatially confined spin waves in Ni thin films on piezoelectric substrates; citation_author=F Kargar; citation_volume=501; citation_publication_date=2020; citation_pages=166440; citation_doi=10.1016/j.jmmm.2020.166440; citation_id=CR90"/> <meta name="citation_reference" content="citation_journal_title=Appl. Phys. Lett.; citation_title=Brillouin light scattering spectra as local temperature sensors for thermal magnons and acoustic phonons; citation_author=DR Birt; citation_volume=102; citation_publication_date=2013; citation_pages=082401; citation_doi=10.1063/1.4793538; citation_id=CR91"/> <meta name="citation_reference" content="citation_journal_title=J. Phys. D; citation_title=Brillouin light scattering studies of planar metallic magnonic crystals; citation_author=G Gubbiotti; citation_volume=43; citation_publication_date=2010; citation_pages=264003; citation_doi=10.1088/0022-3727/43/26/264003; citation_id=CR92"/> <meta name="citation_reference" content="citation_journal_title=Sci. Adv.; citation_title=Viscoelastic properties of biopolymer hydrogels determined by Brillouin spectroscopy: a probe of tissue micromechanics; citation_author=M Bailey; citation_volume=6; citation_publication_date=2020; citation_pages=eabc1937; citation_doi=10.1126/sciadv.abc1937; citation_id=CR93"/> <meta name="citation_reference" content="citation_journal_title=Nano Lett.; citation_title=Multiband hypersound filtering in two-dimensional colloidal crystals: adhesion, resonances, and periodicity; citation_author=B Graczykowski, N Vogel, K Bley, H-J Butt, G Fytas; citation_volume=20; citation_publication_date=2020; citation_pages=1883-1889; citation_doi=10.1021/acs.nanolett.9b05101; citation_id=CR94"/> <meta name="citation_reference" content="citation_journal_title=Nanotechnology; citation_title=Elastic wave propagation in smooth and wrinkled stratified polymer films; citation_author=M Hesami; citation_volume=30; citation_publication_date=2019; citation_pages=045709; citation_doi=10.1088/1361-6528/aaee9b; citation_id=CR95"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. B; citation_title=Brillouin light scattering under one-dimensional confinement: symmetry and interference self-canceling; citation_author=B Graczykowski, A Gueddida, B Djafari-Rouhani, H-J Butt, G Fytas; citation_volume=99; citation_publication_date=2019; citation_pages=165431; citation_doi=10.1103/PhysRevB.99.165431; citation_id=CR96"/> <meta name="citation_reference" content="citation_journal_title=Sci Rep.; citation_title=Robustness of elastic properties in polymer nanocomposite films examined over the full volume fraction range; citation_author=E Alonso-Redondo; citation_volume=8; citation_publication_date=2018; citation_doi=10.1038/s41598-018-35335-1; citation_id=CR97"/> <meta name="citation_reference" content="citation_journal_title=New J. Phys.; citation_title=Cavity-type hypersonic phononic crystals; citation_author=A Sato; citation_volume=14; citation_publication_date=2012; citation_pages=113032; citation_doi=10.1088/1367-2630/14/11/113032; citation_id=CR98"/> <meta name="citation_reference" content="citation_journal_title=Nat. Mater.; citation_title=Non-invasive determination of the complete elastic moduli of spider silks; citation_author=KJ Koski, P Akhenblit, K McKiernan, JL Yarger; citation_volume=12; citation_publication_date=2013; citation_pages=262-267; citation_doi=10.1038/nmat3549; citation_id=CR99"/> <meta name="citation_reference" content="citation_journal_title=Nat. Methods; citation_title=Noncontact three-dimensional mapping of intracellular hydromechanical properties by Brillouin microscopy; citation_author=G Scarcelli; citation_volume=12; citation_publication_date=2015; citation_pages=1132-1134; citation_doi=10.1038/nmeth.3616; citation_id=CR100"/> <meta name="citation_reference" content="citation_journal_title=Nat. Methods; citation_title=Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials; citation_author=PJ Wu; citation_volume=15; citation_publication_date=2018; citation_pages=561-562; citation_doi=10.1038/s41592-018-0076-1; citation_id=CR101"/> <meta name="citation_reference" content="citation_journal_title=Nat. Methods; citation_title=Brillouin microscopy: an emerging tool for mechanobiology; citation_author=R Prevedel, A Diz-Muñoz, G Ruocco, G Antonacci; citation_volume=16; citation_publication_date=2019; citation_pages=969-977; citation_doi=10.1038/s41592-019-0543-3; citation_id=CR102"/> <meta name="citation_reference" content="citation_journal_title=Nat. Photonics; citation_title=Brillouin bioimaging; citation_author=P So; citation_volume=2; citation_publication_date=2008; citation_pages=13-14; citation_doi=10.1038/nphoton.2007.260; citation_id=CR103"/> <meta name="citation_reference" content="citation_journal_title=Nat. Photonics; citation_title=Confocal Brillouin microscopy for three-dimensional mechanical imaging; citation_author=G Scarcelli, SH Yun; citation_volume=2; citation_publication_date=2008; citation_pages=39-43; citation_doi=10.1038/nphoton.2007.250; citation_id=CR104"/> <meta name="citation_reference" content="citation_journal_title=Sci Rep.; citation_title=High resolution 3D imaging of living cells with sub-optical wavelength phonons; citation_author=F Pérez-Cota; citation_volume=6; citation_publication_date=2016; citation_doi=10.1038/srep39326; citation_id=CR105"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Topological phononic crystals with one-way elastic edge waves; citation_author=P Wang, L Lu, K Bertoldi; citation_volume=115; citation_publication_date=2015; citation_pages=104302; citation_doi=10.1103/PhysRevLett.115.104302; citation_id=CR106"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Topological acoustics; citation_author=Z Yang; citation_volume=114; citation_publication_date=2015; citation_pages=114301; citation_doi=10.1103/PhysRevLett.114.114301; citation_id=CR107"/> <meta name="citation_reference" content="citation_journal_title=Nat. Commun.; citation_title=Topologically protected elastic waves in phononic metamaterials; citation_author=SH Mousavi, AB Khanikaev, Z Wang; citation_volume=6; citation_publication_date=2015; citation_doi=10.1038/ncomms9682; citation_id=CR108"/> <meta name="citation_reference" content="citation_journal_title=Nat. Phys.; citation_title=Acoustic topological insulator and robust one-way sound transport; citation_author=C He; citation_volume=12; citation_publication_date=2016; citation_pages=1124-1129; citation_doi=10.1038/nphys3867; citation_id=CR109"/> <meta name="citation_reference" content="citation_journal_title=Science; citation_title=Observation of chiral phonons; citation_author=H Zhu; citation_volume=359; citation_publication_date=2018; citation_pages=579-582; citation_doi=10.1126/science.aar2711; citation_id=CR110"/> <meta name="citation_reference" content="citation_journal_title=2D Mater.; citation_title=Chiral phonons in two-dimensional materials; citation_author=H Chen, W Zhang, Q Niu, L Zhang; citation_volume=6; citation_publication_date=2019; citation_pages=012002; citation_doi=10.1088/2053-1583/aaf292; citation_id=CR111"/> <meta name="citation_reference" content="citation_journal_title=Rev. Mod. Phys.; citation_title=Brillouin light scattering from crystals in the hydrodynamic region; citation_author=A Griffin; citation_volume=40; citation_publication_date=1968; citation_pages=167-205; citation_doi=10.1103/RevModPhys.40.167; citation_id=CR112"/> <meta name="citation_reference" content="citation_journal_title=Science; citation_title=Observation of second sound in graphite at temperatures above 100 K; citation_author=S Huberman; citation_volume=364; citation_publication_date=2019; citation_pages=375-379; citation_doi=10.1126/science.aav3548; citation_id=CR113"/> <meta name="citation_reference" content="Lee, S. & Li, X. in Nanoscale Energy Transport (ed. Liao, B.) Ch. 1 (IOP, 2020)."/> <meta name="citation_reference" content="citation_journal_title=Appl. Phys. Lett.; citation_title=Spin–phonon coupling in antiferromagnetic nickel oxide; citation_author=E Aytan; citation_volume=111; citation_publication_date=2017; citation_pages=252402; citation_doi=10.1063/1.5009598; citation_id=CR115"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Magnons and phonons optically driven out of local equilibrium in a magnetic insulator; citation_author=K An; citation_volume=117; citation_publication_date=2016; citation_pages=107202; citation_doi=10.1103/PhysRevLett.117.107202; citation_id=CR116"/> <meta name="citation_reference" content="citation_journal_title=Solid State Commun.; citation_title=Light scattering from thermal acoustic magnons in yttrium iron garnet; citation_author=JR Sandercock, W Wettling; citation_volume=13; citation_publication_date=1973; citation_pages=1729-1732; citation_doi=10.1016/0038-1098(73)90276-7; citation_id=CR117"/> <meta name="citation_reference" content="citation_journal_title=Nature; citation_title=Magnetism in two-dimensional van der Waals materials; citation_author=KS Burch, D Mandrus, JG Park; citation_volume=563; citation_publication_date=2018; citation_pages=47-52; citation_doi=10.1038/s41586-018-0631-z; citation_id=CR118"/> <meta name="citation_reference" content="citation_journal_title=ACS Nano; citation_title=Phonon and thermal properties of quasi-two-dimensional FePS3 and MnPS3 antiferromagnetic semiconductors; citation_author=F Kargar; citation_volume=14; citation_publication_date=2020; citation_pages=2424-2435; citation_doi=10.1021/acsnano.9b09839; citation_id=CR119"/> <meta name="citation_reference" content="citation_journal_title=Nano Lett.; citation_title=Superior thermal conductivity of single-layer graphene; citation_author=AA Balandin; citation_volume=8; citation_publication_date=2008; citation_pages=902-907; citation_doi=10.1021/nl0731872; citation_id=CR120"/> <meta name="citation_author" content="Kargar, Fariborz"/> <meta name="citation_author_institution" content="Nano-Device Laboratory (NDL) and Phonon Optimized Engineered Materials (POEM) Center, Department of Electrical and Computer Engineering, University of California, Riverside, Riverside, USA"/> <meta name="citation_author" content="Balandin, Alexander A."/> <meta name="citation_author_institution" content="Nano-Device Laboratory (NDL) and Phonon Optimized Engineered Materials (POEM) Center, Department of Electrical and Computer Engineering, University of California, Riverside, Riverside, USA"/> <meta name="access_endpoint" content="https://www.nature.com/platform/readcube-access"/> <meta name="twitter:site" content="@NaturePhotonics"/> <meta name="twitter:card" content="summary_large_image"/> <meta name="twitter:image:alt" content="Content cover image"/> <meta name="twitter:title" content="Advances in Brillouin–Mandelstam light-scattering spectroscopy"/> <meta name="twitter:description" content="Nature Photonics - Nearly 100 years after the prediction of Brillouin light-scattering spectroscopy, or Brillouin–Mandelstam light-scattering spectroscopy, the effect has proved itself a..."/> <meta name="twitter:image" content="https://media.springernature.com/full/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig1_HTML.png"/> <meta property="og:url" content="https://www.nature.com/articles/s41566-021-00836-5"/> <meta property="og:type" content="article"/> <meta property="og:site_name" content="Nature"/> <meta property="og:title" content="Advances in Brillouin–Mandelstam light-scattering spectroscopy - Nature Photonics"/> <meta property="og:description" content="Nearly 100 years after the prediction of Brillouin light-scattering spectroscopy, or Brillouin–Mandelstam light-scattering spectroscopy, the effect has proved itself a powerful tool for decades. Now its application to probing confined acoustic phonons, phononic metamaterials and magnons is reviewed."/> <meta property="og:image" content="https://media.springernature.com/m685/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig1_HTML.png"/> <script> window.eligibleForRa21 = 'true'; </script> </head> <body class="article-page"> <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-MRVXSHQ" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <div class="position-relative cleared z-index-50 background-white" data-test="top-containers"> <a class="c-skip-link" href="#content">Skip to main content</a> <div class="c-grade-c-banner u-hide"> <div class="c-grade-c-banner__container"> <p>Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.</p> </div> </div> <div class="u-hide u-show-following-ad"></div> <aside class="c-ad c-ad--728x90"> <div class="c-ad__inner" data-container-type="banner-advert"> <p class="c-ad__label">Advertisement</p> <div id="div-gpt-ad-top-1" class="div-gpt-ad advert leaderboard js-ad text-center hide-print grade-c-hide" data-ad-type="top" data-test="top-ad" data-pa11y-ignore data-gpt data-gpt-unitpath="/285/photonics.nature.com/article" data-gpt-sizes="728x90" data-gpt-targeting="type=article;pos=top;artid=s41566-021-00836-5;doi=10.1038/s41566-021-00836-5;techmeta=122,132,133,140;subjmeta=1107,1821,527,624,639,766,930;kwrd=Raman+spectroscopy"> <noscript> <a href="//pubads.g.doubleclick.net/gampad/jump?iu=/285/photonics.nature.com/article&sz=728x90&c=713622705&t=pos%3Dtop%26type%3Darticle%26artid%3Ds41566-021-00836-5%26doi%3D10.1038/s41566-021-00836-5%26techmeta%3D122,132,133,140%26subjmeta%3D1107,1821,527,624,639,766,930%26kwrd%3DRaman+spectroscopy"> <img data-test="gpt-advert-fallback-img" src="//pubads.g.doubleclick.net/gampad/ad?iu=/285/photonics.nature.com/article&sz=728x90&c=713622705&t=pos%3Dtop%26type%3Darticle%26artid%3Ds41566-021-00836-5%26doi%3D10.1038/s41566-021-00836-5%26techmeta%3D122,132,133,140%26subjmeta%3D1107,1821,527,624,639,766,930%26kwrd%3DRaman+spectroscopy" alt="Advertisement" width="728" height="90"></a> </noscript> </div> </div> </aside> <header class="c-header" id="header" data-header data-track-component="nature-150-split-header" style="border-color:#006eb7"> <div class="c-header__row"> <div class="c-header__container"> <div class="c-header__split"> <div class="c-header__logo-container"> <a href="/nphoton" data-track="click" data-track-action="home" data-track-label="image"> <picture class="c-header__logo"> <source srcset="https://media.springernature.com/full/nature-cms/uploads/product/nphoton/header-310d06b045328f70fcc40e14da42c0ca.svg" media="(min-width: 875px)"> <img src="https://media.springernature.com/full/nature-cms/uploads/product/nphoton/header-310d06b045328f70fcc40e14da42c0ca.svg" height="32" alt="Nature Photonics"> </picture> </a> </div> <ul class="c-header__menu c-header__menu--global"> <li class="c-header__item c-header__item--padding c-header__item--hide-md-max"> <a class="c-header__link" href="https://www.nature.com/siteindex" data-test="siteindex-link" data-track="click" data-track-action="open nature research index" data-track-label="link"> <span>View all journals</span> </a> </li> <li class="c-header__item c-header__item--padding c-header__item--pipe"> <a class="c-header__link c-header__link--search" href="#search-menu" data-header-expander data-test="search-link" data-track="click" data-track-action="open search tray" data-track-label="button"> <svg role="img" aria-hidden="true" focusable="false" height="22" width="22" viewBox="0 0 18 18" xmlns="http://www.w3.org/2000/svg"><path d="M16.48 15.455c.283.282.29.749.007 1.032a.738.738 0 01-1.032-.007l-3.045-3.044a7 7 0 111.026-1.026zM8 14A6 6 0 108 2a6 6 0 000 12z"/></svg><span>Search</span> </a> </li> <li class="c-header__item c-header__item--padding c-header__item--snid-account-widget c-header__item--pipe"> <a class="c-header__link eds-c-header__link" id="identity-account-widget" href='https://idp.nature.com/auth/personal/springernature?redirect_uri=https://www.nature.com/articles/s41566-021-00836-5?error=cookies_not_supported&code=ef0b8842-14b6-47ac-9d68-ca0db7f5df5e'><span class="eds-c-header__widget-fragment-title">Log in</span></a> </li> </ul> </div> </div> </div> <div class="c-header__row"> <div class="c-header__container" data-test="navigation-row"> <div class="c-header__split"> <ul class="c-header__menu c-header__menu--journal"> <li class="c-header__item c-header__item--dropdown-menu" data-test="explore-content-button"> <a href="#explore" class="c-header__link" data-header-expander data-test="menu-button--explore" data-track="click" data-track-action="open explore expander" data-track-label="button"> <span><span class="c-header__show-text">Explore</span> content</span><svg role="img" aria-hidden="true" focusable="false" height="16" viewBox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"><path d="m5.58578644 3-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z" transform="matrix(0 1 -1 0 11 3)"/></svg> </a> </li> <li class="c-header__item c-header__item--dropdown-menu"> <a href="#about-the-journal" class="c-header__link" data-header-expander data-test="menu-button--about-the-journal" data-track="click" data-track-action="open about the journal expander" data-track-label="button"> <span>About <span class="c-header__show-text">the journal</span></span><svg role="img" aria-hidden="true" focusable="false" height="16" viewBox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"><path d="m5.58578644 3-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z" transform="matrix(0 1 -1 0 11 3)"/></svg> </a> </li> <li class="c-header__item c-header__item--dropdown-menu" data-test="publish-with-us-button"> <a href="#publish-with-us" class="c-header__link c-header__link--dropdown-menu" data-header-expander data-test="menu-button--publish" data-track="click" data-track-action="open publish with us expander" data-track-label="button"> <span>Publish <span class="c-header__show-text">with us</span></span><svg role="img" aria-hidden="true" focusable="false" height="16" viewBox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"><path d="m5.58578644 3-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z" transform="matrix(0 1 -1 0 11 3)"/></svg> </a> </li> <li class="c-header__item c-header__item--pipe c-header__item--hide-lg-max"> <a class="c-header__link" href="/nphoton/subscribe" data-track="click" data-track-action="subscribe" data-track-label="link" data-test="menu-button-subscribe"> <span>Subscribe</span> </a> </li> </ul> <ul class="c-header__menu c-header__menu--hide-lg-max"> <li class="c-header__item"> <a class="c-header__link" href="https://idp.nature.com/auth/personal/springernature?redirect_uri=https%3A%2F%2Fwww.nature.com%2Fmy-account%2Falerts%2Fsubscribe-journal%3Flist-id%3D151%26journal-link%3Dhttps%253A%252F%252Fwww.nature.com%252Fnphoton%252F" rel="nofollow" data-track="click" data-track-action="Sign up for alerts" data-track-label="link (desktop site header)" data-track-external> <span>Sign up for alerts</span><svg role="img" aria-hidden="true" focusable="false" height="18" viewBox="0 0 18 18" width="18" xmlns="http://www.w3.org/2000/svg"><path d="m4 10h2.5c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-3.08578644l-1.12132034 1.1213203c-.18753638.1875364-.29289322.4418903-.29289322.7071068v.1715729h14v-.1715729c0-.2652165-.1053568-.5195704-.2928932-.7071068l-1.7071068-1.7071067v-3.4142136c0-2.76142375-2.2385763-5-5-5-2.76142375 0-5 2.23857625-5 5zm3 4c0 1.1045695.8954305 2 2 2s2-.8954305 2-2zm-5 0c-.55228475 0-1-.4477153-1-1v-.1715729c0-.530433.21071368-1.0391408.58578644-1.4142135l1.41421356-1.4142136v-3c0-3.3137085 2.6862915-6 6-6s6 2.6862915 6 6v3l1.4142136 1.4142136c.3750727.3750727.5857864.8837805.5857864 1.4142135v.1715729c0 .5522847-.4477153 1-1 1h-4c0 1.6568542-1.3431458 3-3 3-1.65685425 0-3-1.3431458-3-3z" fill="#222"/></svg> </a> </li> <li class="c-header__item c-header__item--pipe"> <a class="c-header__link" href="https://www.nature.com/nphoton.rss" data-track="click" data-track-action="rss feed" data-track-label="link"> <span>RSS feed</span> </a> </li> </ul> </div> </div> </div> </header> <nav class="u-mb-16" aria-label="breadcrumbs"> <div class="u-container"> <ol class="c-breadcrumbs" itemscope itemtype="https://schema.org/BreadcrumbList"> <li class="c-breadcrumbs__item" id="breadcrumb0" itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"><a class="c-breadcrumbs__link" href="/" itemprop="item" data-track="click" data-track-action="breadcrumb" data-track-category="header" data-track-label="link:nature"><span itemprop="name">nature</span></a><meta itemprop="position" content="1"> <svg class="c-breadcrumbs__chevron" role="img" aria-hidden="true" focusable="false" height="10" viewBox="0 0 10 10" width="10" xmlns="http://www.w3.org/2000/svg"> <path d="m5.96738168 4.70639573 2.39518594-2.41447274c.37913917-.38219212.98637524-.38972225 1.35419292-.01894278.37750606.38054586.37784436.99719163-.00013556 1.37821513l-4.03074001 4.06319683c-.37758093.38062133-.98937525.38100976-1.367372-.00003075l-4.03091981-4.06337806c-.37759778-.38063832-.38381821-.99150444-.01600053-1.3622839.37750607-.38054587.98772445-.38240057 1.37006824.00302197l2.39538588 2.4146743.96295325.98624457z" fill="#666" fill-rule="evenodd" transform="matrix(0 -1 1 0 0 10)"/> </svg> </li><li class="c-breadcrumbs__item" id="breadcrumb1" itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"><a class="c-breadcrumbs__link" href="/nphoton" itemprop="item" data-track="click" data-track-action="breadcrumb" data-track-category="header" data-track-label="link:nature photonics"><span itemprop="name">nature photonics</span></a><meta itemprop="position" content="2"> <svg class="c-breadcrumbs__chevron" role="img" aria-hidden="true" focusable="false" height="10" viewBox="0 0 10 10" width="10" xmlns="http://www.w3.org/2000/svg"> <path d="m5.96738168 4.70639573 2.39518594-2.41447274c.37913917-.38219212.98637524-.38972225 1.35419292-.01894278.37750606.38054586.37784436.99719163-.00013556 1.37821513l-4.03074001 4.06319683c-.37758093.38062133-.98937525.38100976-1.367372-.00003075l-4.03091981-4.06337806c-.37759778-.38063832-.38381821-.99150444-.01600053-1.3622839.37750607-.38054587.98772445-.38240057 1.37006824.00302197l2.39538588 2.4146743.96295325.98624457z" fill="#666" fill-rule="evenodd" transform="matrix(0 -1 1 0 0 10)"/> </svg> </li><li class="c-breadcrumbs__item" id="breadcrumb2" itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"><a class="c-breadcrumbs__link" href="/nphoton/articles?type=review-article" itemprop="item" data-track="click" data-track-action="breadcrumb" data-track-category="header" data-track-label="link:review articles"><span itemprop="name">review articles</span></a><meta itemprop="position" content="3"> <svg class="c-breadcrumbs__chevron" role="img" aria-hidden="true" focusable="false" height="10" viewBox="0 0 10 10" width="10" xmlns="http://www.w3.org/2000/svg"> <path d="m5.96738168 4.70639573 2.39518594-2.41447274c.37913917-.38219212.98637524-.38972225 1.35419292-.01894278.37750606.38054586.37784436.99719163-.00013556 1.37821513l-4.03074001 4.06319683c-.37758093.38062133-.98937525.38100976-1.367372-.00003075l-4.03091981-4.06337806c-.37759778-.38063832-.38381821-.99150444-.01600053-1.3622839.37750607-.38054587.98772445-.38240057 1.37006824.00302197l2.39538588 2.4146743.96295325.98624457z" fill="#666" fill-rule="evenodd" transform="matrix(0 -1 1 0 0 10)"/> </svg> </li><li class="c-breadcrumbs__item" id="breadcrumb3" itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"> <span itemprop="name">article</span><meta itemprop="position" content="4"></li> </ol> </div> </nav> </div> <div class="u-container u-mt-32 u-mb-32 u-clearfix" id="content" data-component="article-container" data-container-type="article"> <main class="c-article-main-column u-float-left js-main-column" data-track-component="article body"> <article lang="en"> <div class="c-article-header"> <header> <ul class="c-article-identifiers" data-test="article-identifier"> <li class="c-article-identifiers__item" data-test="article-category">Review Article</li> <li class="c-article-identifiers__item">Published: <time datetime="2021-07-22">22 July 2021</time></li> </ul> <h1 class="c-article-title" data-test="article-title" data-article-title="">Advances in Brillouin–Mandelstam light-scattering spectroscopy</h1> <ul class="c-article-author-list c-article-author-list--short" data-test="authors-list" data-component-authors-activator="authors-list"><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Fariborz-Kargar-Aff1" data-author-popup="auth-Fariborz-Kargar-Aff1" data-author-search="Kargar, Fariborz" data-corresp-id="c1">Fariborz Kargar<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-mail-medium"></use></svg></a><span class="u-js-hide"> <a class="js-orcid" href="http://orcid.org/0000-0003-2192-2023"><span class="u-visually-hidden">ORCID: </span>orcid.org/0000-0003-2192-2023</a></span><sup class="u-js-hide"><a href="#Aff1">1</a></sup> & </li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Alexander_A_-Balandin-Aff1" data-author-popup="auth-Alexander_A_-Balandin-Aff1" data-author-search="Balandin, Alexander A.">Alexander A. Balandin</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup> </li></ul> <p class="c-article-info-details" data-container-section="info"> <a data-test="journal-link" href="/nphoton" data-track="click" data-track-action="journal homepage" data-track-category="article body" data-track-label="link"><i data-test="journal-title">Nature Photonics</i></a> <b data-test="journal-volume"><span class="u-visually-hidden">volume</span> 15</b>, <span class="u-visually-hidden">pages </span>720–731 (<span data-test="article-publication-year">2021</span>)<a href="#citeas" class="c-article-info-details__cite-as u-hide-print" data-track="click" data-track-action="cite this article" data-track-label="link">Cite this article</a> </p> <div class="c-article-metrics-bar__wrapper u-clear-both"> <ul class="c-article-metrics-bar u-list-reset"> <li class=" c-article-metrics-bar__item" data-test="access-count"> <p class="c-article-metrics-bar__count">7120 <span class="c-article-metrics-bar__label">Accesses</span></p> </li> <li class="c-article-metrics-bar__item" data-test="citation-count"> <p class="c-article-metrics-bar__count">55 <span class="c-article-metrics-bar__label">Citations</span></p> </li> <li class="c-article-metrics-bar__item" data-test="altmetric-score"> <p class="c-article-metrics-bar__count">16 <span class="c-article-metrics-bar__label">Altmetric</span></p> </li> <li class="c-article-metrics-bar__item"> <p class="c-article-metrics-bar__details"><a href="/articles/s41566-021-00836-5/metrics" data-track="click" data-track-action="view metrics" data-track-label="link" rel="nofollow">Metrics <span class="u-visually-hidden">details</span></a></p> </li> </ul> </div> </header> <div class="u-js-hide" data-component="article-subject-links"> <h3 class="c-article__sub-heading">Subjects</h3> <ul class="c-article-subject-list"> <li class="c-article-subject-list__subject"><a href="/subjects/raman-spectroscopy" data-track="click" data-track-action="view subject" data-track-label="link">Raman spectroscopy</a></li> </ul> </div> </div> <div class="c-article-body"> <section aria-labelledby="Abs1" data-title="Abstract" lang="en"><div class="c-article-section" id="Abs1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Abs1">Abstract</h2><div class="c-article-section__content" id="Abs1-content"><p>Recent years have witnessed a much broader use of Brillouin inelastic light-scattering spectroscopy for the investigation of phonons and magnons in novel materials, nanostructures and devices. Driven by the developments in instrumentation and the strong need for accurate knowledge on the energies of elemental excitations, Brillouin–Mandelstam spectroscopy is rapidly becoming an essential technique that is complementary to Raman inelastic light-scattering spectroscopy. We provide an overview of recent progress in the Brillouin light-scattering technique, focusing on the use of this photonic method for the investigation of confined acoustic phonons, phononic metamaterials and magnon propagation and scattering. This Review emphasizes the emerging applications of Brillouin–Mandelstam spectroscopy for phonon-engineered structures and spintronic devices, and concludes with a perspective on future directions.</p></div></div></section> <noscript> <div class="c-nature-box c-nature-box--side " data-component="entitlement-box"> <div class="js-access-button"> <a href="https://wayf.springernature.com?redirect_uri=https%3A%2F%2Fwww.nature.com%2Farticles%2Fs41566-021-00836-5" class="c-article__button" data-test="ra21"> <svg class="u-icon" width="18" height="18" aria-hidden="true" focusable="false"><use href="#icon-institution"></use></svg> <span class="c-article__button-text">Access through your institution</span> </a> </div> <div class="js-buy-button"> <a href="#access-options" class="c-article__button c-article__button--inverted" data-test="ra21"> <span>Buy or subscribe</span> </a> </div> </div> </noscript> <div class="js-context-bar-sticky-point-mobile" data-track-context="article body"> </div> <div class="c-article-access-provider u-mb-32 u-mt-0"> <p class="c-article-access-provider__text u-sans-serif">This is a preview of subscription content, <a href="https://wayf.springernature.com?redirect_uri=https%3A%2F%2Fwww.nature.com%2Farticles%2Fs41566-021-00836-5" data-track="click_institution_login" data-track-context="article body link" data-track-action="institution access preview subscription" data-track-label="link">access via your institution</a></p> </div> <h2 class="c-article-section__title u-h2 u-mb-24" id="access-options">Access options</h2> <noscript> <div class="c-nature-box c-nature-box--side " data-component="entitlement-box"> <div class="js-access-button"> <a href="https://wayf.springernature.com?redirect_uri=https%3A%2F%2Fwww.nature.com%2Farticles%2Fs41566-021-00836-5" class="c-article__button" data-test="ra21"> <svg class="u-icon" width="18" height="18" aria-hidden="true" focusable="false"><use href="#icon-institution"></use></svg> <span class="c-article__button-text">Access through your institution</span> </a> </div> </div> </noscript> <div class="c-nature-box c-nature-box--side u-display-none u-hide-print" aria-hidden="true" data-component="entitlement-box" id=entitlement-box-main-column-unentitled data-force-hide-buy-button="true" data-unsubscribe-media-query-change="true" > <p class="c-nature-box__text js-text u-display-none" aria-hidden="true"></p> <div class="js-access-button u-display-none"> <a href="https://wayf.springernature.com?redirect_uri=https%3A%2F%2Fwww.nature.com%2Farticles%2Fs41566-021-00836-5" class="c-article__button" aria-hidden="true" data-test="ra21" data-track="click_institution_login" data-track-context="article body button" data-track-action="institution access above buybox" data-track-label="button"> <svg class="u-icon" width="18" height="18" aria-hidden="true" focusable="false"><use xlink:href="#icon-institution"></use></svg> <span class="c-article__button-text">Access through your institution</span> </a> </div> <div class="js-change-institution-button u-display-none"> <a href="https://wayf.springernature.com?redirect_uri=https%3A%2F%2Fwww.nature.com%2Farticles%2Fs41566-021-00836-5" class="c-article__button c-article__button--inverted" aria-hidden="true" data-test="ra21" data-track="click" data-track-action="change institution above buybox" data-track-label="button"> <span class="c-article__button-text">Change institution</span> </a> </div> <div class="js-buy-button u-display-none"> <a href="#access-options" class="c-article__button c-article__button--inverted" aria-hidden="true" data-test="ra21" data-track="click" data-track-action="buy or subscribe" data-track-label="button"> <span>Buy or subscribe</span> </a> </div> </div> <div class="LiveAreaSection"><style type="text/css">/* style specs start */ /* style specs end */</style><section class="BuyBoxSection"><div class="subscribe-buybox-nature-plus"> <div class="box-inner"> <p class="title-buybox"> Access Nature and 54 other Nature Portfolio journals </p> <p class="access-buybox"> Get Nature+, our best-value online-access subscription </p> <div> <p class="price-buybox" id="nature-plus-subscription-price"> <span class="price-value">24,99 €<span class="price-per-period" style="font-size: 0.9rem"> / 30 days</span></span> </p> <p class="issue-buybox">cancel any time</p> </div> <div class="button-container"> <a href="https://shop.nature.com/products/plus" class="Button-505204839" data-track="click" data-track-action="nature+" data-track-label="link" data-track-category="article body" ><span class="ButtonLabel-3869432492">Learn more</span></a > </div> </div> </div><div class="subscribe-buybox"> <div class="box-inner"> <p class="title-buybox">Subscribe to this journal</p> <p class="access-buybox"> Receive 12 print issues and online access </p> <div> <p class="price-buybox" id="subscription-price">195,33 € per year</p> <p class="issue-buybox">only 16,28 € per issue</p> </div> <div class="button-container"> <a href="/nphoton/subscribe" class="Button-1078489254" data-track="click" data-track-action="subscribe" data-track-label="link" data-track-category="article body" ><span class="ButtonLabel-3296148077">Learn more</span></a > </div> </div> </div><div class="readcube-buybox"> <div class="box-inner"> <p class="title-readcube">Buy this article</p> <ul> <li class="link-usp"><span>Purchase on SpringerLink</span></li> <li class="link-usp"> <span>Instant access to full article PDF</span> </li> </ul> <div class="button-container"> <a href="//link.springer.com/article/10.1038/s41566-021-00836-5?utm_source=nature&utm_medium=referral&utm_campaign=buyArticle" class="btn-secondary Button-2737859108" data-track="click" data-track-action="Go to SL article page" data-track-label="link" data-track-category="article body" rel="noreferrer" ><span class="btn-secondary-label ButtonLabel-1636778223" >Buy now</span ></a > </div> </div> </div><p class="tax-buybox">Prices may be subject to local taxes which are calculated during checkout</p></section><style type="text/css"> /* style specs start */ style { display: none !important; } .LiveAreaSection * { align-content: stretch; align-items: stretch; align-self: auto; animation-delay: 0s; animation-direction: normal; animation-duration: 0s; animation-fill-mode: none; animation-iteration-count: 1; animation-name: none; animation-play-state: running; animation-timing-function: ease; azimuth: center; backface-visibility: visible; background-attachment: scroll; background-blend-mode: normal; background-clip: borderBox; background-color: transparent; background-image: none; background-origin: paddingBox; background-position: 0 0; background-repeat: repeat; background-size: auto auto; block-size: auto; border-block-end-color: currentcolor; border-block-end-style: none; border-block-end-width: medium; border-block-start-color: currentcolor; border-block-start-style: none; border-block-start-width: medium; border-bottom-color: currentcolor; border-bottom-left-radius: 0; border-bottom-right-radius: 0; border-bottom-style: none; border-bottom-width: medium; border-collapse: separate; border-image-outset: 0s; border-image-repeat: stretch; border-image-slice: 100%; border-image-source: none; border-image-width: 1; border-inline-end-color: currentcolor; border-inline-end-style: none; border-inline-end-width: medium; border-inline-start-color: currentcolor; border-inline-start-style: none; border-inline-start-width: medium; border-left-color: currentcolor; border-left-style: none; border-left-width: medium; border-right-color: currentcolor; border-right-style: none; border-right-width: medium; border-spacing: 0; border-top-color: currentcolor; border-top-left-radius: 0; border-top-right-radius: 0; border-top-style: none; border-top-width: medium; bottom: auto; box-decoration-break: slice; box-shadow: none; box-sizing: border-box; break-after: auto; break-before: auto; break-inside: auto; caption-side: top; caret-color: auto; clear: none; clip: auto; clip-path: none; color: initial; column-count: auto; column-fill: balance; column-gap: normal; column-rule-color: currentcolor; column-rule-style: none; column-rule-width: medium; column-span: none; column-width: auto; content: normal; counter-increment: none; counter-reset: none; cursor: auto; display: inline; empty-cells: show; filter: none; flex-basis: auto; flex-direction: row; flex-grow: 0; flex-shrink: 1; flex-wrap: nowrap; float: none; font-family: initial; font-feature-settings: normal; font-kerning: auto; font-language-override: normal; font-size: medium; font-size-adjust: none; font-stretch: normal; font-style: normal; font-synthesis: weight style; font-variant: normal; font-variant-alternates: normal; font-variant-caps: normal; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-position: normal; font-weight: 400; grid-auto-columns: auto; grid-auto-flow: row; grid-auto-rows: auto; grid-column-end: auto; grid-column-gap: 0; grid-column-start: auto; grid-row-end: auto; grid-row-gap: 0; grid-row-start: auto; grid-template-areas: none; grid-template-columns: none; grid-template-rows: none; height: auto; hyphens: manual; image-orientation: 0deg; image-rendering: auto; image-resolution: 1dppx; ime-mode: auto; inline-size: auto; isolation: auto; justify-content: flexStart; left: auto; letter-spacing: normal; line-break: auto; line-height: normal; list-style-image: none; list-style-position: outside; list-style-type: disc; margin-block-end: 0; margin-block-start: 0; margin-bottom: 0; margin-inline-end: 0; margin-inline-start: 0; margin-left: 0; margin-right: 0; margin-top: 0; mask-clip: borderBox; mask-composite: add; mask-image: none; mask-mode: matchSource; mask-origin: borderBox; mask-position: 0 0; mask-repeat: repeat; mask-size: auto; mask-type: luminance; max-height: none; max-width: none; min-block-size: 0; min-height: 0; min-inline-size: 0; min-width: 0; mix-blend-mode: normal; object-fit: fill; object-position: 50% 50%; offset-block-end: auto; offset-block-start: auto; offset-inline-end: auto; offset-inline-start: auto; opacity: 1; order: 0; orphans: 2; outline-color: initial; outline-offset: 0; outline-style: none; outline-width: medium; overflow: visible; overflow-wrap: normal; overflow-x: visible; overflow-y: visible; padding-block-end: 0; padding-block-start: 0; padding-bottom: 0; padding-inline-end: 0; padding-inline-start: 0; padding-left: 0; padding-right: 0; padding-top: 0; page-break-after: auto; page-break-before: auto; page-break-inside: auto; perspective: none; perspective-origin: 50% 50%; pointer-events: auto; position: static; quotes: initial; resize: none; right: auto; ruby-align: spaceAround; ruby-merge: separate; ruby-position: over; scroll-behavior: auto; scroll-snap-coordinate: none; scroll-snap-destination: 0 0; scroll-snap-points-x: none; scroll-snap-points-y: none; scroll-snap-type: none; shape-image-threshold: 0; shape-margin: 0; shape-outside: none; tab-size: 8; table-layout: auto; text-align: initial; text-align-last: auto; text-combine-upright: none; text-decoration-color: currentcolor; text-decoration-line: none; text-decoration-style: solid; text-emphasis-color: currentcolor; text-emphasis-position: over right; text-emphasis-style: none; text-indent: 0; text-justify: auto; text-orientation: mixed; text-overflow: clip; text-rendering: auto; text-shadow: none; text-transform: none; text-underline-position: auto; top: auto; touch-action: auto; transform: none; transform-box: borderBox; transform-origin: 50% 50%0; transform-style: flat; transition-delay: 0s; transition-duration: 0s; transition-property: all; transition-timing-function: ease; vertical-align: baseline; visibility: visible; white-space: normal; widows: 2; width: auto; will-change: auto; word-break: normal; word-spacing: normal; word-wrap: normal; writing-mode: horizontalTb; z-index: auto; -webkit-appearance: none; -moz-appearance: none; -ms-appearance: none; appearance: none; margin: 0; } .LiveAreaSection { width: 100%; } .LiveAreaSection .login-option-buybox { display: block; width: 100%; font-size: 17px; line-height: 30px; color: #222; padding-top: 30px; font-family: Harding, Palatino, serif; } .LiveAreaSection .additional-access-options { display: block; font-weight: 700; font-size: 17px; line-height: 30px; color: #222; font-family: Harding, Palatino, serif; } .LiveAreaSection .additional-login > li:not(:first-child)::before { transform: translateY(-50%); content: ""; height: 1rem; position: absolute; top: 50%; left: 0; border-left: 2px solid #999; } .LiveAreaSection .additional-login > li:not(:first-child) { padding-left: 10px; } .LiveAreaSection .additional-login > li { display: inline-block; position: relative; vertical-align: middle; padding-right: 10px; } .BuyBoxSection { display: flex; flex-wrap: wrap; flex: 1; flex-direction: row-reverse; margin: -30px -15px 0; } .BuyBoxSection .box-inner { width: 100%; height: 100%; padding: 30px 5px; display: flex; flex-direction: column; justify-content: space-between; } .BuyBoxSection p { margin: 0; } .BuyBoxSection .readcube-buybox { background-color: #f3f3f3; flex-shrink: 1; flex-grow: 1; flex-basis: 255px; background-clip: content-box; padding: 0 15px; margin-top: 30px; } .BuyBoxSection .subscribe-buybox { background-color: #f3f3f3; flex-shrink: 1; flex-grow: 4; flex-basis: 300px; background-clip: content-box; padding: 0 15px; margin-top: 30px; } .BuyBoxSection .subscribe-buybox-nature-plus { background-color: #f3f3f3; flex-shrink: 1; flex-grow: 4; flex-basis: 100%; background-clip: content-box; padding: 0 15px; margin-top: 30px; } .BuyBoxSection .title-readcube, .BuyBoxSection .title-buybox { display: block; margin: 0; margin-right: 10%; margin-left: 10%; font-size: 24px; line-height: 32px; color: #222; text-align: center; font-family: Harding, Palatino, serif; } .BuyBoxSection .title-asia-buybox { display: block; margin: 0; margin-right: 5%; margin-left: 5%; font-size: 24px; line-height: 32px; color: #222; text-align: center; font-family: Harding, Palatino, serif; } .BuyBoxSection .asia-link, .Link-328123652, .Link-2926870917, .Link-2291679238, .Link-595459207 { color: #069; cursor: pointer; text-decoration: none; font-size: 1.05em; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; line-height: 1.05em6; } .BuyBoxSection .access-readcube { display: block; margin: 0; margin-right: 10%; margin-left: 10%; font-size: 14px; color: #222; padding-top: 10px; text-align: center; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; line-height: 20px; } .BuyBoxSection ul { margin: 0; } .BuyBoxSection .link-usp { display: list-item; margin: 0; margin-left: 20px; padding-top: 6px; list-style-position: inside; } .BuyBoxSection .link-usp span { font-size: 14px; color: #222; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; line-height: 20px; } .BuyBoxSection .access-asia-buybox { display: block; margin: 0; margin-right: 5%; margin-left: 5%; font-size: 14px; color: #222; padding-top: 10px; text-align: center; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; line-height: 20px; } .BuyBoxSection .access-buybox { display: block; margin: 0; margin-right: 10%; margin-left: 10%; font-size: 14px; color: #222; opacity: 0.8px; padding-top: 10px; text-align: center; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; line-height: 20px; } .BuyBoxSection .price-buybox { display: block; font-size: 30px; color: #222; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; padding-top: 30px; text-align: center; } .BuyBoxSection .price-buybox-to { display: block; font-size: 30px; color: #222; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; text-align: center; } .BuyBoxSection .price-info-text { font-size: 16px; padding-right: 10px; color: #222; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; } .BuyBoxSection .price-value { font-size: 30px; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; } .BuyBoxSection .price-per-period { font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; } .BuyBoxSection .price-from { font-size: 14px; padding-right: 10px; color: #222; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; line-height: 20px; } .BuyBoxSection .issue-buybox { display: block; font-size: 13px; text-align: center; color: #222; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; line-height: 19px; } .BuyBoxSection .no-price-buybox { display: block; font-size: 13px; line-height: 18px; text-align: center; padding-right: 10%; padding-left: 10%; padding-bottom: 20px; padding-top: 30px; color: #222; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; } .BuyBoxSection .vat-buybox { display: block; margin-top: 5px; margin-right: 20%; margin-left: 20%; font-size: 11px; color: #222; padding-top: 10px; padding-bottom: 15px; text-align: center; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; line-height: 17px; } .BuyBoxSection .tax-buybox { display: block; width: 100%; color: #222; padding: 20px 16px; text-align: center; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; line-height: NaNpx; } .BuyBoxSection .button-container { display: flex; padding-right: 20px; padding-left: 20px; justify-content: center; } .BuyBoxSection .button-container > * { flex: 1px; } .BuyBoxSection .button-container > a:hover, .Button-505204839:hover, .Button-1078489254:hover, .Button-2737859108:hover { text-decoration: none; } .BuyBoxSection .btn-secondary { background: #fff; } .BuyBoxSection .button-asia { background: #069; border: 1px solid #069; border-radius: 0; cursor: pointer; display: block; padding: 9px; outline: 0; text-align: center; text-decoration: none; min-width: 80px; margin-top: 75px; } .BuyBoxSection .button-label-asia, .ButtonLabel-3869432492, .ButtonLabel-3296148077, .ButtonLabel-1636778223 { display: block; color: #fff; font-size: 17px; line-height: 20px; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; text-align: center; text-decoration: none; cursor: pointer; } .Button-505204839, .Button-1078489254, .Button-2737859108 { background: #069; border: 1px solid #069; border-radius: 0; cursor: pointer; display: block; padding: 9px; outline: 0; text-align: center; text-decoration: none; min-width: 80px; max-width: 320px; margin-top: 20px; } .Button-505204839 .btn-secondary-label, .Button-1078489254 .btn-secondary-label, .Button-2737859108 .btn-secondary-label { color: #069; } .uList-2102244549 { list-style: none; padding: 0; margin: 0; } /* style specs end */</style><div></div></div> <nav class="c-access-options"> <h3 class="c-access-options__heading">Additional access options:</h3> <ul class="c-access-options__list"> <li> <a href="https://idp.nature.com/authorize/natureuser?client_id=grover&redirect_uri=https%3A%2F%2Fwww.nature.com%2Farticles%2Fs41566-021-00836-5" data-track="click" data-track-action="login" data-track-category="article body" data-track-label="link">Log in</a> </li> <li> <a href="https://www.springernature.com/gp/librarians/licensing/license-options" data-track="click" data-track-action="learn-subscription" data-track-category="article body" data-track-label="link">Learn about institutional subscriptions</a> </li> <li> <a href="https://support.nature.com/en/support/home" data-track="click" data-track-action="read our faqs" data-track-category="article body" data-track-label="link">Read our FAQs</a> </li> <li> <a href="https://www.springernature.com/gp/contact" data-track="click" data-track-action="contact customer support" data-track-category="article body" data-track-label="link">Contact customer support</a> </li> </ul> </nav> <div class="u-display-none"> <div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-1"><figure><figcaption><b id="Fig1" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 1: Fundamentals of Brillouin–Mandelstam light scattering.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><picture><source type="image/webp" srcset="//media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig1_HTML.png?as=webp"><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig1_HTML.png" alt="" loading="lazy" width="273" height="312"></picture></div></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-2"><figure><figcaption><b id="Fig2" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 2: Observation of phonon confinement in nanostructured materials via the BLS technique.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><picture><source type="image/webp" srcset="//media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig2_HTML.png?as=webp"><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig2_HTML.png" alt="" loading="lazy" width="220" height="312"></picture></div></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-3"><figure><figcaption><b id="Fig3" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 3: Phonon spectrum modification in PnCs and PxCs investigated using the BLS technique.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><picture><source type="image/webp" srcset="//media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig3_HTML.png?as=webp"><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig3_HTML.png" alt="" loading="lazy" width="236" height="312"></picture></div></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-4"><figure><figcaption><b id="Fig4" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 4: Investigation of spin waves using BLS.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><picture><source type="image/webp" srcset="//media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig4_HTML.png?as=webp"><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fs41566-021-00836-5/MediaObjects/41566_2021_836_Fig4_HTML.png" alt="" loading="lazy" width="249" height="312"></picture></div></div></figure></div> </div> <section aria-labelledby="inline-recommendations" data-title="Inline Recommendations" class="c-article-recommendations" data-track-component="inline-recommendations"> <h3 class="c-article-recommendations-title" id="inline-recommendations">Similar content being viewed by others</h3> <div class="c-article-recommendations-list"> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1038%2Fs42005-023-01214-z/MediaObjects/42005_2023_1214_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://www.nature.com/articles/s42005-023-01214-z?fromPaywallRec=true" data-track="select_recommendations_1" data-track-context="inline recommendations" data-track-action="click recommendations inline - 1" data-track-label="10.1038/s42005-023-01214-z">Observing high-k magnons with Mie-resonance-enhanced Brillouin light scattering </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">09 May 2023</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1038%2Fs41467-024-51010-8/MediaObjects/41467_2024_51010_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://www.nature.com/articles/s41467-024-51010-8?fromPaywallRec=true" data-track="select_recommendations_2" data-track-context="inline recommendations" data-track-action="click recommendations inline - 2" data-track-label="10.1038/s41467-024-51010-8">Electrically interfaced Brillouin-active waveguide for microwave photonic measurements </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">09 August 2024</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1038%2Fs41467-020-20283-0/MediaObjects/41467_2020_20283_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://www.nature.com/articles/s41467-020-20283-0?fromPaywallRec=true" data-track="select_recommendations_3" data-track-context="inline recommendations" data-track-action="click recommendations inline - 3" data-track-label="10.1038/s41467-020-20283-0">Functional THz emitters based on Pancharatnam-Berry phase nonlinear metasurfaces </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">04 January 2021</span> </div> </div> </article> </div> </div> </section> <script> window.dataLayer = window.dataLayer || []; window.dataLayer.push({ recommendations: { recommender: 'semantic', model: 'specter', policy_id: 'NA', timestamp: 1732378905, embedded_user: 'null' } }); </script> <div> <div id="MagazineFulltextArticleBodySuffix"><section aria-labelledby="Bib1" data-title="References"><div class="c-article-section" id="Bib1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Bib1">References</h2><div class="c-article-section__content" id="Bib1-content"><div data-container-section="references"><ol class="c-article-references" data-track-component="outbound reference" data-track-context="references section"><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="1."><p class="c-article-references__text" id="ref-CR1">Brillouin, L. Diffusion de la lumière et des rayons X par un corps transparent homogène. Influence de l’agitation thermique. <i>Ann. Phys.</i> <b>17</b>, 88–122 (1922).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1051/anphys/192209170088" data-track-item_id="10.1051/anphys/192209170088" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1051%2Fanphys%2F192209170088" aria-label="Article reference 1" data-doi="10.1051/anphys/192209170088">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 1" href="http://scholar.google.com/scholar_lookup?&title=Diffusion%20de%20la%20lumi%C3%A8re%20et%20des%20rayons%20X%20par%20un%20corps%20transparent%20homog%C3%A8ne.%20Influence%20de%20l%E2%80%99agitation%20thermique&journal=Ann.%20Phys.&doi=10.1051%2Fanphys%2F192209170088&volume=17&pages=88-122&publication_year=1922&author=Brillouin%2CL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="2."><p class="c-article-references__text" id="ref-CR2">Mandelstam, L. Light scattering by inhomogeneous media. <i>Zh. Russ. Fiz. Khim. Ova.</i> <b>58</b>, 381 (1926).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 2" href="http://scholar.google.com/scholar_lookup?&title=Light%20scattering%20by%20inhomogeneous%20media&journal=Zh.%20Russ.%20Fiz.%20Khim.%20Ova.&volume=58&publication_year=1926&author=Mandelstam%2CL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="3."><p class="c-article-references__text" id="ref-CR3">Meng, Z., Traverso, A. J., Ballmann, C. W., Troyanova-Wood, M. A. & Yakovlev, V. V. Seeing cells in a new light: a renaissance of Brillouin spectroscopy. <i>Adv. Opt. Photonics</i> <b>8</b>, 300–327 (2016).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1364/AOP.8.000300" data-track-item_id="10.1364/AOP.8.000300" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1364%2FAOP.8.000300" aria-label="Article reference 3" data-doi="10.1364/AOP.8.000300">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016AdOP....8..300M" aria-label="ADS reference 3">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 3" href="http://scholar.google.com/scholar_lookup?&title=Seeing%20cells%20in%20a%20new%20light%3A%20a%20renaissance%20of%20Brillouin%20spectroscopy&journal=Adv.%20Opt.%20Photonics&doi=10.1364%2FAOP.8.000300&volume=8&pages=300-327&publication_year=2016&author=Meng%2CZ&author=Traverso%2CAJ&author=Ballmann%2CCW&author=Troyanova-Wood%2CMA&author=Yakovlev%2CVV"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="4."><p class="c-article-references__text" id="ref-CR4">Raman, C. V. & Krishnan, K. S. A new type of secondary radiation. <i>Nature</i> <b>121</b>, 501–502 (1928).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/121501c0" data-track-item_id="10.1038/121501c0" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2F121501c0" aria-label="Article reference 4" data-doi="10.1038/121501c0">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1928Natur.121..501R" aria-label="ADS reference 4">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 4" href="http://scholar.google.com/scholar_lookup?&title=A%20new%20type%20of%20secondary%20radiation&journal=Nature&doi=10.1038%2F121501c0&volume=121&pages=501-502&publication_year=1928&author=Raman%2CCV&author=Krishnan%2CKS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="5."><p class="c-article-references__text" id="ref-CR5">Cardona, M. & Merlin, R. in <i>Light Scattering in Solids IX</i> Vol. 108 (eds Cardona, M. & Merlin, R.) Ch. 1 (Springer, 2006).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="6."><p class="c-article-references__text" id="ref-CR6">Fabelinskiĭ, I. L. The prediction and discovery of Rayleigh line fine structure. <i>Usp. Fiz. Nauk</i> <b>170</b>, 107–108 (2000).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.3367/UFNr.0170.200001f.0093" data-track-item_id="10.3367/UFNr.0170.200001f.0093" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.3367%2FUFNr.0170.200001f.0093" aria-label="Article reference 6" data-doi="10.3367/UFNr.0170.200001f.0093">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 6" href="http://scholar.google.com/scholar_lookup?&title=The%20prediction%20and%20discovery%20of%20Rayleigh%20line%20fine%20structure&journal=Usp.%20Fiz.%20Nauk&doi=10.3367%2FUFNr.0170.200001f.0093&volume=170&pages=107-108&publication_year=2000&author=Fabelinski%C4%AD%2CIL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="7."><p class="c-article-references__text" id="ref-CR7">Fabelinskiĭ, I. L. The discovery of combination scattering of light in Russia and India. <i>Phys. Usp.</i> <b>46</b>, 1105–1112 (2003).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1070/PU2003v046n10ABEH001624" data-track-item_id="10.1070/PU2003v046n10ABEH001624" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1070%2FPU2003v046n10ABEH001624" aria-label="Article reference 7" data-doi="10.1070/PU2003v046n10ABEH001624">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2003PhyU...46.1105F" aria-label="ADS reference 7">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 7" href="http://scholar.google.com/scholar_lookup?&title=The%20discovery%20of%20combination%20scattering%20of%20light%20in%20Russia%20and%20India&journal=Phys.%20Usp.&doi=10.1070%2FPU2003v046n10ABEH001624&volume=46&pages=1105-1112&publication_year=2003&author=Fabelinski%C4%AD%2CIL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="8."><p class="c-article-references__text" id="ref-CR8">Gross, E. Change of wave-length of light due to elastic waves at scattering in liquids. <i>Nature</i> <b>126</b>, 201–202 (1930).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/126201a0" data-track-item_id="10.1038/126201a0" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2F126201a0" aria-label="Article reference 8" data-doi="10.1038/126201a0">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1930Natur.126..201G" aria-label="ADS reference 8">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="math reference" data-track-action="math reference" href="http://www.emis.de/MATH-item?56.0764.05" aria-label="MATH reference 8">MATH</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 8" href="http://scholar.google.com/scholar_lookup?&title=Change%20of%20wave-length%20of%20light%20due%20to%20elastic%20waves%20at%20scattering%20in%20liquids&journal=Nature&doi=10.1038%2F126201a0&volume=126&pages=201-202&publication_year=1930&author=Gross%2CE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="9."><p class="c-article-references__text" id="ref-CR9">Gross, E. The splitting of spectral lines at scattering of light by liquids. <i>Nature</i> <b>126</b>, 400 (1930).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/126400a0" data-track-item_id="10.1038/126400a0" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2F126400a0" aria-label="Article reference 9" data-doi="10.1038/126400a0">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1930Natur.126..400G" aria-label="ADS reference 9">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="math reference" data-track-action="math reference" href="http://www.emis.de/MATH-item?56.0764.06" aria-label="MATH reference 9">MATH</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 9" href="http://scholar.google.com/scholar_lookup?&title=The%20splitting%20of%20spectral%20lines%20at%20scattering%20of%20light%20by%20liquids&journal=Nature&doi=10.1038%2F126400a0&volume=126&publication_year=1930&author=Gross%2CE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="10."><p class="c-article-references__text" id="ref-CR10">Gross, E. über Änderung der WellenlÄnge bei Lichtzerstreuung in Kristallen. <i>Z. Phys.</i> <b>63</b>, 685–687 (1930).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/BF01340308" data-track-item_id="10.1007/BF01340308" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/BF01340308" aria-label="Article reference 10" data-doi="10.1007/BF01340308">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1930ZPhy...63..685G" aria-label="ADS reference 10">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 10" href="http://scholar.google.com/scholar_lookup?&title=%C3%BCber%20%C3%84nderung%20der%20Wellenl%C3%84nge%20bei%20Lichtzerstreuung%20in%20Kristallen&journal=Z.%20Phys.&doi=10.1007%2FBF01340308&volume=63&pages=685-687&publication_year=1930&author=Gross%2CE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="11."><p class="c-article-references__text" id="ref-CR11">Sandercock, J. R. in <i>Light Scattering in Solids III</i> Vol. 51 (eds Cardona, M. & Güntherodt, G.) 173–206 (Springer, 1982).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="12."><p class="c-article-references__text" id="ref-CR12">Scarponi, F. et al. High-performance versatile setup for simultaneous Brillouin–Raman microspectroscopy. <i>Phys. Rev. X</i> <b>7</b>, 031015 (2017).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 12" href="http://scholar.google.com/scholar_lookup?&title=High-performance%20versatile%20setup%20for%20simultaneous%20Brillouin%E2%80%93Raman%20microspectroscopy&journal=Phys.%20Rev.%20X&volume=7&publication_year=2017&author=Scarponi%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="13."><p class="c-article-references__text" id="ref-CR13">Speziale, S., Marquardt, H. & Duffy, T. S. Brillouin scattering and its application in geosciences. <i>Rev. Mineral. Geochem.</i> <b>78</b>, 543–603 (2014).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.2138/rmg.2014.78.14" data-track-item_id="10.2138/rmg.2014.78.14" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.2138%2Frmg.2014.78.14" aria-label="Article reference 13" data-doi="10.2138/rmg.2014.78.14">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 13" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20scattering%20and%20its%20application%20in%20geosciences&journal=Rev.%20Mineral.%20Geochem.&doi=10.2138%2Frmg.2014.78.14&volume=78&pages=543-603&publication_year=2014&author=Speziale%2CS&author=Marquardt%2CH&author=Duffy%2CTS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="14."><p class="c-article-references__text" id="ref-CR14">Huang, C. Y. T. et al. Phononic and photonic properties of shape-engineered silicon nanoscale pillar arrays. <i>Nanotechnology</i> <b>31</b>, 30LT01 (2020).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1361-6528/ab85ee" data-track-item_id="10.1088/1361-6528/ab85ee" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1361-6528%2Fab85ee" aria-label="Article reference 14" data-doi="10.1088/1361-6528/ab85ee">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 14" href="http://scholar.google.com/scholar_lookup?&title=Phononic%20and%20photonic%20properties%20of%20shape-engineered%20silicon%20nanoscale%20pillar%20arrays&journal=Nanotechnology&doi=10.1088%2F1361-6528%2Fab85ee&volume=31&publication_year=2020&author=Huang%2CCYT"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="15."><p class="c-article-references__text" id="ref-CR15">Sledzinska, M. et al. 2D phononic crystals: progress and prospects in hypersound and thermal transport engineering. <i>Adv. Funct. Mater.</i> <b>30</b>, 1904434 (2019).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1002/adfm.201904434" data-track-item_id="10.1002/adfm.201904434" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1002%2Fadfm.201904434" aria-label="Article reference 15" data-doi="10.1002/adfm.201904434">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 15" href="http://scholar.google.com/scholar_lookup?&title=2D%20phononic%20crystals%3A%20progress%20and%20prospects%20in%20hypersound%20and%20thermal%20transport%20engineering&journal=Adv.%20Funct.%20Mater.&doi=10.1002%2Fadfm.201904434&volume=30&publication_year=2019&author=Sledzinska%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="16."><p class="c-article-references__text" id="ref-CR16">Graczykowski, B. et al. Phonon dispersion in hypersonic two-dimensional phononic crystal membranes. <i>Phys. Rev. B</i> <b>91</b>, 075414 (2015).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevB.91.075414" data-track-item_id="10.1103/PhysRevB.91.075414" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevB.91.075414" aria-label="Article reference 16" data-doi="10.1103/PhysRevB.91.075414">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015PhRvB..91g5414G" aria-label="ADS reference 16">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 16" href="http://scholar.google.com/scholar_lookup?&title=Phonon%20dispersion%20in%20hypersonic%20two-dimensional%20phononic%20crystal%20membranes&journal=Phys.%20Rev.%20B&doi=10.1103%2FPhysRevB.91.075414&volume=91&publication_year=2015&author=Graczykowski%2CB"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="17."><p class="c-article-references__text" id="ref-CR17">Yudistira, D. et al. Nanoscale pillar hypersonic surface phononic crystals. <i>Phys. Rev. B</i> <b>94</b>, 094304 (2016).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevB.94.094304" data-track-item_id="10.1103/PhysRevB.94.094304" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevB.94.094304" aria-label="Article reference 17" data-doi="10.1103/PhysRevB.94.094304">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016PhRvB..94i4304Y" aria-label="ADS reference 17">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 17" href="http://scholar.google.com/scholar_lookup?&title=Nanoscale%20pillar%20hypersonic%20surface%20phononic%20crystals&journal=Phys.%20Rev.%20B&doi=10.1103%2FPhysRevB.94.094304&volume=94&publication_year=2016&author=Yudistira%2CD"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="18."><p class="c-article-references__text" id="ref-CR18">Rakhymzhanov, A. M. et al. Band structure of cavity-type hypersonic phononic crystals fabricated by femtosecond laser-induced two-photon polymerization. <i>Appl. Phys. Lett.</i> <b>108</b>, 201901 (2016).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.4949013" data-track-item_id="10.1063/1.4949013" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.4949013" aria-label="Article reference 18" data-doi="10.1063/1.4949013">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016ApPhL.108t1901R" aria-label="ADS reference 18">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 18" href="http://scholar.google.com/scholar_lookup?&title=Band%20structure%20of%20cavity-type%20hypersonic%20phononic%20crystals%20fabricated%20by%20femtosecond%20laser-induced%20two-photon%20polymerization&journal=Appl.%20Phys.%20Lett.&doi=10.1063%2F1.4949013&volume=108&publication_year=2016&author=Rakhymzhanov%2CAM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="19."><p class="c-article-references__text" id="ref-CR19">Alonso-Redondo, E. et al. Phoxonic hybrid superlattice. <i>ACS Appl. Mater. Interfaces</i> <b>7</b>, 12488–12495 (2015).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1021/acsami.5b01247" data-track-item_id="10.1021/acsami.5b01247" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1021%2Facsami.5b01247" aria-label="Article reference 19" data-doi="10.1021/acsami.5b01247">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 19" href="http://scholar.google.com/scholar_lookup?&title=Phoxonic%20hybrid%20superlattice&journal=ACS%20Appl.%20Mater.%20Interfaces&doi=10.1021%2Facsami.5b01247&volume=7&pages=12488-12495&publication_year=2015&author=Alonso-Redondo%2CE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="20."><p class="c-article-references__text" id="ref-CR20">Gomopoulos, N. et al. One-dimensional hypersonic phononic crystals. <i>Nano Lett.</i> <b>10</b>, 980–984 (2010).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1021/nl903959r" data-track-item_id="10.1021/nl903959r" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1021%2Fnl903959r" aria-label="Article reference 20" data-doi="10.1021/nl903959r">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2010NanoL..10..980G" aria-label="ADS reference 20">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 20" href="http://scholar.google.com/scholar_lookup?&title=One-dimensional%20hypersonic%20phononic%20crystals&journal=Nano%20Lett.&doi=10.1021%2Fnl903959r&volume=10&pages=980-984&publication_year=2010&author=Gomopoulos%2CN"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="21."><p class="c-article-references__text" id="ref-CR21">Schneider, D. et al. Engineering the hypersonic phononic band gap of hybrid Bragg stacks. <i>Nano Lett.</i> <b>12</b>, 3101–3108 (2012).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1021/nl300982d" data-track-item_id="10.1021/nl300982d" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1021%2Fnl300982d" aria-label="Article reference 21" data-doi="10.1021/nl300982d">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012NanoL..12.3101S" aria-label="ADS reference 21">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 21" href="http://scholar.google.com/scholar_lookup?&title=Engineering%20the%20hypersonic%20phononic%20band%20gap%20of%20hybrid%20Bragg%20stacks&journal=Nano%20Lett.&doi=10.1021%2Fnl300982d&volume=12&pages=3101-3108&publication_year=2012&author=Schneider%2CD"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="22."><p class="c-article-references__text" id="ref-CR22">Parsons, L. C. & Andrews, G. T. Off-axis phonon and photon propagation in porous silicon superlattices studied by Brillouin spectroscopy and optical reflectance. <i>J. Appl. Phys.</i> <b>116</b>, 033510 (2014).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.4890319" data-track-item_id="10.1063/1.4890319" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.4890319" aria-label="Article reference 22" data-doi="10.1063/1.4890319">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014JAP...116c3510P" aria-label="ADS reference 22">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 22" href="http://scholar.google.com/scholar_lookup?&title=Off-axis%20phonon%20and%20photon%20propagation%20in%20porous%20silicon%20superlattices%20studied%20by%20Brillouin%20spectroscopy%20and%20optical%20reflectance&journal=J.%20Appl.%20Phys.&doi=10.1063%2F1.4890319&volume=116&publication_year=2014&author=Parsons%2CLC&author=Andrews%2CGT"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="23."><p class="c-article-references__text" id="ref-CR23">Kargar, F. et al. Acoustic phonon dispersion engineering in bulk crystals via incorporation of dopant atoms. <i>Appl. Phys. Lett.</i> <b>112</b>, 191902 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.5030558" data-track-item_id="10.1063/1.5030558" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.5030558" aria-label="Article reference 23" data-doi="10.1063/1.5030558">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018ApPhL.112s1902K" aria-label="ADS reference 23">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 23" href="http://scholar.google.com/scholar_lookup?&title=Acoustic%20phonon%20dispersion%20engineering%20in%20bulk%20crystals%20via%20incorporation%20of%20dopant%20atoms&journal=Appl.%20Phys.%20Lett.&doi=10.1063%2F1.5030558&volume=112&publication_year=2018&author=Kargar%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="24."><p class="c-article-references__text" id="ref-CR24">Kargar, F. et al. Direct observation of confined acoustic phonon polarization branches in free-standing semiconductor nanowires. <i>Nat. Commun.</i> <b>7</b>, 13400 (2016).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/ncomms13400" data-track-item_id="10.1038/ncomms13400" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fncomms13400" aria-label="Article reference 24" data-doi="10.1038/ncomms13400">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016NatCo...713400K" aria-label="ADS reference 24">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 24" href="http://scholar.google.com/scholar_lookup?&title=Direct%20observation%20of%20confined%20acoustic%20phonon%20polarization%20branches%20in%20free-standing%20semiconductor%20nanowires&journal=Nat.%20Commun.&doi=10.1038%2Fncomms13400&volume=7&publication_year=2016&author=Kargar%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="25."><p class="c-article-references__text" id="ref-CR25">Kuok, M. H., Lim, H. S., Ng, S. C., Liu, N. N. & Wang, Z. K. Brillouin study of the quantization of acoustic modes in nanospheres. <i>Phys. Rev. Lett.</i> <b>90</b>, 255502 (2003).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.90.255502" data-track-item_id="10.1103/PhysRevLett.90.255502" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.90.255502" aria-label="Article reference 25" data-doi="10.1103/PhysRevLett.90.255502">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2003PhRvL..90y5502K" aria-label="ADS reference 25">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 25" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20study%20of%20the%20quantization%20of%20acoustic%20modes%20in%20nanospheres&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.90.255502&volume=90&publication_year=2003&author=Kuok%2CMH&author=Lim%2CHS&author=Ng%2CSC&author=Liu%2CNN&author=Wang%2CZK"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="26."><p class="c-article-references__text" id="ref-CR26">Cuffe, J. et al. Phonons in slow motion: dispersion relations in ultrathin Si membranes. <i>Nano Lett.</i> <b>12</b>, 3569–3573 (2012).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1021/nl301204u" data-track-item_id="10.1021/nl301204u" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1021%2Fnl301204u" aria-label="Article reference 26" data-doi="10.1021/nl301204u">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012NanoL..12.3569C" aria-label="ADS reference 26">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 26" href="http://scholar.google.com/scholar_lookup?&title=Phonons%20in%20slow%20motion%3A%20dispersion%20relations%20in%20ultrathin%20Si%20membranes&journal=Nano%20Lett.&doi=10.1021%2Fnl301204u&volume=12&pages=3569-3573&publication_year=2012&author=Cuffe%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="27."><p class="c-article-references__text" id="ref-CR27">Graczykowski, B. et al. Elastic properties of few nanometers thick polycrystalline MoS<sub>2</sub> membranes: a nondestructive study. <i>Nano Lett.</i> <b>17</b>, 7647–7651 (2017).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1021/acs.nanolett.7b03669" data-track-item_id="10.1021/acs.nanolett.7b03669" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1021%2Facs.nanolett.7b03669" aria-label="Article reference 27" data-doi="10.1021/acs.nanolett.7b03669">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017NanoL..17.7647G" aria-label="ADS reference 27">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 27" href="http://scholar.google.com/scholar_lookup?&title=Elastic%20properties%20of%20few%20nanometers%20thick%20polycrystalline%20MoS2%20membranes%3A%20a%20nondestructive%20study&journal=Nano%20Lett.&doi=10.1021%2Facs.nanolett.7b03669&volume=17&pages=7647-7651&publication_year=2017&author=Graczykowski%2CB"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="28."><p class="c-article-references__text" id="ref-CR28">Li, Y. et al. Brillouin study of acoustic phonon confinement in GeO<sub>2</sub> nanocubes. <i>Appl. Phys. Lett.</i> <b>91</b>, 093116 (2007).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.2777174" data-track-item_id="10.1063/1.2777174" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.2777174" aria-label="Article reference 28" data-doi="10.1063/1.2777174">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2007ApPhL..91i3116L" aria-label="ADS reference 28">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 28" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20study%20of%20acoustic%20phonon%20confinement%20in%20GeO2%20nanocubes&journal=Appl.%20Phys.%20Lett.&doi=10.1063%2F1.2777174&volume=91&publication_year=2007&author=Li%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="29."><p class="c-article-references__text" id="ref-CR29">Kargar, F. et al. Acoustic phonon spectrum and thermal transport in nanoporous alumina arrays. <i>Appl. Phys. Lett.</i> <b>107</b>, 171904 (2015).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.4934883" data-track-item_id="10.1063/1.4934883" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.4934883" aria-label="Article reference 29" data-doi="10.1063/1.4934883">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015ApPhL.107q1904K" aria-label="ADS reference 29">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 29" href="http://scholar.google.com/scholar_lookup?&title=Acoustic%20phonon%20spectrum%20and%20thermal%20transport%20in%20nanoporous%20alumina%20arrays&journal=Appl.%20Phys.%20Lett.&doi=10.1063%2F1.4934883&volume=107&publication_year=2015&author=Kargar%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="30."><p class="c-article-references__text" id="ref-CR30">Berrod, Q., Lagrené, K., Ollivier, J. & Zanotti, J.-M. Inelastic and quasi-elastic neutron scattering. Application to soft-matter. <i>EPJ Web Conf.</i> <b>188</b>, 05001 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1051/epjconf/201818805001" data-track-item_id="10.1051/epjconf/201818805001" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1051%2Fepjconf%2F201818805001" aria-label="Article reference 30" data-doi="10.1051/epjconf/201818805001">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 30" href="http://scholar.google.com/scholar_lookup?&title=Inelastic%20and%20quasi-elastic%20neutron%20scattering.%20Application%20to%20soft-matter&journal=EPJ%20Web%20Conf.&doi=10.1051%2Fepjconf%2F201818805001&volume=188&publication_year=2018&author=Berrod%2CQ&author=Lagren%C3%A9%2CK&author=Ollivier%2CJ&author=Zanotti%2CJ-M"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="31."><p class="c-article-references__text" id="ref-CR31">Demokritov, S. O. et al. Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping. <i>Nature</i> <b>443</b>, 430–433 (2006).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/nature05117" data-track-item_id="10.1038/nature05117" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fnature05117" aria-label="Article reference 31" data-doi="10.1038/nature05117">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2006Natur.443..430D" aria-label="ADS reference 31">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 31" href="http://scholar.google.com/scholar_lookup?&title=Bose%E2%80%93Einstein%20condensation%20of%20quasi-equilibrium%20magnons%20at%20room%20temperature%20under%20pumping&journal=Nature&doi=10.1038%2Fnature05117&volume=443&pages=430-433&publication_year=2006&author=Demokritov%2CSO"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="32."><p class="c-article-references__text" id="ref-CR32">Demidov, V. E. et al. Excitation of coherent propagating spin waves by pure spin currents. <i>Nat. Commun.</i> <b>7</b>, 10446 (2016).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/ncomms10446" data-track-item_id="10.1038/ncomms10446" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fncomms10446" aria-label="Article reference 32" data-doi="10.1038/ncomms10446">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016NatCo...710446D" aria-label="ADS reference 32">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 32" href="http://scholar.google.com/scholar_lookup?&title=Excitation%20of%20coherent%20propagating%20spin%20waves%20by%20pure%20spin%20currents&journal=Nat.%20Commun.&doi=10.1038%2Fncomms10446&volume=7&publication_year=2016&author=Demidov%2CVE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="33."><p class="c-article-references__text" id="ref-CR33">Holanda, J., Maior, D. S., Azevedo, A. & Rezende, S. M. Detecting the phonon spin in magnon–phonon conversion experiments. <i>Nat. Phys.</i> <b>14</b>, 500–506 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/s41567-018-0079-y" data-track-item_id="10.1038/s41567-018-0079-y" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fs41567-018-0079-y" aria-label="Article reference 33" data-doi="10.1038/s41567-018-0079-y">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 33" href="http://scholar.google.com/scholar_lookup?&title=Detecting%20the%20phonon%20spin%20in%20magnon%E2%80%93phonon%20conversion%20experiments&journal=Nat.%20Phys.&doi=10.1038%2Fs41567-018-0079-y&volume=14&pages=500-506&publication_year=2018&author=Holanda%2CJ&author=Maior%2CDS&author=Azevedo%2CA&author=Rezende%2CSM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="34."><p class="c-article-references__text" id="ref-CR34">Cho, J. et al. Thickness dependence of the interfacial Dzyaloshinskii–Moriya interaction in inversion symmetry broken systems. <i>Nat. Commun</i>. <b>6</b>, 7635 (2015).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="35."><p class="c-article-references__text" id="ref-CR35">Balinskiy, M., Kargar, F., Chiang, H., Balandin, A. A. & Khitun, A. G. Brillouin–Mandelstam spectroscopy of standing spin waves in a ferrite waveguide. <i>AIP Adv.</i> <b>8</b>, 056017 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.5007165" data-track-item_id="10.1063/1.5007165" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.5007165" aria-label="Article reference 35" data-doi="10.1063/1.5007165">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018AIPA....8e6017B" aria-label="ADS reference 35">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 35" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%E2%80%93Mandelstam%20spectroscopy%20of%20standing%20spin%20waves%20in%20a%20ferrite%20waveguide&journal=AIP%20Adv.&doi=10.1063%2F1.5007165&volume=8&publication_year=2018&author=Balinskiy%2CM&author=Kargar%2CF&author=Chiang%2CH&author=Balandin%2CAA&author=Khitun%2CAG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="36."><p class="c-article-references__text" id="ref-CR36">Rumyantsev, S., Balinskiy, M., Kargar, F., Khitun, A. & Balandin, A. A. The discrete noise of magnons. <i>Appl. Phys. Lett.</i> <b>114</b>, 090601 (2019).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.5088651" data-track-item_id="10.1063/1.5088651" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.5088651" aria-label="Article reference 36" data-doi="10.1063/1.5088651">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2019ApPhL.114i0601R" aria-label="ADS reference 36">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 36" href="http://scholar.google.com/scholar_lookup?&title=The%20discrete%20noise%20of%20magnons&journal=Appl.%20Phys.%20Lett.&doi=10.1063%2F1.5088651&volume=114&publication_year=2019&author=Rumyantsev%2CS&author=Balinskiy%2CM&author=Kargar%2CF&author=Khitun%2CA&author=Balandin%2CAA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="37."><p class="c-article-references__text" id="ref-CR37">Eggleton, B. J., Poulton, C. G., Rakich, P. T., Steel, M. J. & Bahl, G. Brillouin integrated photonics. <i>Nat. Photonics</i> <b>13</b>, 664–677 (2019).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/s41566-019-0498-z" data-track-item_id="10.1038/s41566-019-0498-z" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fs41566-019-0498-z" aria-label="Article reference 37" data-doi="10.1038/s41566-019-0498-z">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2019NaPho..13..664E" aria-label="ADS reference 37">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 37" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20integrated%20photonics&journal=Nat.%20Photonics&doi=10.1038%2Fs41566-019-0498-z&volume=13&pages=664-677&publication_year=2019&author=Eggleton%2CBJ&author=Poulton%2CCG&author=Rakich%2CPT&author=Steel%2CMJ&author=Bahl%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="38."><p class="c-article-references__text" id="ref-CR38">Zarifi, A. et al. Brillouin spectroscopy of a hybrid silicon-chalcogenide waveguide with geometrical variations. <i>Opt. Lett.</i> <b>43</b>, 3493–3496 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1364/OL.43.003493" data-track-item_id="10.1364/OL.43.003493" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1364%2FOL.43.003493" aria-label="Article reference 38" data-doi="10.1364/OL.43.003493">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018OptL...43.3493Z" aria-label="ADS reference 38">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 38" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20spectroscopy%20of%20a%20hybrid%20silicon-chalcogenide%20waveguide%20with%20geometrical%20variations&journal=Opt.%20Lett.&doi=10.1364%2FOL.43.003493&volume=43&pages=3493-3496&publication_year=2018&author=Zarifi%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="39."><p class="c-article-references__text" id="ref-CR39">Boyd, R. W. <i>Nonlinear Optics</i> 4th edn (Elsevier, 2020).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="40."><p class="c-article-references__text" id="ref-CR40">Hayes, W. & Loudon, R. <i>Scattering of Light by Crystals</i> (Wiley, 1978).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="41."><p class="c-article-references__text" id="ref-CR41">Mutti, P. et al. in <i>Advances in Acoustic Microscopy</i> Vol. 1 (ed. Briggs, A.) 249–300 (Springer, 1995).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="42."><p class="c-article-references__text" id="ref-CR42">Bottani, C. E. & Fioretto, D. Brillouin scattering of phonons in complex materials. <i>Adv. Phys. X</i> <b>3</b>, 607–633 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 42" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20scattering%20of%20phonons%20in%20complex%20materials&journal=Adv.%20Phys.%20X&volume=3&pages=607-633&publication_year=2018&author=Bottani%2CCE&author=Fioretto%2CD"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="43."><p class="c-article-references__text" id="ref-CR43">Olsson, K. S., An, K. & Li, X. Magnon and phonon thermometry with inelastic light scattering. <i>J. Phys. D</i> <b>51</b>, 133001 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1361-6463/aaadde" data-track-item_id="10.1088/1361-6463/aaadde" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1361-6463%2Faaadde" aria-label="Article reference 43" data-doi="10.1088/1361-6463/aaadde">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018JPhD...51m3001O" aria-label="ADS reference 43">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 43" href="http://scholar.google.com/scholar_lookup?&title=Magnon%20and%20phonon%20thermometry%20with%20inelastic%20light%20scattering&journal=J.%20Phys.%20D&doi=10.1088%2F1361-6463%2Faaadde&volume=51&publication_year=2018&author=Olsson%2CKS&author=An%2CK&author=Li%2CX"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="44."><p class="c-article-references__text" id="ref-CR44">Loudon, R. Theory of surface-ripple Brillouin scattering by solids. <i>Phys. Rev. Lett.</i> <b>40</b>, 581–583 (1978).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.40.581" data-track-item_id="10.1103/PhysRevLett.40.581" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.40.581" aria-label="Article reference 44" data-doi="10.1103/PhysRevLett.40.581">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1978PhRvL..40..581L" aria-label="ADS reference 44">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 44" href="http://scholar.google.com/scholar_lookup?&title=Theory%20of%20surface-ripple%20Brillouin%20scattering%20by%20solids&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.40.581&volume=40&pages=581-583&publication_year=1978&author=Loudon%2CR"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="45."><p class="c-article-references__text" id="ref-CR45">Balandin, A. A. & Nika, D. L. Phononics in low-dimensional materials. <i>Mater. Today</i> <b>15</b>, 266–275 (2012).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/S1369-7021(12)70117-7" data-track-item_id="10.1016/S1369-7021(12)70117-7" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2FS1369-7021%2812%2970117-7" aria-label="Article reference 45" data-doi="10.1016/S1369-7021(12)70117-7">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 45" href="http://scholar.google.com/scholar_lookup?&title=Phononics%20in%20low-dimensional%20materials&journal=Mater.%20Today&doi=10.1016%2FS1369-7021%2812%2970117-7&volume=15&pages=266-275&publication_year=2012&author=Balandin%2CAA&author=Nika%2CDL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="46."><p class="c-article-references__text" id="ref-CR46">Balandin, A. A. Phononics of graphene and related materials. <i>ACS Nano</i> <b>14</b>, 5170–5178 (2020).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1021/acsnano.0c02718" data-track-item_id="10.1021/acsnano.0c02718" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1021%2Facsnano.0c02718" aria-label="Article reference 46" data-doi="10.1021/acsnano.0c02718">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 46" href="http://scholar.google.com/scholar_lookup?&title=Phononics%20of%20graphene%20and%20related%20materials&journal=ACS%20Nano&doi=10.1021%2Facsnano.0c02718&volume=14&pages=5170-5178&publication_year=2020&author=Balandin%2CAA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="47."><p class="c-article-references__text" id="ref-CR47">Balandin, A. A. Thermal properties of graphene and nanostructured carbon materials. <i>Nat. Mater.</i> <b>10</b>, 569–581 (2011).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/nmat3064" data-track-item_id="10.1038/nmat3064" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fnmat3064" aria-label="Article reference 47" data-doi="10.1038/nmat3064">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2011NatMa..10..569B" aria-label="ADS reference 47">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 47" href="http://scholar.google.com/scholar_lookup?&title=Thermal%20properties%20of%20graphene%20and%20nanostructured%20carbon%20materials&journal=Nat.%20Mater.&doi=10.1038%2Fnmat3064&volume=10&pages=569-581&publication_year=2011&author=Balandin%2CAA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="48."><p class="c-article-references__text" id="ref-CR48">Xiao, Y., Chen, Q., Ma, D., Yang, N. & Hao, Q. Phonon transport within periodic porous structures—from classical phonon size effects to wave effects. <i>ES Mater. Manuf.</i> <b>5</b>, 2–18 (2019).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 48" href="http://scholar.google.com/scholar_lookup?&title=Phonon%20transport%20within%20periodic%20porous%20structures%E2%80%94from%20classical%20phonon%20size%20effects%20to%20wave%20effects&journal=ES%20Mater.%20Manuf.&volume=5&pages=2-18&publication_year=2019&author=Xiao%2CY&author=Chen%2CQ&author=Ma%2CD&author=Yang%2CN&author=Hao%2CQ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="49."><p class="c-article-references__text" id="ref-CR49">Hussein, M. I., Tsai, C. & Honarvar, H. Thermal conductivity reduction in a nanophononic metamaterial versus a nanophononic crystal: a review and comparative analysis. <i>Adv. Funct. Mater.</i> <b>30</b>, 1906718 (2020).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1002/adfm.201906718" data-track-item_id="10.1002/adfm.201906718" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1002%2Fadfm.201906718" aria-label="Article reference 49" data-doi="10.1002/adfm.201906718">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 49" href="http://scholar.google.com/scholar_lookup?&title=Thermal%20conductivity%20reduction%20in%20a%20nanophononic%20metamaterial%20versus%20a%20nanophononic%20crystal%3A%20a%20review%20and%20comparative%20analysis&journal=Adv.%20Funct.%20Mater.&doi=10.1002%2Fadfm.201906718&volume=30&publication_year=2020&author=Hussein%2CMI&author=Tsai%2CC&author=Honarvar%2CH"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="50."><p class="c-article-references__text" id="ref-CR50">Djafari-Rouhani, B., El-Jallal, S. & Pennec, Y. Phoxonic crystals and cavity optomechanics. <i>C. R. Phys.</i> <b>17</b>, 555–564 (2016).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.crhy.2016.02.001" data-track-item_id="10.1016/j.crhy.2016.02.001" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.crhy.2016.02.001" aria-label="Article reference 50" data-doi="10.1016/j.crhy.2016.02.001">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016CRPhy..17..555D" aria-label="ADS reference 50">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 50" href="http://scholar.google.com/scholar_lookup?&title=Phoxonic%20crystals%20and%20cavity%20optomechanics&journal=C.%20R.%20Phys.&doi=10.1016%2Fj.crhy.2016.02.001&volume=17&pages=555-564&publication_year=2016&author=Djafari-Rouhani%2CB&author=El-Jallal%2CS&author=Pennec%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="51."><p class="c-article-references__text" id="ref-CR51">Johnson, W. L. et al. Vibrational modes of GaN nanowires in the gigahertz range. <i>Nanotechnology</i> <b>23</b>, 495709 (2012).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/0957-4484/23/49/495709" data-track-item_id="10.1088/0957-4484/23/49/495709" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F0957-4484%2F23%2F49%2F495709" aria-label="Article reference 51" data-doi="10.1088/0957-4484/23/49/495709">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 51" href="http://scholar.google.com/scholar_lookup?&title=Vibrational%20modes%20of%20GaN%20nanowires%20in%20the%20gigahertz%20range&journal=Nanotechnology&doi=10.1088%2F0957-4484%2F23%2F49%2F495709&volume=23&publication_year=2012&author=Johnson%2CWL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="52."><p class="c-article-references__text" id="ref-CR52">Still, T. et al. The ‘music’ of core–shell spheres and hollow capsules: influence of the architecture on the mechanical properties at the nanoscale. <i>Nano Lett.</i> <b>8</b>, 3194–3199 (2008).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1021/nl801500n" data-track-item_id="10.1021/nl801500n" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1021%2Fnl801500n" aria-label="Article reference 52" data-doi="10.1021/nl801500n">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2008NanoL...8.3194S" aria-label="ADS reference 52">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 52" href="http://scholar.google.com/scholar_lookup?&title=The%20%E2%80%98music%E2%80%99%20of%20core%E2%80%93shell%20spheres%20and%20hollow%20capsules%3A%20influence%20of%20the%20architecture%20on%20the%20mechanical%20properties%20at%20the%20nanoscale&journal=Nano%20Lett.&doi=10.1021%2Fnl801500n&volume=8&pages=3194-3199&publication_year=2008&author=Still%2CT"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="53."><p class="c-article-references__text" id="ref-CR53">Sun, J. Y. et al. Hypersonic vibrations of Ag@SiO<sub>2</sub> (cubic core)–shell nanospheres. <i>ACS Nano</i> <b>4</b>, 7692–7698 (2010).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1021/nn102581g" data-track-item_id="10.1021/nn102581g" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1021%2Fnn102581g" aria-label="Article reference 53" data-doi="10.1021/nn102581g">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 53" href="http://scholar.google.com/scholar_lookup?&title=Hypersonic%20vibrations%20of%20Ag%40SiO2%20%28cubic%20core%29%E2%80%93shell%20nanospheres&journal=ACS%20Nano&doi=10.1021%2Fnn102581g&volume=4&pages=7692-7698&publication_year=2010&author=Sun%2CJY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="54."><p class="c-article-references__text" id="ref-CR54">Balandin, A. & Wang, K. L. Significant decrease of the lattice thermal conductivity due to phonon confinement in a free-standing semiconductor quantum well. <i>Phys. Rev. B</i> <b>58</b>, 1544–1549 (1998).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevB.58.1544" data-track-item_id="10.1103/PhysRevB.58.1544" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevB.58.1544" aria-label="Article reference 54" data-doi="10.1103/PhysRevB.58.1544">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1998PhRvB..58.1544B" aria-label="ADS reference 54">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 54" href="http://scholar.google.com/scholar_lookup?&title=Significant%20decrease%20of%20the%20lattice%20thermal%20conductivity%20due%20to%20phonon%20confinement%20in%20a%20free-standing%20semiconductor%20quantum%20well&journal=Phys.%20Rev.%20B&doi=10.1103%2FPhysRevB.58.1544&volume=58&pages=1544-1549&publication_year=1998&author=Balandin%2CA&author=Wang%2CKL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="55."><p class="c-article-references__text" id="ref-CR55">Pokatilov, E. P., Nika, D. L. & Balandin, A. A. Confined electron-confined phonon scattering rates in wurtzite AlN/GaN/AlN heterostructures. <i>J. Appl. Phys.</i> <b>95</b>, 5626–5632 (2004).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.1710705" data-track-item_id="10.1063/1.1710705" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.1710705" aria-label="Article reference 55" data-doi="10.1063/1.1710705">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2004JAP....95.5626P" aria-label="ADS reference 55">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 55" href="http://scholar.google.com/scholar_lookup?&title=Confined%20electron-confined%20phonon%20scattering%20rates%20in%20wurtzite%20AlN%2FGaN%2FAlN%20heterostructures&journal=J.%20Appl.%20Phys.&doi=10.1063%2F1.1710705&volume=95&pages=5626-5632&publication_year=2004&author=Pokatilov%2CEP&author=Nika%2CDL&author=Balandin%2CAA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="56."><p class="c-article-references__text" id="ref-CR56">Duval, E. Far-infrared and Raman vibrational transitions of a solid sphere: selection rules. <i>Phys. Rev. B</i> <b>46</b>, 5795–5797 (1992).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevB.46.5795" data-track-item_id="10.1103/PhysRevB.46.5795" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevB.46.5795" aria-label="Article reference 56" data-doi="10.1103/PhysRevB.46.5795">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1992PhRvB..46.5795D" aria-label="ADS reference 56">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 56" href="http://scholar.google.com/scholar_lookup?&title=Far-infrared%20and%20Raman%20vibrational%20transitions%20of%20a%20solid%20sphere%3A%20selection%20rules&journal=Phys.%20Rev.%20B&doi=10.1103%2FPhysRevB.46.5795&volume=46&pages=5795-5797&publication_year=1992&author=Duval%2CE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="57."><p class="c-article-references__text" id="ref-CR57">Dainese, P. et al. Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres. <i>Nat. Phys.</i> <b>2</b>, 388–392 (2006).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/nphys315" data-track-item_id="10.1038/nphys315" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fnphys315" aria-label="Article reference 57" data-doi="10.1038/nphys315">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 57" href="http://scholar.google.com/scholar_lookup?&title=Stimulated%20Brillouin%20scattering%20from%20multi-GHz-guided%20acoustic%20phonons%20in%20nanostructured%20photonic%20crystal%20fibres&journal=Nat.%20Phys.&doi=10.1038%2Fnphys315&volume=2&pages=388-392&publication_year=2006&author=Dainese%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="58."><p class="c-article-references__text" id="ref-CR58">Pennec, Y. et al. Sensing light and sound velocities of fluids in 2D phoxonic crystal slab. In <i>Proc. IEEE Sensors</i> 355–357 (IEEE, 2014).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="59."><p class="c-article-references__text" id="ref-CR59">Eichenfield, M., Chan, J., Camacho, R. M., Vahala, K. J. & Painter, O. Optomechanical crystals. <i>Nature</i> <b>462</b>, 78–82 (2009).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/nature08524" data-track-item_id="10.1038/nature08524" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fnature08524" aria-label="Article reference 59" data-doi="10.1038/nature08524">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2009Natur.462...78E" aria-label="ADS reference 59">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 59" href="http://scholar.google.com/scholar_lookup?&title=Optomechanical%20crystals&journal=Nature&doi=10.1038%2Fnature08524&volume=462&pages=78-82&publication_year=2009&author=Eichenfield%2CM&author=Chan%2CJ&author=Camacho%2CRM&author=Vahala%2CKJ&author=Painter%2CO"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="60."><p class="c-article-references__text" id="ref-CR60">Garín, M., Solà, M., Julian, A. & Ortega, P. Enabling silicon-on-silicon photonics with pedestalled Mie resonators. <i>Nanoscale</i> <b>10</b>, 14406–14413 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1039/C8NR02259C" data-track-item_id="10.1039/C8NR02259C" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1039%2FC8NR02259C" aria-label="Article reference 60" data-doi="10.1039/C8NR02259C">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 60" href="http://scholar.google.com/scholar_lookup?&title=Enabling%20silicon-on-silicon%20photonics%20with%20pedestalled%20Mie%20resonators&journal=Nanoscale&doi=10.1039%2FC8NR02259C&volume=10&pages=14406-14413&publication_year=2018&author=Gar%C3%ADn%2CM&author=Sol%C3%A0%2CM&author=Julian%2CA&author=Ortega%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="61."><p class="c-article-references__text" id="ref-CR61">Sebastian, T., Schultheiss, K., Obry, B., Hillebrands, B. & Schultheiss, H. Micro-focused Brillouin light scattering: imaging spin waves at the nanoscale. <i>Front. Phys.</i> <b>3</b>, 35 (2015).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.3389/fphy.2015.00035" data-track-item_id="10.3389/fphy.2015.00035" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.3389%2Ffphy.2015.00035" aria-label="Article reference 61" data-doi="10.3389/fphy.2015.00035">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 61" href="http://scholar.google.com/scholar_lookup?&title=Micro-focused%20Brillouin%20light%20scattering%3A%20imaging%20spin%20waves%20at%20the%20nanoscale&journal=Front.%20Phys.&doi=10.3389%2Ffphy.2015.00035&volume=3&publication_year=2015&author=Sebastian%2CT&author=Schultheiss%2CK&author=Obry%2CB&author=Hillebrands%2CB&author=Schultheiss%2CH"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="62."><p class="c-article-references__text" id="ref-CR62">Madami, M., Gubbiotti, G., Tacchi, S., Carlotti, G. & Stamps, R. L. Application of microfocused Brillouin light scattering to the study of spin waves in low-dimensional magnetic systems. <i>Solid State Phys.</i> <b>63</b>, 79–150 (2012).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/B978-0-12-397028-2.00002-3" data-track-item_id="10.1016/B978-0-12-397028-2.00002-3" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2FB978-0-12-397028-2.00002-3" aria-label="Article reference 62" data-doi="10.1016/B978-0-12-397028-2.00002-3">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 62" href="http://scholar.google.com/scholar_lookup?&title=Application%20of%20microfocused%20Brillouin%20light%20scattering%20to%20the%20study%20of%20spin%20waves%20in%20low-dimensional%20magnetic%20systems&journal=Solid%20State%20Phys.&doi=10.1016%2FB978-0-12-397028-2.00002-3&volume=63&pages=79-150&publication_year=2012&author=Madami%2CM&author=Gubbiotti%2CG&author=Tacchi%2CS&author=Carlotti%2CG&author=Stamps%2CRL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="63."><p class="c-article-references__text" id="ref-CR63">Cottam, M. G. & Lockwood, D. J. <i>Light Scattering in Magnetic Solids</i> (Wiley, 1986).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="64."><p class="c-article-references__text" id="ref-CR64">Rezende, S. M. <i>Fundamentals of Magnonics</i> Vol. 969 (Springer, 2020)</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="65."><p class="c-article-references__text" id="ref-CR65">Fleury, P. A. & Loudon, R. Scattering of light by one- and two-magnon excitations. <i>Phys. Rev.</i> <b>166</b>, 514–530 (1968).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRev.166.514" data-track-item_id="10.1103/PhysRev.166.514" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRev.166.514" aria-label="Article reference 65" data-doi="10.1103/PhysRev.166.514">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1968PhRv..166..514F" aria-label="ADS reference 65">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 65" href="http://scholar.google.com/scholar_lookup?&title=Scattering%20of%20light%20by%20one-%20and%20two-magnon%20excitations&journal=Phys.%20Rev.&doi=10.1103%2FPhysRev.166.514&volume=166&pages=514-530&publication_year=1968&author=Fleury%2CPA&author=Loudon%2CR"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="66."><p class="c-article-references__text" id="ref-CR66">Demidov, V. E. & Demokritov, S. O. Magnonic waveguides studied by microfocus brillouin light scattering. <i>IEEE Trans. Magn.</i> <b>51</b>, 0800215 (2015).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1109/TMAG.2014.2388196" data-track-item_id="10.1109/TMAG.2014.2388196" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1109%2FTMAG.2014.2388196" aria-label="Article reference 66" data-doi="10.1109/TMAG.2014.2388196">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 66" href="http://scholar.google.com/scholar_lookup?&title=Magnonic%20waveguides%20studied%20by%20microfocus%20brillouin%20light%20scattering&journal=IEEE%20Trans.%20Magn.&doi=10.1109%2FTMAG.2014.2388196&volume=51&publication_year=2015&author=Demidov%2CVE&author=Demokritov%2CSO"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="67."><p class="c-article-references__text" id="ref-CR67">Demokritov, S. O., Hillebrands, B. & Slavin, A. N. Brillouin light scattering studies of confined spin waves: linear and nonlinear confinement. <i>Phys. Rep.</i> <b>348</b>, 441–489 (2001).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/S0370-1573(00)00116-2" data-track-item_id="10.1016/S0370-1573(00)00116-2" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2FS0370-1573%2800%2900116-2" aria-label="Article reference 67" data-doi="10.1016/S0370-1573(00)00116-2">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2001PhR...348..441D" aria-label="ADS reference 67">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 67" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20light%20scattering%20studies%20of%20confined%20spin%20waves%3A%20linear%20and%20nonlinear%20confinement&journal=Phys.%20Rep.&doi=10.1016%2FS0370-1573%2800%2900116-2&volume=348&pages=441-489&publication_year=2001&author=Demokritov%2CSO&author=Hillebrands%2CB&author=Slavin%2CAN"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="68."><p class="c-article-references__text" id="ref-CR68">Serga, A. A., Schneider, T., Hillebrands, B., Demokritov, S. O. & Kostylev, M. P. Phase-sensitive Brillouin light scattering spectroscopy from spin-wave packets. <i>Appl. Phys. Lett.</i> <b>89</b>, 063506 (2006).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.2335627" data-track-item_id="10.1063/1.2335627" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.2335627" aria-label="Article reference 68" data-doi="10.1063/1.2335627">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2006ApPhL..89f3506S" aria-label="ADS reference 68">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 68" href="http://scholar.google.com/scholar_lookup?&title=Phase-sensitive%20Brillouin%20light%20scattering%20spectroscopy%20from%20spin-wave%20packets&journal=Appl.%20Phys.%20Lett.&doi=10.1063%2F1.2335627&volume=89&publication_year=2006&author=Serga%2CAA&author=Schneider%2CT&author=Hillebrands%2CB&author=Demokritov%2CSO&author=Kostylev%2CMP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="69."><p class="c-article-references__text" id="ref-CR69">Vogt, K. et al. All-optical detection of phase fronts of propagating spin waves in a Ni<sub>81</sub>Fe<sub>19</sub> microstripe. <i>Appl. Phys. Lett.</i> <b>95</b>, 182508 (2009).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.3262348" data-track-item_id="10.1063/1.3262348" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.3262348" aria-label="Article reference 69" data-doi="10.1063/1.3262348">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2009ApPhL..95r2508V" aria-label="ADS reference 69">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 69" href="http://scholar.google.com/scholar_lookup?&title=All-optical%20detection%20of%20phase%20fronts%20of%20propagating%20spin%20waves%20in%20a%20Ni81Fe19%20microstripe&journal=Appl.%20Phys.%20Lett.&doi=10.1063%2F1.3262348&volume=95&publication_year=2009&author=Vogt%2CK"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="70."><p class="c-article-references__text" id="ref-CR70">Pirro, P. et al. Interference of coherent spin waves in micron-sized ferromagnetic waveguides. <i>Phys. Status Solidi B</i> <b>248</b>, 2404–2408 (2011).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1002/pssb.201147093" data-track-item_id="10.1002/pssb.201147093" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1002%2Fpssb.201147093" aria-label="Article reference 70" data-doi="10.1002/pssb.201147093">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2011PSSBR.248.2404P" aria-label="ADS reference 70">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 70" href="http://scholar.google.com/scholar_lookup?&title=Interference%20of%20coherent%20spin%20waves%20in%20micron-sized%20ferromagnetic%20waveguides&journal=Phys.%20Status%20Solidi%20B&doi=10.1002%2Fpssb.201147093&volume=248&pages=2404-2408&publication_year=2011&author=Pirro%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="71."><p class="c-article-references__text" id="ref-CR71">Vogt, K. et al. Spin waves turning a corner. <i>Appl. Phys. Lett.</i> <b>101</b>, 042410 (2012).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.4738887" data-track-item_id="10.1063/1.4738887" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.4738887" aria-label="Article reference 71" data-doi="10.1063/1.4738887">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012ApPhL.101d2410V" aria-label="ADS reference 71">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 71" href="http://scholar.google.com/scholar_lookup?&title=Spin%20waves%20turning%20a%20corner&journal=Appl.%20Phys.%20Lett.&doi=10.1063%2F1.4738887&volume=101&publication_year=2012&author=Vogt%2CK"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="72."><p class="c-article-references__text" id="ref-CR72">Vogt, K. et al. Realization of a spin-wave multiplexer. <i>Nat. Commun.</i> <b>5</b>, 3727 (2014).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/ncomms4727" data-track-item_id="10.1038/ncomms4727" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fncomms4727" aria-label="Article reference 72" data-doi="10.1038/ncomms4727">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014NatCo...5.3727V" aria-label="ADS reference 72">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 72" href="http://scholar.google.com/scholar_lookup?&title=Realization%20of%20a%20spin-wave%20multiplexer&journal=Nat.%20Commun.&doi=10.1038%2Fncomms4727&volume=5&publication_year=2014&author=Vogt%2CK"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="73."><p class="c-article-references__text" id="ref-CR73">Borisenko, I. V. et al. Direct evidence of spatial stability of Bose-Einstein condensate of magnons. <i>Nat. Commun.</i> <b>11</b>, 1691 (2020).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/s41467-020-15468-6" data-track-item_id="10.1038/s41467-020-15468-6" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fs41467-020-15468-6" aria-label="Article reference 73" data-doi="10.1038/s41467-020-15468-6">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2020NatCo..11.1691B" aria-label="ADS reference 73">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 73" href="http://scholar.google.com/scholar_lookup?&title=Direct%20evidence%20of%20spatial%20stability%20of%20Bose-Einstein%20condensate%20of%20magnons&journal=Nat.%20Commun.&doi=10.1038%2Fs41467-020-15468-6&volume=11&publication_year=2020&author=Borisenko%2CIV"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="74."><p class="c-article-references__text" id="ref-CR74">Nembach, H. T., Shaw, J. M., Weiler, M., Jué, E. & Silva, T. J. Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii–Moriya interaction in metal films. <i>Nat. Phys.</i> <b>11</b>, 825–829 (2015).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/nphys3418" data-track-item_id="10.1038/nphys3418" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fnphys3418" aria-label="Article reference 74" data-doi="10.1038/nphys3418">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 74" href="http://scholar.google.com/scholar_lookup?&title=Linear%20relation%20between%20Heisenberg%20exchange%20and%20interfacial%20Dzyaloshinskii%E2%80%93Moriya%20interaction%20in%20metal%20films&journal=Nat.%20Phys.&doi=10.1038%2Fnphys3418&volume=11&pages=825-829&publication_year=2015&author=Nembach%2CHT&author=Shaw%2CJM&author=Weiler%2CM&author=Ju%C3%A9%2CE&author=Silva%2CTJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="75."><p class="c-article-references__text" id="ref-CR75">Ma, X. et al. Interfacial Dzyaloshinskii-Moriya interaction: effect of 5d band filling and correlation with spin mixing conductance. <i>Phys. Rev. Lett.</i> <b>120</b>, 157204 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.120.157204" data-track-item_id="10.1103/PhysRevLett.120.157204" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.120.157204" aria-label="Article reference 75" data-doi="10.1103/PhysRevLett.120.157204">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018PhRvL.120o7204M" aria-label="ADS reference 75">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 75" href="http://scholar.google.com/scholar_lookup?&title=Interfacial%20Dzyaloshinskii-Moriya%20interaction%3A%20effect%20of%205d%20band%20filling%20and%20correlation%20with%20spin%20mixing%20conductance&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.120.157204&volume=120&publication_year=2018&author=Ma%2CX"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="76."><p class="c-article-references__text" id="ref-CR76">Benguettat-El Mokhtari, I. et al. Interfacial Dzyaloshinskii-Moriya interaction, interface-induced damping and perpendicular magnetic anisotropy in Pt/Co/W based multilayers. <i>J. Appl. Phys.</i> <b>126</b>, 133902 (2019).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.5119193" data-track-item_id="10.1063/1.5119193" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.5119193" aria-label="Article reference 76" data-doi="10.1063/1.5119193">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2019JAP...126m3902B" aria-label="ADS reference 76">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 76" href="http://scholar.google.com/scholar_lookup?&title=Interfacial%20Dzyaloshinskii-Moriya%20interaction%2C%20interface-induced%20damping%20and%20perpendicular%20magnetic%20anisotropy%20in%20Pt%2FCo%2FW%20based%20multilayers&journal=J.%20Appl.%20Phys.&doi=10.1063%2F1.5119193&volume=126&publication_year=2019&author=Benguettat-El%20Mokhtari%2CI"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="77."><p class="c-article-references__text" id="ref-CR77">Bouloussa, H. et al. Dzyaloshinskii-Moriya interaction induced asymmetry in dispersion of magnonic Bloch modes. <i>Phys. Rev. B</i> <b>102</b>, 014412 (2020).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevB.102.014412" data-track-item_id="10.1103/PhysRevB.102.014412" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevB.102.014412" aria-label="Article reference 77" data-doi="10.1103/PhysRevB.102.014412">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2020PhRvB.102a4412B" aria-label="ADS reference 77">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 77" href="http://scholar.google.com/scholar_lookup?&title=Dzyaloshinskii-Moriya%20interaction%20induced%20asymmetry%20in%20dispersion%20of%20magnonic%20Bloch%20modes&journal=Phys.%20Rev.%20B&doi=10.1103%2FPhysRevB.102.014412&volume=102&publication_year=2020&author=Bouloussa%2CH"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="78."><p class="c-article-references__text" id="ref-CR78">Stashkevich, A. A., Djemia, P., Fetisov, Y. K., Bizière, N. & Fermon, C. High-intensity Brillouin light scattering by spin waves in a permalloy film under microwave resonance pumping. <i>J. Appl. Phys.</i> <b>102</b>, 103905 (2007).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.2815673" data-track-item_id="10.1063/1.2815673" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.2815673" aria-label="Article reference 78" data-doi="10.1063/1.2815673">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2007JAP...102j3905S" aria-label="ADS reference 78">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 78" href="http://scholar.google.com/scholar_lookup?&title=High-intensity%20Brillouin%20light%20scattering%20by%20spin%20waves%20in%20a%20permalloy%20film%20under%20microwave%20resonance%20pumping&journal=J.%20Appl.%20Phys.&doi=10.1063%2F1.2815673&volume=102&publication_year=2007&author=Stashkevich%2CAA&author=Djemia%2CP&author=Fetisov%2CYK&author=Bizi%C3%A8re%2CN&author=Fermon%2CC"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="79."><p class="c-article-references__text" id="ref-CR79">Demidov, V. E. et al. Generation of the second harmonic by spin waves propagating in microscopic stripes. <i>Phys. Rev. B</i> <b>83</b>, 054408 (2011).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevB.83.054408" data-track-item_id="10.1103/PhysRevB.83.054408" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevB.83.054408" aria-label="Article reference 79" data-doi="10.1103/PhysRevB.83.054408">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2011PhRvB..83e4408D" aria-label="ADS reference 79">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 79" href="http://scholar.google.com/scholar_lookup?&title=Generation%20of%20the%20second%20harmonic%20by%20spin%20waves%20propagating%20in%20microscopic%20stripes&journal=Phys.%20Rev.%20B&doi=10.1103%2FPhysRevB.83.054408&volume=83&publication_year=2011&author=Demidov%2CVE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="80."><p class="c-article-references__text" id="ref-CR80">Demidov, V. E. et al. Nonlinear propagation of spin waves in microscopic magnetic stripes. <i>Phys. Rev. Lett.</i> <b>102</b>, 177207 (2009).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.102.177207" data-track-item_id="10.1103/PhysRevLett.102.177207" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.102.177207" aria-label="Article reference 80" data-doi="10.1103/PhysRevLett.102.177207">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2009PhRvL.102q7207D" aria-label="ADS reference 80">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 80" href="http://scholar.google.com/scholar_lookup?&title=Nonlinear%20propagation%20of%20spin%20waves%20in%20microscopic%20magnetic%20stripes&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.102.177207&volume=102&publication_year=2009&author=Demidov%2CVE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="81."><p class="c-article-references__text" id="ref-CR81">Jersch, J. et al. Mapping of localized spin-wave excitations by near-field Brillouin light scattering. <i>Appl. Phys. Lett.</i> <b>97</b>, 152502 (2010).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.3502599" data-track-item_id="10.1063/1.3502599" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.3502599" aria-label="Article reference 81" data-doi="10.1063/1.3502599">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2010ApPhL..97o2502J" aria-label="ADS reference 81">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 81" href="http://scholar.google.com/scholar_lookup?&title=Mapping%20of%20localized%20spin-wave%20excitations%20by%20near-field%20Brillouin%20light%20scattering&journal=Appl.%20Phys.%20Lett.&doi=10.1063%2F1.3502599&volume=97&publication_year=2010&author=Jersch%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="82."><p class="c-article-references__text" id="ref-CR82">Rezende, S. M. Theory of coherence in Bose–Einstein condensation phenomena in a microwave-driven interacting magnon gas. <i>Phys. Rev. B</i> <b>79</b>, 174411 (2009).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevB.79.174411" data-track-item_id="10.1103/PhysRevB.79.174411" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevB.79.174411" aria-label="Article reference 82" data-doi="10.1103/PhysRevB.79.174411">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2009PhRvB..79q4411R" aria-label="ADS reference 82">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 82" href="http://scholar.google.com/scholar_lookup?&title=Theory%20of%20coherence%20in%20Bose%E2%80%93Einstein%20condensation%20phenomena%20in%20a%20microwave-driven%20interacting%20magnon%20gas&journal=Phys.%20Rev.%20B&doi=10.1103%2FPhysRevB.79.174411&volume=79&publication_year=2009&author=Rezende%2CSM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="83."><p class="c-article-references__text" id="ref-CR83">Rüegg, C. et al. Bose–Einstein condensation of the triplet states in the magnetic insulator TlCuCl<sub>3</sub>. <i>Nature</i> <b>423</b>, 62–65 (2003).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/nature01617" data-track-item_id="10.1038/nature01617" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fnature01617" aria-label="Article reference 83" data-doi="10.1038/nature01617">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2003Natur.423...62R" aria-label="ADS reference 83">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 83" href="http://scholar.google.com/scholar_lookup?&title=Bose%E2%80%93Einstein%20condensation%20of%20the%20triplet%20states%20in%20the%20magnetic%20insulator%20TlCuCl3&journal=Nature&doi=10.1038%2Fnature01617&volume=423&pages=62-65&publication_year=2003&author=R%C3%BCegg%2CC"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="84."><p class="c-article-references__text" id="ref-CR84">Demidov, V. E., Dzyapko, O., Demokritov, S. O., Melkov, G. A. & Slavin, A. N. Observation of spontaneous coherence in Bose–Einstein condensate of magnons. <i>Phys. Rev. Lett.</i> <b>100</b>, 047205 (2008).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.100.047205" data-track-item_id="10.1103/PhysRevLett.100.047205" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.100.047205" aria-label="Article reference 84" data-doi="10.1103/PhysRevLett.100.047205">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2008PhRvL.100d7205D" aria-label="ADS reference 84">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 84" href="http://scholar.google.com/scholar_lookup?&title=Observation%20of%20spontaneous%20coherence%20in%20Bose%E2%80%93Einstein%20condensate%20of%20magnons&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.100.047205&volume=100&publication_year=2008&author=Demidov%2CVE&author=Dzyapko%2CO&author=Demokritov%2CSO&author=Melkov%2CGA&author=Slavin%2CAN"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="85."><p class="c-article-references__text" id="ref-CR85">Tupitsyn, I. S., Stamp, P. C. E. & Burin, A. L. Stability of Bose–Einstein condensates of hot magnons in yttrium iron garnet films. <i>Phys. Rev. Lett.</i> <b>100</b>, 257202 (2008).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.100.257202" data-track-item_id="10.1103/PhysRevLett.100.257202" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.100.257202" aria-label="Article reference 85" data-doi="10.1103/PhysRevLett.100.257202">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2008PhRvL.100y7202T" aria-label="ADS reference 85">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 85" href="http://scholar.google.com/scholar_lookup?&title=Stability%20of%20Bose%E2%80%93Einstein%20condensates%20of%20hot%20magnons%20in%20yttrium%20iron%20garnet%20films&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.100.257202&volume=100&publication_year=2008&author=Tupitsyn%2CIS&author=Stamp%2CPCE&author=Burin%2CAL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="86."><p class="c-article-references__text" id="ref-CR86">Gubbiotti, G. et al. Finite size effects in patterned magnetic permalloy films. <i>J. Appl. Phys.</i> <b>87</b>, 5633–5635 (2000).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.372473" data-track-item_id="10.1063/1.372473" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.372473" aria-label="Article reference 86" data-doi="10.1063/1.372473">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2000JAP....87.5633G" aria-label="ADS reference 86">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 86" href="http://scholar.google.com/scholar_lookup?&title=Finite%20size%20effects%20in%20patterned%20magnetic%20permalloy%20films&journal=J.%20Appl.%20Phys.&doi=10.1063%2F1.372473&volume=87&pages=5633-5635&publication_year=2000&author=Gubbiotti%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="87."><p class="c-article-references__text" id="ref-CR87">Roussigné, Y., Chérif, S. M., Dugautier, C. & Moch, P. Experimental and theoretical study of quantized spin-wave modes in micrometer-size permalloy wires. <i>Phys. Rev. B</i> <b>63</b>, 134429 (2001).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevB.63.134429" data-track-item_id="10.1103/PhysRevB.63.134429" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevB.63.134429" aria-label="Article reference 87" data-doi="10.1103/PhysRevB.63.134429">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2001PhRvB..63m4429R" aria-label="ADS reference 87">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 87" href="http://scholar.google.com/scholar_lookup?&title=Experimental%20and%20theoretical%20study%20of%20quantized%20spin-wave%20modes%20in%20micrometer-size%20permalloy%20wires&journal=Phys.%20Rev.%20B&doi=10.1103%2FPhysRevB.63.134429&volume=63&publication_year=2001&author=Roussign%C3%A9%2CY&author=Ch%C3%A9rif%2CSM&author=Dugautier%2CC&author=Moch%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="88."><p class="c-article-references__text" id="ref-CR88">Chérif, S. M., Roussigné, Y. E. & Moch, P. Finite-size effects in arrays of permalloy square dots. <i>IEEE Trans. Magn.</i> <b>38</b>, 2529–2531 (2002).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1109/TMAG.2002.801917" data-track-item_id="10.1109/TMAG.2002.801917" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1109%2FTMAG.2002.801917" aria-label="Article reference 88" data-doi="10.1109/TMAG.2002.801917">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2002ITM....38.2529C" aria-label="ADS reference 88">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 88" href="http://scholar.google.com/scholar_lookup?&title=Finite-size%20effects%20in%20arrays%20of%20permalloy%20square%20dots&journal=IEEE%20Trans.%20Magn.&doi=10.1109%2FTMAG.2002.801917&volume=38&pages=2529-2531&publication_year=2002&author=Ch%C3%A9rif%2CSM&author=Roussign%C3%A9%2CYE&author=Moch%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="89."><p class="c-article-references__text" id="ref-CR89">Gubbiotti, G. et al. Magnetostatic interaction in arrays of nanometric permalloy wires: a magneto-optic Kerr effect and a Brillouin light scattering study. <i>Phys. Rev. B</i> <b>72</b>, 224413 (2005).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevB.72.224413" data-track-item_id="10.1103/PhysRevB.72.224413" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevB.72.224413" aria-label="Article reference 89" data-doi="10.1103/PhysRevB.72.224413">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2005PhRvB..72v4413G" aria-label="ADS reference 89">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 89" href="http://scholar.google.com/scholar_lookup?&title=Magnetostatic%20interaction%20in%20arrays%20of%20nanometric%20permalloy%20wires%3A%20a%20magneto-optic%20Kerr%20effect%20and%20a%20Brillouin%20light%20scattering%20study&journal=Phys.%20Rev.%20B&doi=10.1103%2FPhysRevB.72.224413&volume=72&publication_year=2005&author=Gubbiotti%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="90."><p class="c-article-references__text" id="ref-CR90">Kargar, F. et al. Brillouin–Mandelstam spectroscopy of stress-modulated spatially confined spin waves in Ni thin films on piezoelectric substrates. <i>J. Magn. Magn. Mater.</i> <b>501</b>, 166440 (2020).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.jmmm.2020.166440" data-track-item_id="10.1016/j.jmmm.2020.166440" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.jmmm.2020.166440" aria-label="Article reference 90" data-doi="10.1016/j.jmmm.2020.166440">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 90" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%E2%80%93Mandelstam%20spectroscopy%20of%20stress-modulated%20spatially%20confined%20spin%20waves%20in%20Ni%20thin%20films%20on%20piezoelectric%20substrates&journal=J.%20Magn.%20Magn.%20Mater.&doi=10.1016%2Fj.jmmm.2020.166440&volume=501&publication_year=2020&author=Kargar%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="91."><p class="c-article-references__text" id="ref-CR91">Birt, D. R. et al. Brillouin light scattering spectra as local temperature sensors for thermal magnons and acoustic phonons. <i>Appl. Phys. Lett.</i> <b>102</b>, 082401 (2013).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.4793538" data-track-item_id="10.1063/1.4793538" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.4793538" aria-label="Article reference 91" data-doi="10.1063/1.4793538">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013ApPhL.102h2401B" aria-label="ADS reference 91">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 91" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20light%20scattering%20spectra%20as%20local%20temperature%20sensors%20for%20thermal%20magnons%20and%20acoustic%20phonons&journal=Appl.%20Phys.%20Lett.&doi=10.1063%2F1.4793538&volume=102&publication_year=2013&author=Birt%2CDR"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="92."><p class="c-article-references__text" id="ref-CR92">Gubbiotti, G. et al. Brillouin light scattering studies of planar metallic magnonic crystals. <i>J. Phys. D</i> <b>43</b>, 264003 (2010).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/0022-3727/43/26/264003" data-track-item_id="10.1088/0022-3727/43/26/264003" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F0022-3727%2F43%2F26%2F264003" aria-label="Article reference 92" data-doi="10.1088/0022-3727/43/26/264003">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2010JPhD...43z4003G" aria-label="ADS reference 92">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 92" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20light%20scattering%20studies%20of%20planar%20metallic%20magnonic%20crystals&journal=J.%20Phys.%20D&doi=10.1088%2F0022-3727%2F43%2F26%2F264003&volume=43&publication_year=2010&author=Gubbiotti%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="93."><p class="c-article-references__text" id="ref-CR93">Bailey, M. et al. Viscoelastic properties of biopolymer hydrogels determined by Brillouin spectroscopy: a probe of tissue micromechanics. <i>Sci. Adv.</i> <b>6</b>, eabc1937 (2020).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1126/sciadv.abc1937" data-track-item_id="10.1126/sciadv.abc1937" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1126%2Fsciadv.abc1937" aria-label="Article reference 93" data-doi="10.1126/sciadv.abc1937">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2020SciA....6.1937B" aria-label="ADS reference 93">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 93" href="http://scholar.google.com/scholar_lookup?&title=Viscoelastic%20properties%20of%20biopolymer%20hydrogels%20determined%20by%20Brillouin%20spectroscopy%3A%20a%20probe%20of%20tissue%20micromechanics&journal=Sci.%20Adv.&doi=10.1126%2Fsciadv.abc1937&volume=6&publication_year=2020&author=Bailey%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="94."><p class="c-article-references__text" id="ref-CR94">Graczykowski, B., Vogel, N., Bley, K., Butt, H.-J. & Fytas, G. Multiband hypersound filtering in two-dimensional colloidal crystals: adhesion, resonances, and periodicity. <i>Nano Lett.</i> <b>20</b>, 1883–1889 (2020).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1021/acs.nanolett.9b05101" data-track-item_id="10.1021/acs.nanolett.9b05101" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1021%2Facs.nanolett.9b05101" aria-label="Article reference 94" data-doi="10.1021/acs.nanolett.9b05101">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2020NanoL..20.1883G" aria-label="ADS reference 94">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 94" href="http://scholar.google.com/scholar_lookup?&title=Multiband%20hypersound%20filtering%20in%20two-dimensional%20colloidal%20crystals%3A%20adhesion%2C%20resonances%2C%20and%20periodicity&journal=Nano%20Lett.&doi=10.1021%2Facs.nanolett.9b05101&volume=20&pages=1883-1889&publication_year=2020&author=Graczykowski%2CB&author=Vogel%2CN&author=Bley%2CK&author=Butt%2CH-J&author=Fytas%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="95."><p class="c-article-references__text" id="ref-CR95">Hesami, M. et al. Elastic wave propagation in smooth and wrinkled stratified polymer films. <i>Nanotechnology</i> <b>30</b>, 045709 (2019).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1361-6528/aaee9b" data-track-item_id="10.1088/1361-6528/aaee9b" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1361-6528%2Faaee9b" aria-label="Article reference 95" data-doi="10.1088/1361-6528/aaee9b">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2019Nanot..30d5709H" aria-label="ADS reference 95">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 95" href="http://scholar.google.com/scholar_lookup?&title=Elastic%20wave%20propagation%20in%20smooth%20and%20wrinkled%20stratified%20polymer%20films&journal=Nanotechnology&doi=10.1088%2F1361-6528%2Faaee9b&volume=30&publication_year=2019&author=Hesami%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="96."><p class="c-article-references__text" id="ref-CR96">Graczykowski, B., Gueddida, A., Djafari-Rouhani, B., Butt, H.-J. & Fytas, G. Brillouin light scattering under one-dimensional confinement: symmetry and interference self-canceling. <i>Phys. Rev. B</i> <b>99</b>, 165431 (2019).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevB.99.165431" data-track-item_id="10.1103/PhysRevB.99.165431" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevB.99.165431" aria-label="Article reference 96" data-doi="10.1103/PhysRevB.99.165431">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2019PhRvB..99p5431G" aria-label="ADS reference 96">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 96" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20light%20scattering%20under%20one-dimensional%20confinement%3A%20symmetry%20and%20interference%20self-canceling&journal=Phys.%20Rev.%20B&doi=10.1103%2FPhysRevB.99.165431&volume=99&publication_year=2019&author=Graczykowski%2CB&author=Gueddida%2CA&author=Djafari-Rouhani%2CB&author=Butt%2CH-J&author=Fytas%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="97."><p class="c-article-references__text" id="ref-CR97">Alonso-Redondo, E. et al. Robustness of elastic properties in polymer nanocomposite films examined over the full volume fraction range. <i>Sci Rep.</i> <b>8</b>, 16986 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/s41598-018-35335-1" data-track-item_id="10.1038/s41598-018-35335-1" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fs41598-018-35335-1" aria-label="Article reference 97" data-doi="10.1038/s41598-018-35335-1">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018NatSR...816986A" aria-label="ADS reference 97">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 97" href="http://scholar.google.com/scholar_lookup?&title=Robustness%20of%20elastic%20properties%20in%20polymer%20nanocomposite%20films%20examined%20over%20the%20full%20volume%20fraction%20range&journal=Sci%20Rep.&doi=10.1038%2Fs41598-018-35335-1&volume=8&publication_year=2018&author=Alonso-Redondo%2CE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="98."><p class="c-article-references__text" id="ref-CR98">Sato, A. et al. Cavity-type hypersonic phononic crystals. <i>New J. Phys.</i> <b>14</b>, 113032 (2012).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1367-2630/14/11/113032" data-track-item_id="10.1088/1367-2630/14/11/113032" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1367-2630%2F14%2F11%2F113032" aria-label="Article reference 98" data-doi="10.1088/1367-2630/14/11/113032">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012NJPh...14k3032S" aria-label="ADS reference 98">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 98" href="http://scholar.google.com/scholar_lookup?&title=Cavity-type%20hypersonic%20phononic%20crystals&journal=New%20J.%20Phys.&doi=10.1088%2F1367-2630%2F14%2F11%2F113032&volume=14&publication_year=2012&author=Sato%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="99."><p class="c-article-references__text" id="ref-CR99">Koski, K. J., Akhenblit, P., McKiernan, K. & Yarger, J. L. Non-invasive determination of the complete elastic moduli of spider silks. <i>Nat. Mater.</i> <b>12</b>, 262–267 (2013).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/nmat3549" data-track-item_id="10.1038/nmat3549" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fnmat3549" aria-label="Article reference 99" data-doi="10.1038/nmat3549">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013NatMa..12..262K" aria-label="ADS reference 99">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 99" href="http://scholar.google.com/scholar_lookup?&title=Non-invasive%20determination%20of%20the%20complete%20elastic%20moduli%20of%20spider%20silks&journal=Nat.%20Mater.&doi=10.1038%2Fnmat3549&volume=12&pages=262-267&publication_year=2013&author=Koski%2CKJ&author=Akhenblit%2CP&author=McKiernan%2CK&author=Yarger%2CJL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="100."><p class="c-article-references__text" id="ref-CR100">Scarcelli, G. et al. Noncontact three-dimensional mapping of intracellular hydromechanical properties by Brillouin microscopy. <i>Nat. Methods</i> <b>12</b>, 1132–1134 (2015).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/nmeth.3616" data-track-item_id="10.1038/nmeth.3616" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fnmeth.3616" aria-label="Article reference 100" data-doi="10.1038/nmeth.3616">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 100" href="http://scholar.google.com/scholar_lookup?&title=Noncontact%20three-dimensional%20mapping%20of%20intracellular%20hydromechanical%20properties%20by%20Brillouin%20microscopy&journal=Nat.%20Methods&doi=10.1038%2Fnmeth.3616&volume=12&pages=1132-1134&publication_year=2015&author=Scarcelli%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="101."><p class="c-article-references__text" id="ref-CR101">Wu, P. J. et al. Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials. <i>Nat. Methods</i> <b>15</b>, 561–562 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/s41592-018-0076-1" data-track-item_id="10.1038/s41592-018-0076-1" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fs41592-018-0076-1" aria-label="Article reference 101" data-doi="10.1038/s41592-018-0076-1">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 101" href="http://scholar.google.com/scholar_lookup?&title=Water%20content%2C%20not%20stiffness%2C%20dominates%20Brillouin%20spectroscopy%20measurements%20in%20hydrated%20materials&journal=Nat.%20Methods&doi=10.1038%2Fs41592-018-0076-1&volume=15&pages=561-562&publication_year=2018&author=Wu%2CPJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="102."><p class="c-article-references__text" id="ref-CR102">Prevedel, R., Diz-Muñoz, A., Ruocco, G. & Antonacci, G. Brillouin microscopy: an emerging tool for mechanobiology. <i>Nat. Methods</i> <b>16</b>, 969–977 (2019).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/s41592-019-0543-3" data-track-item_id="10.1038/s41592-019-0543-3" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fs41592-019-0543-3" aria-label="Article reference 102" data-doi="10.1038/s41592-019-0543-3">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 102" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20microscopy%3A%20an%20emerging%20tool%20for%20mechanobiology&journal=Nat.%20Methods&doi=10.1038%2Fs41592-019-0543-3&volume=16&pages=969-977&publication_year=2019&author=Prevedel%2CR&author=Diz-Mu%C3%B1oz%2CA&author=Ruocco%2CG&author=Antonacci%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="103."><p class="c-article-references__text" id="ref-CR103">So, P. Brillouin bioimaging. <i>Nat. Photonics</i> <b>2</b>, 13–14 (2008).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/nphoton.2007.260" data-track-item_id="10.1038/nphoton.2007.260" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fnphoton.2007.260" aria-label="Article reference 103" data-doi="10.1038/nphoton.2007.260">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2008NaPho...2...13S" aria-label="ADS reference 103">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 103" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20bioimaging&journal=Nat.%20Photonics&doi=10.1038%2Fnphoton.2007.260&volume=2&pages=13-14&publication_year=2008&author=So%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="104."><p class="c-article-references__text" id="ref-CR104">Scarcelli, G. & Yun, S. H. Confocal Brillouin microscopy for three-dimensional mechanical imaging. <i>Nat. Photonics</i> <b>2</b>, 39–43 (2008).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/nphoton.2007.250" data-track-item_id="10.1038/nphoton.2007.250" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fnphoton.2007.250" aria-label="Article reference 104" data-doi="10.1038/nphoton.2007.250">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2008NaPho...2...39S" aria-label="ADS reference 104">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 104" href="http://scholar.google.com/scholar_lookup?&title=Confocal%20Brillouin%20microscopy%20for%20three-dimensional%20mechanical%20imaging&journal=Nat.%20Photonics&doi=10.1038%2Fnphoton.2007.250&volume=2&pages=39-43&publication_year=2008&author=Scarcelli%2CG&author=Yun%2CSH"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="105."><p class="c-article-references__text" id="ref-CR105">Pérez-Cota, F. et al. High resolution 3D imaging of living cells with sub-optical wavelength phonons. <i>Sci Rep.</i> <b>6</b>, 39326 (2016).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/srep39326" data-track-item_id="10.1038/srep39326" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fsrep39326" aria-label="Article reference 105" data-doi="10.1038/srep39326">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016NatSR...639326P" aria-label="ADS reference 105">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 105" href="http://scholar.google.com/scholar_lookup?&title=High%20resolution%203D%20imaging%20of%20living%20cells%20with%20sub-optical%20wavelength%20phonons&journal=Sci%20Rep.&doi=10.1038%2Fsrep39326&volume=6&publication_year=2016&author=P%C3%A9rez-Cota%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="106."><p class="c-article-references__text" id="ref-CR106">Wang, P., Lu, L. & Bertoldi, K. Topological phononic crystals with one-way elastic edge waves. <i>Phys. Rev. Lett.</i> <b>115</b>, 104302 (2015).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.115.104302" data-track-item_id="10.1103/PhysRevLett.115.104302" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.115.104302" aria-label="Article reference 106" data-doi="10.1103/PhysRevLett.115.104302">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015PhRvL.115j4302W" aria-label="ADS reference 106">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 106" href="http://scholar.google.com/scholar_lookup?&title=Topological%20phononic%20crystals%20with%20one-way%20elastic%20edge%20waves&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.115.104302&volume=115&publication_year=2015&author=Wang%2CP&author=Lu%2CL&author=Bertoldi%2CK"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="107."><p class="c-article-references__text" id="ref-CR107">Yang, Z. et al. Topological acoustics. <i>Phys. Rev. Lett.</i> <b>114</b>, 114301 (2015).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.114.114301" data-track-item_id="10.1103/PhysRevLett.114.114301" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.114.114301" aria-label="Article reference 107" data-doi="10.1103/PhysRevLett.114.114301">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015PhRvL.114k4301Y" aria-label="ADS reference 107">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 107" href="http://scholar.google.com/scholar_lookup?&title=Topological%20acoustics&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.114.114301&volume=114&publication_year=2015&author=Yang%2CZ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="108."><p class="c-article-references__text" id="ref-CR108">Mousavi, S. H., Khanikaev, A. B. & Wang, Z. Topologically protected elastic waves in phononic metamaterials. <i>Nat. Commun.</i> <b>6</b>, 8682 (2015).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/ncomms9682" data-track-item_id="10.1038/ncomms9682" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fncomms9682" aria-label="Article reference 108" data-doi="10.1038/ncomms9682">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015NatCo...6.8682M" aria-label="ADS reference 108">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 108" href="http://scholar.google.com/scholar_lookup?&title=Topologically%20protected%20elastic%20waves%20in%20phononic%20metamaterials&journal=Nat.%20Commun.&doi=10.1038%2Fncomms9682&volume=6&publication_year=2015&author=Mousavi%2CSH&author=Khanikaev%2CAB&author=Wang%2CZ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="109."><p class="c-article-references__text" id="ref-CR109">He, C. et al. Acoustic topological insulator and robust one-way sound transport. <i>Nat. Phys.</i> <b>12</b>, 1124–1129 (2016).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/nphys3867" data-track-item_id="10.1038/nphys3867" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fnphys3867" aria-label="Article reference 109" data-doi="10.1038/nphys3867">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 109" href="http://scholar.google.com/scholar_lookup?&title=Acoustic%20topological%20insulator%20and%20robust%20one-way%20sound%20transport&journal=Nat.%20Phys.&doi=10.1038%2Fnphys3867&volume=12&pages=1124-1129&publication_year=2016&author=He%2CC"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="110."><p class="c-article-references__text" id="ref-CR110">Zhu, H. et al. Observation of chiral phonons. <i>Science</i> <b>359</b>, 579–582 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1126/science.aar2711" data-track-item_id="10.1126/science.aar2711" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1126%2Fscience.aar2711" aria-label="Article reference 110" data-doi="10.1126/science.aar2711">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018Sci...359..579Z" aria-label="ADS reference 110">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=3728849" aria-label="MathSciNet reference 110">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 110" href="http://scholar.google.com/scholar_lookup?&title=Observation%20of%20chiral%20phonons&journal=Science&doi=10.1126%2Fscience.aar2711&volume=359&pages=579-582&publication_year=2018&author=Zhu%2CH"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="111."><p class="c-article-references__text" id="ref-CR111">Chen, H., Zhang, W., Niu, Q. & Zhang, L. Chiral phonons in two-dimensional materials. <i>2D Mater.</i> <b>6</b>, 012002 (2019).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/2053-1583/aaf292" data-track-item_id="10.1088/2053-1583/aaf292" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F2053-1583%2Faaf292" aria-label="Article reference 111" data-doi="10.1088/2053-1583/aaf292">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 111" href="http://scholar.google.com/scholar_lookup?&title=Chiral%20phonons%20in%20two-dimensional%20materials&journal=2D%20Mater.&doi=10.1088%2F2053-1583%2Faaf292&volume=6&publication_year=2019&author=Chen%2CH&author=Zhang%2CW&author=Niu%2CQ&author=Zhang%2CL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="112."><p class="c-article-references__text" id="ref-CR112">Griffin, A. Brillouin light scattering from crystals in the hydrodynamic region. <i>Rev. Mod. Phys.</i> <b>40</b>, 167–205 (1968).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/RevModPhys.40.167" data-track-item_id="10.1103/RevModPhys.40.167" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FRevModPhys.40.167" aria-label="Article reference 112" data-doi="10.1103/RevModPhys.40.167">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1968RvMP...40..167G" aria-label="ADS reference 112">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 112" href="http://scholar.google.com/scholar_lookup?&title=Brillouin%20light%20scattering%20from%20crystals%20in%20the%20hydrodynamic%20region&journal=Rev.%20Mod.%20Phys.&doi=10.1103%2FRevModPhys.40.167&volume=40&pages=167-205&publication_year=1968&author=Griffin%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="113."><p class="c-article-references__text" id="ref-CR113">Huberman, S. et al. Observation of second sound in graphite at temperatures above 100 K. <i>Science</i> <b>364</b>, 375–379 (2019).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1126/science.aav3548" data-track-item_id="10.1126/science.aav3548" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1126%2Fscience.aav3548" aria-label="Article reference 113" data-doi="10.1126/science.aav3548">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2019Sci...364..375H" aria-label="ADS reference 113">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 113" href="http://scholar.google.com/scholar_lookup?&title=Observation%20of%20second%20sound%20in%20graphite%20at%20temperatures%20above%20100%20K&journal=Science&doi=10.1126%2Fscience.aav3548&volume=364&pages=375-379&publication_year=2019&author=Huberman%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="114."><p class="c-article-references__text" id="ref-CR114">Lee, S. & Li, X. in <i>Nanoscale Energy Transport</i> (ed. Liao, B.) Ch. 1 (IOP, 2020).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="115."><p class="c-article-references__text" id="ref-CR115">Aytan, E. et al. Spin–phonon coupling in antiferromagnetic nickel oxide. <i>Appl. Phys. Lett.</i> <b>111</b>, 252402 (2017).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.5009598" data-track-item_id="10.1063/1.5009598" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.5009598" aria-label="Article reference 115" data-doi="10.1063/1.5009598">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017ApPhL.111y2402A" aria-label="ADS reference 115">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 115" href="http://scholar.google.com/scholar_lookup?&title=Spin%E2%80%93phonon%20coupling%20in%20antiferromagnetic%20nickel%20oxide&journal=Appl.%20Phys.%20Lett.&doi=10.1063%2F1.5009598&volume=111&publication_year=2017&author=Aytan%2CE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="116."><p class="c-article-references__text" id="ref-CR116">An, K. et al. Magnons and phonons optically driven out of local equilibrium in a magnetic insulator. <i>Phys. Rev. Lett.</i> <b>117</b>, 107202 (2016).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.117.107202" data-track-item_id="10.1103/PhysRevLett.117.107202" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.117.107202" aria-label="Article reference 116" data-doi="10.1103/PhysRevLett.117.107202">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016PhRvL.117j7202A" aria-label="ADS reference 116">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 116" href="http://scholar.google.com/scholar_lookup?&title=Magnons%20and%20phonons%20optically%20driven%20out%20of%20local%20equilibrium%20in%20a%20magnetic%20insulator&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.117.107202&volume=117&publication_year=2016&author=An%2CK"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="117."><p class="c-article-references__text" id="ref-CR117">Sandercock, J. R. & Wettling, W. Light scattering from thermal acoustic magnons in yttrium iron garnet. <i>Solid State Commun.</i> <b>13</b>, 1729–1732 (1973).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/0038-1098(73)90276-7" data-track-item_id="10.1016/0038-1098(73)90276-7" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2F0038-1098%2873%2990276-7" aria-label="Article reference 117" data-doi="10.1016/0038-1098(73)90276-7">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1973SSCom..13.1729S" aria-label="ADS reference 117">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 117" href="http://scholar.google.com/scholar_lookup?&title=Light%20scattering%20from%20thermal%20acoustic%20magnons%20in%20yttrium%20iron%20garnet&journal=Solid%20State%20Commun.&doi=10.1016%2F0038-1098%2873%2990276-7&volume=13&pages=1729-1732&publication_year=1973&author=Sandercock%2CJR&author=Wettling%2CW"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="118."><p class="c-article-references__text" id="ref-CR118">Burch, K. S., Mandrus, D. & Park, J. G. Magnetism in two-dimensional van der Waals materials. <i>Nature</i> <b>563</b>, 47–52 (2018).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1038/s41586-018-0631-z" data-track-item_id="10.1038/s41586-018-0631-z" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1038%2Fs41586-018-0631-z" aria-label="Article reference 118" data-doi="10.1038/s41586-018-0631-z">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018Natur.563...47B" aria-label="ADS reference 118">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 118" href="http://scholar.google.com/scholar_lookup?&title=Magnetism%20in%20two-dimensional%20van%20der%20Waals%20materials&journal=Nature&doi=10.1038%2Fs41586-018-0631-z&volume=563&pages=47-52&publication_year=2018&author=Burch%2CKS&author=Mandrus%2CD&author=Park%2CJG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="119."><p class="c-article-references__text" id="ref-CR119">Kargar, F. et al. Phonon and thermal properties of quasi-two-dimensional FePS<sub>3</sub> and MnPS<sub>3</sub> antiferromagnetic semiconductors. <i>ACS Nano</i> <b>14</b>, 2424–2435 (2020).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1021/acsnano.9b09839" data-track-item_id="10.1021/acsnano.9b09839" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1021%2Facsnano.9b09839" aria-label="Article reference 119" data-doi="10.1021/acsnano.9b09839">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 119" href="http://scholar.google.com/scholar_lookup?&title=Phonon%20and%20thermal%20properties%20of%20quasi-two-dimensional%20FePS3%20and%20MnPS3%20antiferromagnetic%20semiconductors&journal=ACS%20Nano&doi=10.1021%2Facsnano.9b09839&volume=14&pages=2424-2435&publication_year=2020&author=Kargar%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="120."><p class="c-article-references__text" id="ref-CR120">Balandin, A. A. et al. Superior thermal conductivity of single-layer graphene. <i>Nano Lett.</i> <b>8</b>, 902–907 (2008).</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1021/nl0731872" data-track-item_id="10.1021/nl0731872" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1021%2Fnl0731872" aria-label="Article reference 120" data-doi="10.1021/nl0731872">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2008NanoL...8..902B" aria-label="ADS reference 120">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 120" href="http://scholar.google.com/scholar_lookup?&title=Superior%20thermal%20conductivity%20of%20single-layer%20graphene&journal=Nano%20Lett.&doi=10.1021%2Fnl0731872&volume=8&pages=902-907&publication_year=2008&author=Balandin%2CAA"> Google Scholar</a> </p></li></ol><p class="c-article-references__download u-hide-print"><a data-track="click" data-track-action="download citation references" data-track-label="link" rel="nofollow" href="https://citation-needed.springer.com/v2/references/10.1038/s41566-021-00836-5?format=refman&flavour=references">Download references<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-download-medium"></use></svg></a></p></div></div></div></section></div><section data-title="Acknowledgements"><div class="c-article-section" id="Ack1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Ack1">Acknowledgements</h2><div class="c-article-section__content" id="Ack1-content"><p>We acknowledge the support of the National Science Foundation (NSF) via a Major Research Instrumentation (MRI) project DMR 2019056 entitled ‘Development of a Cryogenic Integrated Micro-Raman-Brillouin-Mandelstam Spectrometer’. A.A.B. also acknowledges the support of the Designing Materials to Revolutionize and Engineer our Future (DMREF) program via a project DMR-1921958 entitled ‘Collaborative research: data driven discovery of synthesis pathways and distinguishing electronic phenomena of 1D van der Waals bonded solids’, and the support of the US Department of Energy (DOE) via a project DE-SC0021020 entitled ‘Physical mechanisms and electric-bias control of phase transitions in quasi-2D charge-density-wave quantum materials’. We thank M. Kargar and Z. Barani for their help with the preparation of schematics in Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41566-021-00836-5#Fig1">1e</a> and <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41566-021-00836-5#Fig3">3a</a>.</p></div></div></section><section aria-labelledby="author-information" data-title="Author information"><div class="c-article-section" id="author-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="author-information">Author information</h2><div class="c-article-section__content" id="author-information-content"><h3 class="c-article__sub-heading" id="affiliations">Authors and Affiliations</h3><ol class="c-article-author-affiliation__list"><li id="Aff1"><p class="c-article-author-affiliation__address">Nano-Device Laboratory (NDL) and Phonon Optimized Engineered Materials (POEM) Center, Department of Electrical and Computer Engineering, University of California, Riverside, Riverside, CA, USA</p><p class="c-article-author-affiliation__authors-list">Fariborz Kargar & Alexander A. Balandin</p></li></ol><div class="u-js-hide u-hide-print" data-test="author-info"><span class="c-article__sub-heading">Authors</span><ol class="c-article-authors-search u-list-reset"><li id="auth-Fariborz-Kargar-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">Fariborz Kargar</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Fariborz%20Kargar" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Fariborz%20Kargar" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Fariborz%20Kargar%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Alexander_A_-Balandin-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">Alexander A. Balandin</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Alexander%20A.%20Balandin" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Alexander%20A.%20Balandin" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Alexander%20A.%20Balandin%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li></ol></div><h3 class="c-article__sub-heading" id="corresponding-author">Corresponding author</h3><p id="corresponding-author-list">Correspondence to <a id="corresp-c1" href="mailto:fkargar@ece.ucr.edu">Fariborz Kargar</a>.</p></div></div></section><section data-title="Ethics declarations"><div class="c-article-section" id="ethics-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="ethics">Ethics declarations</h2><div class="c-article-section__content" id="ethics-content"> <h3 class="c-article__sub-heading" id="FPar1">Competing interests</h3> <p>The authors declare no competing interests.</p> </div></div></section><section data-title="Additional information"><div class="c-article-section" id="additional-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="additional-information">Additional information</h2><div class="c-article-section__content" id="additional-information-content"><p><b>Peer review information</b> <i>Nature Photonics</i> thanks Sergej Demokritov, Benjamin Eggleton and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.</p><p><b>Publisher’s note</b> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></div></div></section><section data-title="Rights and permissions"><div class="c-article-section" id="rightslink-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="rightslink">Rights and permissions</h2><div class="c-article-section__content" id="rightslink-content"><p class="c-article-rights"><a data-track="click" data-track-action="view rights and permissions" data-track-label="link" href="https://s100.copyright.com/AppDispatchServlet?title=Advances%20in%20Brillouin%E2%80%93Mandelstam%20light-scattering%20spectroscopy&author=Fariborz%20Kargar%20et%20al&contentID=10.1038%2Fs41566-021-00836-5&copyright=Springer%20Nature%20Limited&publication=1749-4885&publicationDate=2021-07-22&publisherName=SpringerNature&orderBeanReset=true">Reprints and permissions</a></p></div></div></section><section aria-labelledby="article-info" data-title="About this article"><div class="c-article-section" id="article-info-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="article-info">About this article</h2><div class="c-article-section__content" id="article-info-content"><div class="c-bibliographic-information"><div class="u-hide-print c-bibliographic-information__column c-bibliographic-information__column--border"><a data-crossmark="10.1038/s41566-021-00836-5" target="_blank" rel="noopener" href="https://crossmark.crossref.org/dialog/?doi=10.1038/s41566-021-00836-5" data-track="click" data-track-action="Click Crossmark" data-track-label="link" data-test="crossmark"><img loading="lazy" width="57" height="81" alt="Check for updates. Verify currency and authenticity via CrossMark" src="data:image/svg+xml;base64,<svg height="81" width="57" xmlns="http://www.w3.org/2000/svg"><g fill="none" fill-rule="evenodd"><path d="m17.35 35.45 21.3-14.2v-17.03h-21.3" fill="#989898"/><path d="m38.65 35.45-21.3-14.2v-17.03h21.3" fill="#747474"/><path d="m28 .5c-12.98 0-23.5 10.52-23.5 23.5s10.52 23.5 23.5 23.5 23.5-10.52 23.5-23.5c0-6.23-2.48-12.21-6.88-16.62-4.41-4.4-10.39-6.88-16.62-6.88zm0 41.25c-9.8 0-17.75-7.95-17.75-17.75s7.95-17.75 17.75-17.75 17.75 7.95 17.75 17.75c0 4.71-1.87 9.22-5.2 12.55s-7.84 5.2-12.55 5.2z" fill="#535353"/><path d="m41 36c-5.81 6.23-15.23 7.45-22.43 2.9-7.21-4.55-10.16-13.57-7.03-21.5l-4.92-3.11c-4.95 10.7-1.19 23.42 8.78 29.71 9.97 6.3 23.07 4.22 30.6-4.86z" fill="#9c9c9c"/><path d="m.2 58.45c0-.75.11-1.42.33-2.01s.52-1.09.91-1.5c.38-.41.83-.73 1.34-.94.51-.22 1.06-.32 1.65-.32.56 0 1.06.11 1.51.35.44.23.81.5 1.1.81l-.91 1.01c-.24-.24-.49-.42-.75-.56-.27-.13-.58-.2-.93-.2-.39 0-.73.08-1.05.23-.31.16-.58.37-.81.66-.23.28-.41.63-.53 1.04-.13.41-.19.88-.19 1.39 0 1.04.23 1.86.68 2.46.45.59 1.06.88 1.84.88.41 0 .77-.07 1.07-.23s.59-.39.85-.68l.91 1c-.38.43-.8.76-1.28.99-.47.22-1 .34-1.58.34-.59 0-1.13-.1-1.64-.31-.5-.2-.94-.51-1.31-.91-.38-.4-.67-.9-.88-1.48-.22-.59-.33-1.26-.33-2.02zm8.4-5.33h1.61v2.54l-.05 1.33c.29-.27.61-.51.96-.72s.76-.31 1.24-.31c.73 0 1.27.23 1.61.71.33.47.5 1.14.5 2.02v4.31h-1.61v-4.1c0-.57-.08-.97-.25-1.21-.17-.23-.45-.35-.83-.35-.3 0-.56.08-.79.22-.23.15-.49.36-.78.64v4.8h-1.61zm7.37 6.45c0-.56.09-1.06.26-1.51.18-.45.42-.83.71-1.14.29-.3.63-.54 1.01-.71.39-.17.78-.25 1.18-.25.47 0 .88.08 1.23.24.36.16.65.38.89.67s.42.63.54 1.03c.12.41.18.84.18 1.32 0 .32-.02.57-.07.76h-4.36c.07.62.29 1.1.65 1.44.36.33.82.5 1.38.5.29 0 .57-.04.83-.13s.51-.21.76-.37l.55 1.01c-.33.21-.69.39-1.09.53-.41.14-.83.21-1.26.21-.48 0-.92-.08-1.34-.25-.41-.16-.76-.4-1.07-.7-.31-.31-.55-.69-.72-1.13-.18-.44-.26-.95-.26-1.52zm4.6-.62c0-.55-.11-.98-.34-1.28-.23-.31-.58-.47-1.06-.47-.41 0-.77.15-1.07.45-.31.29-.5.73-.58 1.3zm2.5.62c0-.57.09-1.08.28-1.53.18-.44.43-.82.75-1.13s.69-.54 1.1-.71c.42-.16.85-.24 1.31-.24.45 0 .84.08 1.17.23s.61.34.85.57l-.77 1.02c-.19-.16-.38-.28-.56-.37-.19-.09-.39-.14-.61-.14-.56 0-1.01.21-1.35.63-.35.41-.52.97-.52 1.67 0 .69.17 1.24.51 1.66.34.41.78.62 1.32.62.28 0 .54-.06.78-.17.24-.12.45-.26.64-.42l.67 1.03c-.33.29-.69.51-1.08.65-.39.15-.78.23-1.18.23-.46 0-.9-.08-1.31-.24-.4-.16-.75-.39-1.05-.7s-.53-.69-.7-1.13c-.17-.45-.25-.96-.25-1.53zm6.91-6.45h1.58v6.17h.05l2.54-3.16h1.77l-2.35 2.8 2.59 4.07h-1.75l-1.77-2.98-1.08 1.23v1.75h-1.58zm13.69 1.27c-.25-.11-.5-.17-.75-.17-.58 0-.87.39-.87 1.16v.75h1.34v1.27h-1.34v5.6h-1.61v-5.6h-.92v-1.2l.92-.07v-.72c0-.35.04-.68.13-.98.08-.31.21-.57.4-.79s.42-.39.71-.51c.28-.12.63-.18 1.04-.18.24 0 .48.02.69.07.22.05.41.1.57.17zm.48 5.18c0-.57.09-1.08.27-1.53.17-.44.41-.82.72-1.13.3-.31.65-.54 1.04-.71.39-.16.8-.24 1.23-.24s.84.08 1.24.24c.4.17.74.4 1.04.71s.54.69.72 1.13c.19.45.28.96.28 1.53s-.09 1.08-.28 1.53c-.18.44-.42.82-.72 1.13s-.64.54-1.04.7-.81.24-1.24.24-.84-.08-1.23-.24-.74-.39-1.04-.7c-.31-.31-.55-.69-.72-1.13-.18-.45-.27-.96-.27-1.53zm1.65 0c0 .69.14 1.24.43 1.66.28.41.68.62 1.18.62.51 0 .9-.21 1.19-.62.29-.42.44-.97.44-1.66 0-.7-.15-1.26-.44-1.67-.29-.42-.68-.63-1.19-.63-.5 0-.9.21-1.18.63-.29.41-.43.97-.43 1.67zm6.48-3.44h1.33l.12 1.21h.05c.24-.44.54-.79.88-1.02.35-.24.7-.36 1.07-.36.32 0 .59.05.78.14l-.28 1.4-.33-.09c-.11-.01-.23-.02-.38-.02-.27 0-.56.1-.86.31s-.55.58-.77 1.1v4.2h-1.61zm-47.87 15h1.61v4.1c0 .57.08.97.25 1.2.17.24.44.35.81.35.3 0 .57-.07.8-.22.22-.15.47-.39.73-.73v-4.7h1.61v6.87h-1.32l-.12-1.01h-.04c-.3.36-.63.64-.98.86-.35.21-.76.32-1.24.32-.73 0-1.27-.24-1.61-.71-.33-.47-.5-1.14-.5-2.02zm9.46 7.43v2.16h-1.61v-9.59h1.33l.12.72h.05c.29-.24.61-.45.97-.63.35-.17.72-.26 1.1-.26.43 0 .81.08 1.15.24.33.17.61.4.84.71.24.31.41.68.53 1.11.13.42.19.91.19 1.44 0 .59-.09 1.11-.25 1.57-.16.47-.38.85-.65 1.16-.27.32-.58.56-.94.73-.35.16-.72.25-1.1.25-.3 0-.6-.07-.9-.2s-.59-.31-.87-.56zm0-2.3c.26.22.5.37.73.45.24.09.46.13.66.13.46 0 .84-.2 1.15-.6.31-.39.46-.98.46-1.77 0-.69-.12-1.22-.35-1.61-.23-.38-.61-.57-1.13-.57-.49 0-.99.26-1.52.77zm5.87-1.69c0-.56.08-1.06.25-1.51.16-.45.37-.83.65-1.14.27-.3.58-.54.93-.71s.71-.25 1.08-.25c.39 0 .73.07 1 .2.27.14.54.32.81.55l-.06-1.1v-2.49h1.61v9.88h-1.33l-.11-.74h-.06c-.25.25-.54.46-.88.64-.33.18-.69.27-1.06.27-.87 0-1.56-.32-2.07-.95s-.76-1.51-.76-2.65zm1.67-.01c0 .74.13 1.31.4 1.7.26.38.65.58 1.15.58.51 0 .99-.26 1.44-.77v-3.21c-.24-.21-.48-.36-.7-.45-.23-.08-.46-.12-.7-.12-.45 0-.82.19-1.13.59-.31.39-.46.95-.46 1.68zm6.35 1.59c0-.73.32-1.3.97-1.71.64-.4 1.67-.68 3.08-.84 0-.17-.02-.34-.07-.51-.05-.16-.12-.3-.22-.43s-.22-.22-.38-.3c-.15-.06-.34-.1-.58-.1-.34 0-.68.07-1 .2s-.63.29-.93.47l-.59-1.08c.39-.24.81-.45 1.28-.63.47-.17.99-.26 1.54-.26.86 0 1.51.25 1.93.76s.63 1.25.63 2.21v4.07h-1.32l-.12-.76h-.05c-.3.27-.63.48-.98.66s-.73.27-1.14.27c-.61 0-1.1-.19-1.48-.56-.38-.36-.57-.85-.57-1.46zm1.57-.12c0 .3.09.53.27.67.19.14.42.21.71.21.28 0 .54-.07.77-.2s.48-.31.73-.56v-1.54c-.47.06-.86.13-1.18.23-.31.09-.57.19-.76.31s-.33.25-.41.4c-.09.15-.13.31-.13.48zm6.29-3.63h-.98v-1.2l1.06-.07.2-1.88h1.34v1.88h1.75v1.27h-1.75v3.28c0 .8.32 1.2.97 1.2.12 0 .24-.01.37-.04.12-.03.24-.07.34-.11l.28 1.19c-.19.06-.4.12-.64.17-.23.05-.49.08-.76.08-.4 0-.74-.06-1.02-.18-.27-.13-.49-.3-.67-.52-.17-.21-.3-.48-.37-.78-.08-.3-.12-.64-.12-1.01zm4.36 2.17c0-.56.09-1.06.27-1.51s.41-.83.71-1.14c.29-.3.63-.54 1.01-.71.39-.17.78-.25 1.18-.25.47 0 .88.08 1.23.24.36.16.65.38.89.67s.42.63.54 1.03c.12.41.18.84.18 1.32 0 .32-.02.57-.07.76h-4.37c.08.62.29 1.1.65 1.44.36.33.82.5 1.38.5.3 0 .58-.04.84-.13.25-.09.51-.21.76-.37l.54 1.01c-.32.21-.69.39-1.09.53s-.82.21-1.26.21c-.47 0-.92-.08-1.33-.25-.41-.16-.77-.4-1.08-.7-.3-.31-.54-.69-.72-1.13-.17-.44-.26-.95-.26-1.52zm4.61-.62c0-.55-.11-.98-.34-1.28-.23-.31-.58-.47-1.06-.47-.41 0-.77.15-1.08.45-.31.29-.5.73-.57 1.3zm3.01 2.23c.31.24.61.43.92.57.3.13.63.2.98.2.38 0 .65-.08.83-.23s.27-.35.27-.6c0-.14-.05-.26-.13-.37-.08-.1-.2-.2-.34-.28-.14-.09-.29-.16-.47-.23l-.53-.22c-.23-.09-.46-.18-.69-.3-.23-.11-.44-.24-.62-.4s-.33-.35-.45-.55c-.12-.21-.18-.46-.18-.75 0-.61.23-1.1.68-1.49.44-.38 1.06-.57 1.83-.57.48 0 .91.08 1.29.25s.71.36.99.57l-.74.98c-.24-.17-.49-.32-.73-.42-.25-.11-.51-.16-.78-.16-.35 0-.6.07-.76.21-.17.15-.25.33-.25.54 0 .14.04.26.12.36s.18.18.31.26c.14.07.29.14.46.21l.54.19c.23.09.47.18.7.29s.44.24.64.4c.19.16.34.35.46.58.11.23.17.5.17.82 0 .3-.06.58-.17.83-.12.26-.29.48-.51.68-.23.19-.51.34-.84.45-.34.11-.72.17-1.15.17-.48 0-.95-.09-1.41-.27-.46-.19-.86-.41-1.2-.68z" fill="#535353"/></g></svg>"></a></div><div class="c-bibliographic-information__column"><h3 class="c-article__sub-heading" id="citeas">Cite this article</h3><p class="c-bibliographic-information__citation">Kargar, F., Balandin, A.A. Advances in Brillouin–Mandelstam light-scattering spectroscopy. <i>Nat. Photon.</i> <b>15</b>, 720–731 (2021). https://doi.org/10.1038/s41566-021-00836-5</p><p class="c-bibliographic-information__download-citation u-hide-print"><a data-test="citation-link" data-track="click" data-track-action="download article citation" data-track-label="link" data-track-external="" rel="nofollow" href="https://citation-needed.springer.com/v2/references/10.1038/s41566-021-00836-5?format=refman&flavour=citation">Download citation<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-download-medium"></use></svg></a></p><ul class="c-bibliographic-information__list" data-test="publication-history"><li class="c-bibliographic-information__list-item"><p>Received<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2020-11-11">11 November 2020</time></span></p></li><li class="c-bibliographic-information__list-item"><p>Accepted<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2021-05-25">25 May 2021</time></span></p></li><li class="c-bibliographic-information__list-item"><p>Published<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2021-07-22">22 July 2021</time></span></p></li><li class="c-bibliographic-information__list-item"><p>Issue Date<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2021-10">October 2021</time></span></p></li><li class="c-bibliographic-information__list-item c-bibliographic-information__list-item--full-width"><p><abbr title="Digital Object Identifier">DOI</abbr><span class="u-hide">: </span><span class="c-bibliographic-information__value">https://doi.org/10.1038/s41566-021-00836-5</span></p></li></ul><div data-component="share-box"><div class="c-article-share-box u-display-none" hidden=""><h3 class="c-article__sub-heading">Share this article</h3><p class="c-article-share-box__description">Anyone you share the following link with will be able to read this content:</p><button class="js-get-share-url c-article-share-box__button" type="button" id="get-share-url" data-track="click" data-track-label="button" data-track-external="" data-track-action="get shareable link">Get shareable link</button><div class="js-no-share-url-container u-display-none" hidden=""><p class="js-c-article-share-box__no-sharelink-info c-article-share-box__no-sharelink-info">Sorry, a shareable link is not currently available for this article.</p></div><div class="js-share-url-container u-display-none" hidden=""><p class="js-share-url c-article-share-box__only-read-input" id="share-url" data-track="click" data-track-label="button" data-track-action="select share url"></p><button class="js-copy-share-url c-article-share-box__button--link-like" type="button" id="copy-share-url" data-track="click" data-track-label="button" data-track-action="copy share url" data-track-external="">Copy to clipboard</button></div><p class="js-c-article-share-box__additional-info c-article-share-box__additional-info"> Provided by the Springer Nature SharedIt content-sharing initiative </p></div></div><div data-component="article-info-list"></div></div></div></div></div></section> </div> <section> <div class="c-article-section js-article-section" id="further-reading-section" data-test="further-reading-section"> <h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="further-reading">This article is cited by</h2> <div class="c-article-section__content js-collapsible-section" id="further-reading-content"> <ul class="c-article-further-reading__list" id="further-reading-list"> <li class="c-article-further-reading__item js-ref-item"> <h3 class="c-article-further-reading__title" data-test="article-title"> <a class="print-link" data-track="click" data-track-action="view further reading article" data-track-label="link:Birefringence-induced phase delay enables Brillouin mechanical imaging in turbid media" href="https://doi.org/10.1038/s41467-024-49419-2"> Birefringence-induced phase delay enables Brillouin mechanical imaging in turbid media </a> </h3> <ul data-test="author-list" class="c-author-list c-author-list--compact c-author-list--truncated u-sans-serif u-mb-4 u-mt-auto"> <li>Giuseppe Antonacci</li><li>Renzo Vanna</li><li>Giulio Cerullo</li> </ul> <p class="c-article-further-reading__journal-title"><i>Nature Communications</i> (2024)</p> </li> <li class="c-article-further-reading__item js-ref-item"> <h3 class="c-article-further-reading__title" data-test="article-title"> <a class="print-link" data-track="click" data-track-action="view further reading article" data-track-label="link:Cryogenic characteristics of graphene composites—evolution from thermal conductors to thermal insulators" href="https://doi.org/10.1038/s41467-023-38508-3"> Cryogenic characteristics of graphene composites—evolution from thermal conductors to thermal insulators </a> </h3> <ul data-test="author-list" class="c-author-list c-author-list--compact c-author-list--truncated u-sans-serif u-mb-4 u-mt-auto"> <li>Zahra Ebrahim Nataj</li><li>Youming Xu</li><li>Alexander A. Balandin</li> </ul> <p class="c-article-further-reading__journal-title"><i>Nature Communications</i> (2023)</p> </li> <li class="c-article-further-reading__item js-ref-item"> <h3 class="c-article-further-reading__title" data-test="article-title"> <a class="print-link" data-track="click" data-track-action="view further reading article" data-track-label="link:Observing high-k magnons with Mie-resonance-enhanced Brillouin light scattering" href="https://doi.org/10.1038/s42005-023-01214-z"> Observing high-k magnons with Mie-resonance-enhanced Brillouin light scattering </a> </h3> <ul data-test="author-list" class="c-author-list c-author-list--compact c-author-list--truncated u-sans-serif u-mb-4 u-mt-auto"> <li>Ondřej Wojewoda</li><li>Filip Ligmajer</li><li>Michal Urbánek</li> </ul> <p class="c-article-further-reading__journal-title"><i>Communications Physics</i> (2023)</p> </li> <li class="c-article-further-reading__item js-ref-item"> <h3 class="c-article-further-reading__title" data-test="article-title"> <a class="print-link" data-track="click" data-track-action="view further reading article" data-track-label="link:Engineering nanoscale hypersonic phonon transport" href="https://doi.org/10.1038/s41565-022-01178-1"> Engineering nanoscale hypersonic phonon transport </a> </h3> <ul data-test="author-list" class="c-author-list c-author-list--compact c-author-list--truncated u-sans-serif u-mb-4 u-mt-auto"> <li>O. Florez</li><li>G. Arregui</li><li>P. D. García</li> </ul> <p class="c-article-further-reading__journal-title"><i>Nature Nanotechnology</i> (2022)</p> </li> </ul> </div> </div> </section> </div> </article> </main> <aside class="c-article-extras u-hide-print" aria-label="Article navigation" data-component-reading-companion data-container-type="reading-companion" data-track-component="reading companion"> <div class="js-context-bar-sticky-point-desktop" data-track-context="reading companion"> <noscript> <div class="c-nature-box c-nature-box--side " data-component="entitlement-box"> <div class="js-access-button"> <a href="https://wayf.springernature.com?redirect_uri=https%3A%2F%2Fwww.nature.com%2Farticles%2Fs41566-021-00836-5" class="c-article__button" data-test="ra21"> <svg class="u-icon" width="18" height="18" aria-hidden="true" focusable="false"><use href="#icon-institution"></use></svg> <span class="c-article__button-text">Access through your institution</span> </a> </div> <div class="js-buy-button"> <a href="#access-options" class="c-article__button c-article__button--inverted" data-test="ra21"> <span>Buy or subscribe</span> </a> </div> </div> </noscript> <div class="c-nature-box__wrapper c-nature-box__wrapper--placeholder"> <div class="c-nature-box c-nature-box--side u-display-none u-hide-print" aria-hidden="true" data-component="entitlement-box" id=entitlement-box-right-column > <p class="c-nature-box__text js-text u-display-none" aria-hidden="true"></p> <div class="js-access-button u-display-none"> <a href="https://wayf.springernature.com?redirect_uri=https%3A%2F%2Fwww.nature.com%2Farticles%2Fs41566-021-00836-5" class="c-article__button" aria-hidden="true" data-test="ra21" data-track="click_institution_login" data-track-context="reading companion" data-track-action="institution access" data-track-label="button"> <svg class="u-icon" width="18" height="18" aria-hidden="true" focusable="false"><use xlink:href="#icon-institution"></use></svg> <span class="c-article__button-text">Access through your institution</span> </a> </div> <div class="js-change-institution-button u-display-none"> <a href="https://wayf.springernature.com?redirect_uri=https%3A%2F%2Fwww.nature.com%2Farticles%2Fs41566-021-00836-5" class="c-article__button c-article__button--inverted" aria-hidden="true" data-test="ra21" data-track="click" data-track-action="change institution" data-track-label="button"> <span class="c-article__button-text">Change institution</span> </a> </div> <div class="js-buy-button u-display-none"> <a href="#access-options" class="c-article__button c-article__button--inverted" aria-hidden="true" data-test="ra21" data-track="click" data-track-action="buy or subscribe" data-track-label="button"> <span>Buy or subscribe</span> </a> </div> </div> </div> </div> <div class="c-reading-companion"> <div class="c-reading-companion__sticky" data-component="reading-companion-sticky" data-test="reading-companion-sticky"> <div class="c-reading-companion__panel c-reading-companion__sections c-reading-companion__panel--active" id="tabpanel-sections"> <div class="u-lazy-ad-wrapper u-mt-16 u-hide" data-component-mpu> <div class="c-ad c-ad--300x250"> <div class="c-ad__inner"> <p class="c-ad__label">Advertisement</p> <div id="div-gpt-ad-right-2" class="div-gpt-ad advert medium-rectangle js-ad text-center hide-print grade-c-hide" data-ad-type="right" data-test="right-ad" data-pa11y-ignore data-gpt data-gpt-unitpath="/285/photonics.nature.com/article" data-gpt-sizes="300x250" data-gpt-targeting="type=article;pos=right;artid=s41566-021-00836-5;doi=10.1038/s41566-021-00836-5;techmeta=122,132,133,140;subjmeta=1107,1821,527,624,639,766,930;kwrd=Raman+spectroscopy"> <noscript> <a href="//pubads.g.doubleclick.net/gampad/jump?iu=/285/photonics.nature.com/article&sz=300x250&c=-1470801204&t=pos%3Dright%26type%3Darticle%26artid%3Ds41566-021-00836-5%26doi%3D10.1038/s41566-021-00836-5%26techmeta%3D122,132,133,140%26subjmeta%3D1107,1821,527,624,639,766,930%26kwrd%3DRaman+spectroscopy"> <img data-test="gpt-advert-fallback-img" src="//pubads.g.doubleclick.net/gampad/ad?iu=/285/photonics.nature.com/article&sz=300x250&c=-1470801204&t=pos%3Dright%26type%3Darticle%26artid%3Ds41566-021-00836-5%26doi%3D10.1038/s41566-021-00836-5%26techmeta%3D122,132,133,140%26subjmeta%3D1107,1821,527,624,639,766,930%26kwrd%3DRaman+spectroscopy" alt="Advertisement" width="300" height="250"></a> </noscript> </div> </div> </div> </div> </div> <div class="c-reading-companion__panel c-reading-companion__figures c-reading-companion__panel--full-width" id="tabpanel-figures"></div> <div class="c-reading-companion__panel c-reading-companion__references c-reading-companion__panel--full-width" id="tabpanel-references"></div> </div> </div> </aside> </div> <nav class="c-header__dropdown" aria-labelledby="Explore-content" data-test="Explore-content" id="explore" data-track-component="nature-150-split-header"> <div class="c-header__container"> <h2 id="Explore-content" class="c-header__heading c-header__heading--js-hide">Explore content</h2> <ul class="c-header__list c-header__list--js-stack"> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/research-articles" data-track="click" data-track-action="research articles" data-track-label="link" data-test="explore-nav-item"> Research articles </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/reviews-and-analysis" data-track="click" data-track-action="reviews & analysis" data-track-label="link" data-test="explore-nav-item"> Reviews & Analysis </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/news-and-comment" data-track="click" data-track-action="news & comment" data-track-label="link" data-test="explore-nav-item"> News & Comment </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/current-issue" data-track="click" data-track-action="current issue" data-track-label="link" data-test="explore-nav-item"> Current issue </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/collections" data-track="click" data-track-action="collections" data-track-label="link" data-test="explore-nav-item"> Collections </a> </li> </ul> <ul class="c-header__list c-header__list--js-stack"> <li class="c-header__item"> <a class="c-header__link" href="https://twitter.com/NaturePhotonics" data-track="click" data-track-action="twitter" data-track-label="link">Follow us on Twitter </a> </li> <li class="c-header__item c-header__item--hide-lg"> <a data-test="subscribe-button" class="c-header__link" href="https://www.nature.com/nphoton/subscribe" data-track="click" data-track-action="subscribe" data-track-label="link"> <span>Subscribe</span> </a> </li> <li class="c-header__item c-header__item--hide-lg"> <a class="c-header__link" href="https://www.nature.com/my-account/alerts/subscribe-journal?list-id=151" rel="nofollow" data-track="click" data-track-action="Sign up for alerts" data-track-external data-track-label="link (mobile dropdown)">Sign up for alerts<svg role="img" aria-hidden="true" focusable="false" height="18" viewBox="0 0 18 18" width="18" xmlns="http://www.w3.org/2000/svg"><path d="m4 10h2.5c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-3.08578644l-1.12132034 1.1213203c-.18753638.1875364-.29289322.4418903-.29289322.7071068v.1715729h14v-.1715729c0-.2652165-.1053568-.5195704-.2928932-.7071068l-1.7071068-1.7071067v-3.4142136c0-2.76142375-2.2385763-5-5-5-2.76142375 0-5 2.23857625-5 5zm3 4c0 1.1045695.8954305 2 2 2s2-.8954305 2-2zm-5 0c-.55228475 0-1-.4477153-1-1v-.1715729c0-.530433.21071368-1.0391408.58578644-1.4142135l1.41421356-1.4142136v-3c0-3.3137085 2.6862915-6 6-6s6 2.6862915 6 6v3l1.4142136 1.4142136c.3750727.3750727.5857864.8837805.5857864 1.4142135v.1715729c0 .5522847-.4477153 1-1 1h-4c0 1.6568542-1.3431458 3-3 3-1.65685425 0-3-1.3431458-3-3z" fill="#fff"/></svg> </a> </li> <li class="c-header__item c-header__item--hide-lg"> <a class="c-header__link" href="https://www.nature.com/nphoton.rss" data-track="click" data-track-action="rss feed" data-track-label="link"> <span>RSS feed</span> </a> </li> </ul> </div> </nav> <nav class="c-header__dropdown" aria-labelledby="About-the-journal" id="about-the-journal" data-test="about-the-journal" data-track-component="nature-150-split-header"> <div class="c-header__container"> <h2 id="About-the-journal" class="c-header__heading c-header__heading--js-hide">About the journal</h2> <ul class="c-header__list c-header__list--js-stack"> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/aims" data-track="click" data-track-action="aims & scope" data-track-label="link"> Aims & Scope </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/journal-information" data-track="click" data-track-action="journal information" data-track-label="link"> Journal Information </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/journal-impact" data-track="click" data-track-action="journal metrics" data-track-label="link"> Journal Metrics </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/editors" data-track="click" data-track-action="about the editors" data-track-label="link"> About the Editors </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/research-cross-journal-editorial-team" data-track="click" data-track-action="research cross-journal editorial team" data-track-label="link"> Research Cross-Journal Editorial Team </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/reviews-cross-journal-editorial-team" data-track="click" data-track-action="reviews cross-journal editorial team" data-track-label="link"> Reviews Cross-Journal Editorial Team </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/our-publishing-models" data-track="click" data-track-action="our publishing models" data-track-label="link"> Our publishing models </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/editorial-values-statement" data-track="click" data-track-action="editorial values statement" data-track-label="link"> Editorial Values Statement </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/editorial-policies" data-track="click" data-track-action="editorial policies" data-track-label="link"> Editorial Policies </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/content" data-track="click" data-track-action="content types" data-track-label="link"> Content Types </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/web-feeds" data-track="click" data-track-action="web feeds" data-track-label="link"> Web Feeds </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/contact" data-track="click" data-track-action="contact" data-track-label="link"> Contact </a> </li> </ul> </div> </nav> <nav class="c-header__dropdown" aria-labelledby="Publish-with-us-label" id="publish-with-us" data-test="publish-with-us" data-track-component="nature-150-split-header"> <div class="c-header__container"> <h2 id="Publish-with-us-label" class="c-header__heading c-header__heading--js-hide">Publish with us</h2> <ul class="c-header__list c-header__list--js-stack"> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/submission-guidelines" data-track="click" data-track-action="submission guidelines" data-track-label="link"> Submission Guidelines </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nphoton/for-reviewers" data-track="click" data-track-action="for reviewers" data-track-label="link"> For Reviewers </a> </li> <li class="c-header__item"> <a class="c-header__link" data-test="nature-author-services" data-track="nav_language_services" data-track-context="header publish with us dropdown menu" data-track-action="manuscript author services" data-track-label="link manuscript author services" href="https://authorservices.springernature.com/go/sn/?utm_source=For+Authors&utm_medium=Website_Nature&utm_campaign=Platform+Experimentation+2022&utm_id=PE2022"> Language editing services </a> </li> <li class="c-header__item c-header__item--keyline"> <a class="c-header__link" href="https://mts-nphot.nature.com/cgi-bin/main.plex" data-track="click_submit_manuscript" data-track-context="submit link in Nature header dropdown menu" data-track-action="submit manuscript" data-track-label="link (publish with us dropdown menu)" data-track-external>Submit manuscript<svg role="img" aria-hidden="true" focusable="false" height="18" viewBox="0 0 18 18" width="18" xmlns="http://www.w3.org/2000/svg"><path d="m15 0c1.1045695 0 2 .8954305 2 2v5.5c0 .27614237-.2238576.5-.5.5s-.5-.22385763-.5-.5v-5.5c0-.51283584-.3860402-.93550716-.8833789-.99327227l-.1166211-.00672773h-9v3c0 1.1045695-.8954305 2-2 2h-3v10c0 .5128358.38604019.9355072.88337887.9932723l.11662113.0067277h7.5c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-7.5c-1.1045695 0-2-.8954305-2-2v-10.17157288c0-.53043297.21071368-1.0391408.58578644-1.41421356l3.82842712-3.82842712c.37507276-.37507276.88378059-.58578644 1.41421356-.58578644zm-.5442863 8.18867991 3.3545404 3.35454039c.2508994.2508994.2538696.6596433.0035959.909917-.2429543.2429542-.6561449.2462671-.9065387-.0089489l-2.2609825-2.3045251.0010427 7.2231989c0 .3569916-.2898381.6371378-.6473715.6371378-.3470771 0-.6473715-.2852563-.6473715-.6371378l-.0010428-7.2231995-2.2611222 2.3046654c-.2531661.2580415-.6562868.2592444-.9065605.0089707-.24295423-.2429542-.24865597-.6576651.0036132-.9099343l3.3546673-3.35466731c.2509089-.25090888.6612706-.25227691.9135302-.00001728zm-.9557137-3.18867991c.2761424 0 .5.22385763.5.5s-.2238576.5-.5.5h-6c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm-8.5-3.587-3.587 3.587h2.587c.55228475 0 1-.44771525 1-1zm8.5 1.587c.2761424 0 .5.22385763.5.5s-.2238576.5-.5.5h-6c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5z" fill="#fff"/></svg> </a> </li> </ul> </div> </nav> <div id="search-menu" class="c-header__dropdown c-header__dropdown--full-width" data-track-component="nature-150-split-header"> <div class="c-header__container"> <h2 class="c-header__visually-hidden">Search</h2> <form class="c-header__search-form" action="/search" method="get" role="search" autocomplete="off" data-test="inline-search"> <label class="c-header__heading" for="keywords">Search articles by subject, keyword or author</label> <div class="c-header__search-layout c-header__search-layout--max-width"> <div> <input type="text" required="" class="c-header__input" id="keywords" name="q" value=""> </div> <div class="c-header__search-layout"> <div> <label for="results-from" class="c-header__visually-hidden">Show results from</label> <select id="results-from" name="journal" class="c-header__select"> <option value="" selected>All journals</option> <option value="nphoton">This journal</option> </select> </div> <div> <button type="submit" class="c-header__search-button">Search</button> </div> </div> </div> </form> <div class="c-header__flush"> <a class="c-header__link" href="/search/advanced" data-track="click" data-track-action="advanced search" data-track-label="link"> Advanced search </a> </div> <h3 class="c-header__heading c-header__heading--keyline">Quick links</h3> <ul class="c-header__list"> <li><a class="c-header__link" href="/subjects" data-track="click" data-track-action="explore articles by subject" data-track-label="link">Explore articles by subject</a></li> <li><a class="c-header__link" href="/naturecareers" data-track="click" data-track-action="find a job" data-track-label="link">Find a job</a></li> <li><a class="c-header__link" href="/authors/index.html" data-track="click" data-track-action="guide to authors" data-track-label="link">Guide to authors</a></li> <li><a class="c-header__link" href="/authors/editorial_policies/" data-track="click" data-track-action="editorial policies" data-track-label="link">Editorial policies</a></li> </ul> </div> </div> <footer class="composite-layer" itemscope itemtype="http://schema.org/Periodical"> <meta itemprop="publisher" content="Springer Nature"> <div class="u-mt-16 u-mb-16"> <div class="u-container"> <div class="u-display-flex u-flex-wrap u-justify-content-space-between"> <p class="c-meta u-ma-0 u-flex-shrink"> <span class="c-meta__item"> Nature Photonics (<i>Nat. Photon.</i>) </span> <span class="c-meta__item"> <abbr title="International Standard Serial Number">ISSN</abbr> <span itemprop="onlineIssn">1749-4893</span> (online) </span> <span class="c-meta__item"> <abbr title="International Standard Serial Number">ISSN</abbr> <span itemprop="printIssn">1749-4885</span> (print) </span> </p> </div> </div> </div> <div class="c-footer"> <div class="u-hide-print" data-track-component="footer"> <h2 class="u-visually-hidden">nature.com sitemap</h2> <div class="c-footer__container"> <div class="c-footer__grid c-footer__group--separator"> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">About Nature Portfolio</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/npg_/company_info/index.html" data-track="click" data-track-action="about us" data-track-label="link">About us</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/npg_/press_room/press_releases.html" data-track="click" data-track-action="press releases" data-track-label="link">Press releases</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://press.nature.com/" data-track="click" data-track-action="press office" data-track-label="link">Press office</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://support.nature.com/support/home" data-track="click" data-track-action="contact us" data-track-label="link">Contact us</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Discover content</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/siteindex" data-track="click" data-track-action="journals a-z" data-track-label="link">Journals A-Z</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/subjects" data-track="click" data-track-action="article by subject" data-track-label="link">Articles by subject</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.protocols.io/" data-track="click" data-track-action="protocols.io" data-track-label="link">protocols.io</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.natureindex.com/" data-track="click" data-track-action="nature index" data-track-label="link">Nature Index</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Publishing policies</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/authors/editorial_policies" data-track="click" data-track-action="Nature portfolio policies" data-track-label="link">Nature portfolio policies</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/nature-research/open-access" data-track="click" data-track-action="open access" data-track-label="link">Open access</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Author & Researcher services</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/reprints" data-track="click" data-track-action="reprints and permissions" data-track-label="link">Reprints & permissions</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.springernature.com/gp/authors/research-data" data-track="click" data-track-action="data research service" data-track-label="link">Research data</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://authorservices.springernature.com/language-editing/" data-track="click" data-track-action="language editing" data-track-label="link">Language editing</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://authorservices.springernature.com/scientific-editing/" data-track="click" data-track-action="scientific editing" data-track-label="link">Scientific editing</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://masterclasses.nature.com/" data-track="click" data-track-action="nature masterclasses" data-track-label="link">Nature Masterclasses</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://solutions.springernature.com/" data-track="click" data-track-action="research solutions" data-track-label="link">Research Solutions</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Libraries & institutions</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.springernature.com/gp/librarians/tools-services" data-track="click" data-track-action="librarian service and tools" data-track-label="link">Librarian service & tools</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.springernature.com/gp/librarians/manage-your-account/librarianportal" data-track="click" data-track-action="librarian portal" data-track-label="link">Librarian portal</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/openresearch/about-open-access/information-for-institutions" data-track="click" data-track-action="open research" data-track-label="link">Open research</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.springernature.com/gp/librarians/recommend-to-your-library" data-track="click" data-track-action="Recommend to library" data-track-label="link">Recommend to library</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Advertising & partnerships</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://partnerships.nature.com/product/digital-advertising/" data-track="click" data-track-action="advertising" data-track-label="link">Advertising</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://partnerships.nature.com/" data-track="click" data-track-action="partnerships and services" data-track-label="link">Partnerships & Services</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://partnerships.nature.com/media-kits/" data-track="click" data-track-action="media kits" data-track-label="link">Media kits</a> </li> <li class="c-footer__item"><a class="c-footer__link" href="https://partnerships.nature.com/product/branded-content-native-advertising/" data-track-action="branded content" data-track-label="link">Branded content</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Professional development</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/naturecareers/" data-track="click" data-track-action="nature careers" data-track-label="link">Nature Careers</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://conferences.nature.com" data-track="click" data-track-action="nature conferences" data-track-label="link">Nature<span class="u-visually-hidden"> </span> Conferences</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Regional websites</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/natafrica" data-track="click" data-track-action="nature africa" data-track-label="link">Nature Africa</a></li> <li class="c-footer__item"><a class="c-footer__link" href="http://www.naturechina.com" data-track="click" data-track-action="nature china" data-track-label="link">Nature China</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/nindia" data-track="click" data-track-action="nature india" data-track-label="link">Nature India</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/natitaly" data-track="click" data-track-action="nature Italy" data-track-label="link">Nature Italy</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.natureasia.com/ja-jp" data-track="click" data-track-action="nature japan" data-track-label="link">Nature Japan</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/nmiddleeast" data-track="click" data-track-action="nature middle east" data-track-label="link">Nature Middle East</a></li> </ul> </div> </div> </div> <div class="c-footer__container"> <ul class="c-footer__links"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/info/privacy" data-track="click" data-track-action="privacy policy" data-track-label="link">Privacy Policy</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/info/cookies" data-track="click" data-track-action="use of cookies" data-track-label="link">Use of cookies</a></li> <li class="c-footer__item"> <button class="optanon-toggle-display c-footer__link" onclick="javascript:;" data-cc-action="preferences" data-track="click" data-track-action="manage cookies" data-track-label="link">Your privacy choices/Manage cookies </button> </li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/info/legal-notice" data-track="click" data-track-action="legal notice" data-track-label="link">Legal notice</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/info/accessibility-statement" data-track="click" data-track-action="accessibility statement" data-track-label="link">Accessibility statement</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/info/terms-and-conditions" data-track="click" data-track-action="terms and conditions" data-track-label="link">Terms & Conditions</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.springernature.com/ccpa" data-track="click" data-track-action="california privacy statement" data-track-label="link">Your US state privacy rights</a></li> </ul> </div> </div> <div class="c-footer__container"> <a href="https://www.springernature.com/" class="c-footer__link"> <img src="/static/images/logos/sn-logo-white-ea63208b81.svg" alt="Springer Nature" loading="lazy" width="200" height="20"/> </a> <p class="c-footer__legal" data-test="copyright">© 2024 Springer Nature Limited</p> </div> </div> <div class="u-visually-hidden" aria-hidden="true"> <?xml version="1.0" encoding="UTF-8"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="a" d="M0 .74h56.72v55.24H0z"/></defs><symbol id="icon-access" viewBox="0 0 18 18"><path d="m14 8c.5522847 0 1 .44771525 1 1v7h2.5c.2761424 0 .5.2238576.5.5v1.5h-18v-1.5c0-.2761424.22385763-.5.5-.5h2.5v-7c0-.55228475.44771525-1 1-1s1 .44771525 1 1v6.9996556h8v-6.9996556c0-.55228475.4477153-1 1-1zm-8 0 2 1v5l-2 1zm6 0v7l-2-1v-5zm-2.42653766-7.59857636 7.03554716 4.92488299c.4162533.29137735.5174853.86502537.226108 1.28127873-.1721584.24594054-.4534847.39241464-.7536934.39241464h-14.16284822c-.50810197 0-.92-.41189803-.92-.92 0-.30020869.1464741-.58153499.39241464-.75369337l7.03554714-4.92488299c.34432015-.2410241.80260453-.2410241 1.14692468 0zm-.57346234 2.03988748-3.65526982 2.55868888h7.31053962z" fill-rule="evenodd"/></symbol><symbol id="icon-account" viewBox="0 0 18 18"><path d="m10.2379028 16.9048051c1.3083556-.2032362 2.5118471-.7235183 3.5294683-1.4798399-.8731327-2.5141501-2.0638925-3.935978-3.7673711-4.3188248v-1.27684611c1.1651924-.41183641 2-1.52307546 2-2.82929429 0-1.65685425-1.3431458-3-3-3-1.65685425 0-3 1.34314575-3 3 0 1.30621883.83480763 2.41745788 2 2.82929429v1.27684611c-1.70347856.3828468-2.89423845 1.8046747-3.76737114 4.3188248 1.01762123.7563216 2.22111275 1.2766037 3.52946833 1.4798399.40563808.0629726.81921174.0951949 1.23790281.0951949s.83226473-.0322223 1.2379028-.0951949zm4.3421782-2.1721994c1.4927655-1.4532925 2.419919-3.484675 2.419919-5.7326057 0-4.418278-3.581722-8-8-8s-8 3.581722-8 8c0 2.2479307.92715352 4.2793132 2.41991895 5.7326057.75688473-2.0164459 1.83949951-3.6071894 3.48926591-4.3218837-1.14534283-.70360829-1.90918486-1.96796271-1.90918486-3.410722 0-2.209139 1.790861-4 4-4s4 1.790861 4 4c0 1.44275929-.763842 2.70711371-1.9091849 3.410722 1.6497664.7146943 2.7323812 2.3054378 3.4892659 4.3218837zm-5.580081 3.2673943c-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9 4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9z" fill-rule="evenodd"/></symbol><symbol id="icon-alert" viewBox="0 0 18 18"><path d="m4 10h2.5c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-3.08578644l-1.12132034 1.1213203c-.18753638.1875364-.29289322.4418903-.29289322.7071068v.1715729h14v-.1715729c0-.2652165-.1053568-.5195704-.2928932-.7071068l-1.7071068-1.7071067v-3.4142136c0-2.76142375-2.2385763-5-5-5-2.76142375 0-5 2.23857625-5 5zm3 4c0 1.1045695.8954305 2 2 2s2-.8954305 2-2zm-5 0c-.55228475 0-1-.4477153-1-1v-.1715729c0-.530433.21071368-1.0391408.58578644-1.4142135l1.41421356-1.4142136v-3c0-3.3137085 2.6862915-6 6-6s6 2.6862915 6 6v3l1.4142136 1.4142136c.3750727.3750727.5857864.8837805.5857864 1.4142135v.1715729c0 .5522847-.4477153 1-1 1h-4c0 1.6568542-1.3431458 3-3 3-1.65685425 0-3-1.3431458-3-3z" fill-rule="evenodd"/></symbol><symbol id="icon-arrow-broad" viewBox="0 0 16 16"><path d="m6.10307866 2.97190702v7.69043288l2.44965196-2.44676915c.38776071-.38730439 1.0088052-.39493524 1.38498697-.01919617.38609051.38563612.38643641 1.01053024-.00013864 1.39665039l-4.12239817 4.11754683c-.38616704.3857126-1.01187344.3861062-1.39846576-.0000311l-4.12258206-4.11773056c-.38618426-.38572979-.39254614-1.00476697-.01636437-1.38050605.38609047-.38563611 1.01018509-.38751562 1.4012233.00306241l2.44985644 2.4469734v-8.67638639c0-.54139983.43698413-.98042709.98493125-.98159081l7.89910522-.0043627c.5451687 0 .9871152.44142642.9871152.98595351s-.4419465.98595351-.9871152.98595351z" fill-rule="evenodd" transform="matrix(-1 0 0 -1 14 15)"/></symbol><symbol id="icon-arrow-down" viewBox="0 0 16 16"><path d="m3.28337502 11.5302405 4.03074001 4.176208c.37758093.3912076.98937525.3916069 1.367372-.0000316l4.03091977-4.1763942c.3775978-.3912252.3838182-1.0190815.0160006-1.4001736-.3775061-.39113013-.9877245-.39303641-1.3700683.003106l-2.39538585 2.4818345v-11.6147896l-.00649339-.11662112c-.055753-.49733869-.46370161-.88337888-.95867408-.88337888-.49497246 0-.90292107.38604019-.95867408.88337888l-.00649338.11662112v11.6147896l-2.39518594-2.4816273c-.37913917-.39282218-.98637524-.40056175-1.35419292-.0194697-.37750607.3911302-.37784433 1.0249269.00013556 1.4165479z" fill-rule="evenodd"/></symbol><symbol id="icon-arrow-left" viewBox="0 0 16 16"><path d="m4.46975946 3.28337502-4.17620792 4.03074001c-.39120768.37758093-.39160691.98937525.0000316 1.367372l4.1763942 4.03091977c.39122514.3775978 1.01908149.3838182 1.40017357.0160006.39113012-.3775061.3930364-.9877245-.00310603-1.3700683l-2.48183446-2.39538585h11.61478958l.1166211-.00649339c.4973387-.055753.8833789-.46370161.8833789-.95867408 0-.49497246-.3860402-.90292107-.8833789-.95867408l-.1166211-.00649338h-11.61478958l2.4816273-2.39518594c.39282216-.37913917.40056173-.98637524.01946965-1.35419292-.39113012-.37750607-1.02492687-.37784433-1.41654791.00013556z" fill-rule="evenodd"/></symbol><symbol id="icon-arrow-right" viewBox="0 0 16 16"><path d="m11.5302405 12.716625 4.176208-4.03074003c.3912076-.37758093.3916069-.98937525-.0000316-1.367372l-4.1763942-4.03091981c-.3912252-.37759778-1.0190815-.38381821-1.4001736-.01600053-.39113013.37750607-.39303641.98772445.003106 1.37006824l2.4818345 2.39538588h-11.6147896l-.11662112.00649339c-.49733869.055753-.88337888.46370161-.88337888.95867408 0 .49497246.38604019.90292107.88337888.95867408l.11662112.00649338h11.6147896l-2.4816273 2.39518592c-.39282218.3791392-.40056175.9863753-.0194697 1.3541929.3911302.3775061 1.0249269.3778444 1.4165479-.0001355z" fill-rule="evenodd"/></symbol><symbol id="icon-arrow-sub" viewBox="0 0 16 16"><path d="m7.89692134 4.97190702v7.69043288l-2.44965196-2.4467692c-.38776071-.38730434-1.0088052-.39493519-1.38498697-.0191961-.38609047.3856361-.38643643 1.0105302.00013864 1.3966504l4.12239817 4.1175468c.38616704.3857126 1.01187344.3861062 1.39846576-.0000311l4.12258202-4.1177306c.3861843-.3857298.3925462-1.0047669.0163644-1.380506-.3860905-.38563612-1.0101851-.38751563-1.4012233.0030624l-2.44985643 2.4469734v-8.67638639c0-.54139983-.43698413-.98042709-.98493125-.98159081l-7.89910525-.0043627c-.54516866 0-.98711517.44142642-.98711517.98595351s.44194651.98595351.98711517.98595351z" fill-rule="evenodd"/></symbol><symbol id="icon-arrow-up" viewBox="0 0 16 16"><path d="m12.716625 4.46975946-4.03074003-4.17620792c-.37758093-.39120768-.98937525-.39160691-1.367372.0000316l-4.03091981 4.1763942c-.37759778.39122514-.38381821 1.01908149-.01600053 1.40017357.37750607.39113012.98772445.3930364 1.37006824-.00310603l2.39538588-2.48183446v11.61478958l.00649339.1166211c.055753.4973387.46370161.8833789.95867408.8833789.49497246 0 .90292107-.3860402.95867408-.8833789l.00649338-.1166211v-11.61478958l2.39518592 2.4816273c.3791392.39282216.9863753.40056173 1.3541929.01946965.3775061-.39113012.3778444-1.02492687-.0001355-1.41654791z" fill-rule="evenodd"/></symbol><symbol id="icon-article" viewBox="0 0 18 18"><path d="m13 15v-12.9906311c0-.0073595-.0019884-.0093689.0014977-.0093689l-11.00158888.00087166v13.00506804c0 .5482678.44615281.9940603.99415146.9940603h10.27350412c-.1701701-.2941734-.2675644-.6357129-.2675644-1zm-12 .0059397v-13.00506804c0-.5562408.44704472-1.00087166.99850233-1.00087166h11.00299537c.5510129 0 .9985023.45190985.9985023 1.0093689v2.9906311h3v9.9914698c0 1.1065798-.8927712 2.0085302-1.9940603 2.0085302h-12.01187942c-1.09954652 0-1.99406028-.8927712-1.99406028-1.9940603zm13-9.0059397v9c0 .5522847.4477153 1 1 1s1-.4477153 1-1v-9zm-10-2h7v4h-7zm1 1v2h5v-2zm-1 4h7v1h-7zm0 2h7v1h-7zm0 2h7v1h-7z" fill-rule="evenodd"/></symbol><symbol id="icon-audio" viewBox="0 0 18 18"><path d="m13.0957477 13.5588459c-.195279.1937043-.5119137.193729-.7072234.0000551-.1953098-.193674-.1953346-.5077061-.0000556-.7014104 1.0251004-1.0168342 1.6108711-2.3905226 1.6108711-3.85745208 0-1.46604976-.5850634-2.83898246-1.6090736-3.85566829-.1951894-.19379323-.1950192-.50782531.0003802-.70141028.1953993-.19358497.512034-.19341614.7072234.00037709 1.2094886 1.20083761 1.901635 2.8250555 1.901635 4.55670148 0 1.73268608-.6929822 3.35779608-1.9037571 4.55880738zm2.1233994 2.1025159c-.195234.193749-.5118687.1938462-.7072235.0002171-.1953548-.1936292-.1954528-.5076613-.0002189-.7014104 1.5832215-1.5711805 2.4881302-3.6939808 2.4881302-5.96012998 0-2.26581266-.9046382-4.3883241-2.487443-5.95944795-.1952117-.19377107-.1950777-.50780316.0002993-.70141031s.5120117-.19347426.7072234.00029682c1.7683321 1.75528196 2.7800854 4.12911258 2.7800854 6.66056144 0 2.53182498-1.0120556 4.90597838-2.7808529 6.66132328zm-14.21898205-3.6854911c-.5523759 0-1.00016505-.4441085-1.00016505-.991944v-3.96777631c0-.54783558.44778915-.99194407 1.00016505-.99194407h2.0003301l5.41965617-3.8393633c.44948677-.31842296 1.07413994-.21516983 1.39520191.23062232.12116339.16823446.18629727.36981184.18629727.57655577v12.01603479c0 .5478356-.44778914.9919441-1.00016505.9919441-.20845738 0-.41170538-.0645985-.58133413-.184766l-5.41965617-3.8393633zm0-.991944h2.32084805l5.68047235 4.0241292v-12.01603479l-5.68047235 4.02412928h-2.32084805z" fill-rule="evenodd"/></symbol><symbol id="icon-block" viewBox="0 0 24 24"><path d="m0 0h24v24h-24z" fill-rule="evenodd"/></symbol><symbol id="icon-book" viewBox="0 0 18 18"><path d="m4 13v-11h1v11h11v-11h-13c-.55228475 0-1 .44771525-1 1v10.2675644c.29417337-.1701701.63571286-.2675644 1-.2675644zm12 1h-13c-.55228475 0-1 .4477153-1 1s.44771525 1 1 1h13zm0 3h-13c-1.1045695 0-2-.8954305-2-2v-12c0-1.1045695.8954305-2 2-2h13c.5522847 0 1 .44771525 1 1v14c0 .5522847-.4477153 1-1 1zm-8.5-13h6c.2761424 0 .5.22385763.5.5s-.2238576.5-.5.5h-6c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm1 2h4c.2761424 0 .5.22385763.5.5s-.2238576.5-.5.5h-4c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5z" fill-rule="evenodd"/></symbol><symbol id="icon-broad" viewBox="0 0 24 24"><path d="m9.18274226 7.81v7.7999954l2.48162734-2.4816273c.3928221-.3928221 1.0219731-.4005617 1.4030652-.0194696.3911301.3911301.3914806 1.0249268-.0001404 1.4165479l-4.17620796 4.1762079c-.39120769.3912077-1.02508144.3916069-1.41671995-.0000316l-4.1763942-4.1763942c-.39122514-.3912251-.39767006-1.0190815-.01657798-1.4001736.39113012-.3911301 1.02337106-.3930364 1.41951349.0031061l2.48183446 2.4818344v-8.7999954c0-.54911294.4426881-.99439484.99778758-.99557515l8.00221246-.00442485c.5522847 0 1 .44771525 1 1s-.4477153 1-1 1z" fill-rule="evenodd" transform="matrix(-1 0 0 -1 20.182742 24.805206)"/></symbol><symbol id="icon-calendar" viewBox="0 0 18 18"><path d="m12.5 0c.2761424 0 .5.21505737.5.49047852v.50952148h2c1.1072288 0 2 .89451376 2 2v12c0 1.1072288-.8945138 2-2 2h-12c-1.1072288 0-2-.8945138-2-2v-12c0-1.1072288.89451376-2 2-2h1v1h-1c-.55393837 0-1 .44579254-1 1v3h14v-3c0-.55393837-.4457925-1-1-1h-2v1.50952148c0 .27088381-.2319336.49047852-.5.49047852-.2761424 0-.5-.21505737-.5-.49047852v-3.01904296c0-.27088381.2319336-.49047852.5-.49047852zm3.5 7h-14v8c0 .5539384.44579254 1 1 1h12c.5539384 0 1-.4457925 1-1zm-11 6v1h-1v-1zm3 0v1h-1v-1zm3 0v1h-1v-1zm-6-2v1h-1v-1zm3 0v1h-1v-1zm6 0v1h-1v-1zm-3 0v1h-1v-1zm-3-2v1h-1v-1zm6 0v1h-1v-1zm-3 0v1h-1v-1zm-5.5-9c.27614237 0 .5.21505737.5.49047852v.50952148h5v1h-5v1.50952148c0 .27088381-.23193359.49047852-.5.49047852-.27614237 0-.5-.21505737-.5-.49047852v-3.01904296c0-.27088381.23193359-.49047852.5-.49047852z" fill-rule="evenodd"/></symbol><symbol id="icon-cart" viewBox="0 0 18 18"><path d="m5 14c1.1045695 0 2 .8954305 2 2s-.8954305 2-2 2-2-.8954305-2-2 .8954305-2 2-2zm10 0c1.1045695 0 2 .8954305 2 2s-.8954305 2-2 2-2-.8954305-2-2 .8954305-2 2-2zm-10 1c-.55228475 0-1 .4477153-1 1s.44771525 1 1 1 1-.4477153 1-1-.44771525-1-1-1zm10 0c-.5522847 0-1 .4477153-1 1s.4477153 1 1 1 1-.4477153 1-1-.4477153-1-1-1zm-12.82032249-15c.47691417 0 .88746157.33678127.98070211.80449199l.23823144 1.19501025 13.36277974.00045554c.5522847.00001882.9999659.44774934.9999659 1.00004222 0 .07084994-.0075361.14150708-.022474.2107727l-1.2908094 5.98534344c-.1007861.46742419-.5432548.80388386-1.0571651.80388386h-10.24805106c-.59173366 0-1.07142857.4477153-1.07142857 1 0 .5128358.41361449.9355072.94647737.9932723l.1249512.0067277h10.35933776c.2749512 0 .4979349.2228539.4979349.4978051 0 .2749417-.2227336.4978951-.4976753.4980063l-10.35959736.0041886c-1.18346732 0-2.14285714-.8954305-2.14285714-2 0-.6625717.34520317-1.24989198.87690425-1.61383592l-1.63768102-8.19004794c-.01312273-.06561364-.01950005-.131011-.0196107-.19547395l-1.71961253-.00064219c-.27614237 0-.5-.22385762-.5-.5 0-.27614237.22385763-.5.5-.5zm14.53193359 2.99950224h-13.11300004l1.20580469 6.02530174c.11024034-.0163252.22327998-.02480398.33844139-.02480398h10.27064786z"/></symbol><symbol id="icon-chevron-less" viewBox="0 0 10 10"><path d="m5.58578644 4-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z" fill-rule="evenodd" transform="matrix(0 -1 -1 0 9 9)"/></symbol><symbol id="icon-chevron-more" viewBox="0 0 10 10"><path d="m5.58578644 6-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4.00000002c-.39052429.3905243-1.02368927.3905243-1.41421356 0s-.39052429-1.02368929 0-1.41421358z" fill-rule="evenodd" transform="matrix(0 1 -1 0 11 1)"/></symbol><symbol id="icon-chevron-right" viewBox="0 0 10 10"><path d="m5.96738168 4.70639573 2.39518594-2.41447274c.37913917-.38219212.98637524-.38972225 1.35419292-.01894278.37750606.38054586.37784436.99719163-.00013556 1.37821513l-4.03074001 4.06319683c-.37758093.38062133-.98937525.38100976-1.367372-.00003075l-4.03091981-4.06337806c-.37759778-.38063832-.38381821-.99150444-.01600053-1.3622839.37750607-.38054587.98772445-.38240057 1.37006824.00302197l2.39538588 2.4146743.96295325.98624457z" fill-rule="evenodd" transform="matrix(0 -1 1 0 0 10)"/></symbol><symbol id="icon-circle-fill" viewBox="0 0 16 16"><path d="m8 14c-3.3137085 0-6-2.6862915-6-6s2.6862915-6 6-6 6 2.6862915 6 6-2.6862915 6-6 6z" fill-rule="evenodd"/></symbol><symbol id="icon-circle" viewBox="0 0 16 16"><path d="m8 12c2.209139 0 4-1.790861 4-4s-1.790861-4-4-4-4 1.790861-4 4 1.790861 4 4 4zm0 2c-3.3137085 0-6-2.6862915-6-6s2.6862915-6 6-6 6 2.6862915 6 6-2.6862915 6-6 6z" fill-rule="evenodd"/></symbol><symbol id="icon-citation" viewBox="0 0 18 18"><path d="m8.63593473 5.99995183c2.20913897 0 3.99999997 1.79084375 3.99999997 3.99996146 0 1.40730761-.7267788 2.64486871-1.8254829 3.35783281 1.6240224.6764218 2.8754442 2.0093871 3.4610603 3.6412466l-1.0763845.000006c-.5310008-1.2078237-1.5108121-2.1940153-2.7691712-2.7181346l-.79002167-.329052v-1.023992l.63016577-.4089232c.8482885-.5504661 1.3698342-1.4895187 1.3698342-2.51898361 0-1.65683828-1.3431457-2.99996146-2.99999997-2.99996146-1.65685425 0-3 1.34312318-3 2.99996146 0 1.02946491.52154569 1.96851751 1.36983419 2.51898361l.63016581.4089232v1.023992l-.79002171.329052c-1.25835905.5241193-2.23817037 1.5103109-2.76917113 2.7181346l-1.07638453-.000006c.58561612-1.6318595 1.8370379-2.9648248 3.46106024-3.6412466-1.09870405-.7129641-1.82548287-1.9505252-1.82548287-3.35783281 0-2.20911771 1.790861-3.99996146 4-3.99996146zm7.36897597-4.99995183c1.1018574 0 1.9950893.89353404 1.9950893 2.00274083v5.994422c0 1.10608317-.8926228 2.00274087-1.9950893 2.00274087l-3.0049107-.0009037v-1l3.0049107.00091329c.5490631 0 .9950893-.44783123.9950893-1.00275046v-5.994422c0-.55646537-.4450595-1.00275046-.9950893-1.00275046h-14.00982141c-.54906309 0-.99508929.44783123-.99508929 1.00275046v5.9971821c0 .66666024.33333333.99999036 1 .99999036l2-.00091329v1l-2 .0009037c-1 0-2-.99999041-2-1.99998077v-5.9971821c0-1.10608322.8926228-2.00274083 1.99508929-2.00274083zm-8.5049107 2.9999711c.27614237 0 .5.22385547.5.5 0 .2761349-.22385763.5-.5.5h-4c-.27614237 0-.5-.2238651-.5-.5 0-.27614453.22385763-.5.5-.5zm3 0c.2761424 0 .5.22385547.5.5 0 .2761349-.2238576.5-.5.5h-1c-.27614237 0-.5-.2238651-.5-.5 0-.27614453.22385763-.5.5-.5zm4 0c.2761424 0 .5.22385547.5.5 0 .2761349-.2238576.5-.5.5h-2c-.2761424 0-.5-.2238651-.5-.5 0-.27614453.2238576-.5.5-.5z" fill-rule="evenodd"/></symbol><symbol id="icon-close" viewBox="0 0 16 16"><path d="m2.29679575 12.2772478c-.39658757.3965876-.39438847 1.0328109-.00062148 1.4265779.39651227.3965123 1.03246768.3934888 1.42657791-.0006214l4.27724782-4.27724787 4.2772478 4.27724787c.3965876.3965875 1.0328109.3943884 1.4265779.0006214.3965123-.3965122.3934888-1.0324677-.0006214-1.4265779l-4.27724787-4.2772478 4.27724787-4.27724782c.3965875-.39658757.3943884-1.03281091.0006214-1.42657791-.3965122-.39651226-1.0324677-.39348875-1.4265779.00062148l-4.2772478 4.27724782-4.27724782-4.27724782c-.39658757-.39658757-1.03281091-.39438847-1.42657791-.00062148-.39651226.39651227-.39348875 1.03246768.00062148 1.42657791l4.27724782 4.27724782z" fill-rule="evenodd"/></symbol><symbol id="icon-collections" viewBox="0 0 18 18"><path d="m15 4c1.1045695 0 2 .8954305 2 2v9c0 1.1045695-.8954305 2-2 2h-8c-1.1045695 0-2-.8954305-2-2h1c0 .5128358.38604019.9355072.88337887.9932723l.11662113.0067277h8c.5128358 0 .9355072-.3860402.9932723-.8833789l.0067277-.1166211v-9c0-.51283584-.3860402-.93550716-.8833789-.99327227l-.1166211-.00672773h-1v-1zm-4-3c1.1045695 0 2 .8954305 2 2v9c0 1.1045695-.8954305 2-2 2h-8c-1.1045695 0-2-.8954305-2-2v-9c0-1.1045695.8954305-2 2-2zm0 1h-8c-.51283584 0-.93550716.38604019-.99327227.88337887l-.00672773.11662113v9c0 .5128358.38604019.9355072.88337887.9932723l.11662113.0067277h8c.5128358 0 .9355072-.3860402.9932723-.8833789l.0067277-.1166211v-9c0-.51283584-.3860402-.93550716-.8833789-.99327227zm-1.5 7c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-5c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm0-2c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-5c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm0-2c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-5c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5z" fill-rule="evenodd"/></symbol><symbol id="icon-compare" viewBox="0 0 18 18"><path d="m12 3c3.3137085 0 6 2.6862915 6 6s-2.6862915 6-6 6c-1.0928452 0-2.11744941-.2921742-2.99996061-.8026704-.88181407.5102749-1.90678042.8026704-3.00003939.8026704-3.3137085 0-6-2.6862915-6-6s2.6862915-6 6-6c1.09325897 0 2.11822532.29239547 3.00096303.80325037.88158756-.51107621 1.90619177-.80325037 2.99903697-.80325037zm-6 1c-2.76142375 0-5 2.23857625-5 5 0 2.7614237 2.23857625 5 5 5 .74397391 0 1.44999672-.162488 2.08451611-.4539116-1.27652344-1.1000812-2.08451611-2.7287264-2.08451611-4.5460884s.80799267-3.44600721 2.08434391-4.5463015c-.63434719-.29121054-1.34037-.4536985-2.08434391-.4536985zm6 0c-.7439739 0-1.4499967.16248796-2.08451611.45391156 1.27652341 1.10008123 2.08451611 2.72872644 2.08451611 4.54608844s-.8079927 3.4460072-2.08434391 4.5463015c.63434721.2912105 1.34037001.4536985 2.08434391.4536985 2.7614237 0 5-2.2385763 5-5 0-2.76142375-2.2385763-5-5-5zm-1.4162763 7.0005324h-3.16744736c.15614659.3572676.35283837.6927622.58425872 1.0006671h1.99892988c.23142036-.3079049.42811216-.6433995.58425876-1.0006671zm.4162763-2.0005324h-4c0 .34288501.0345146.67770871.10025909 1.0011864h3.79948181c.0657445-.32347769.1002591-.65830139.1002591-1.0011864zm-.4158423-1.99953894h-3.16831543c-.13859957.31730812-.24521946.651783-.31578599.99935097h3.79988742c-.0705665-.34756797-.1771864-.68204285-.315786-.99935097zm-1.58295822-1.999926-.08316107.06199199c-.34550042.27081213-.65446126.58611297-.91825862.93727862h2.00044041c-.28418626-.37830727-.6207872-.71499149-.99902072-.99927061z" fill-rule="evenodd"/></symbol><symbol id="icon-download-file" viewBox="0 0 18 18"><path d="m10.0046024 0c.5497429 0 1.3179837.32258606 1.707238.71184039l4.5763192 4.57631922c.3931386.39313859.7118404 1.16760135.7118404 1.71431368v8.98899651c0 1.1092806-.8945138 2.0085302-1.9940603 2.0085302h-12.01187942c-1.10128908 0-1.99406028-.8926228-1.99406028-1.9950893v-14.00982141c0-1.10185739.88743329-1.99508929 1.99961498-1.99508929zm0 1h-7.00498742c-.55709576 0-.99961498.44271433-.99961498.99508929v14.00982141c0 .5500396.44491393.9950893.99406028.9950893h12.01187942c.5463747 0 .9940603-.4506622.9940603-1.0085302v-8.98899651c0-.28393444-.2150684-.80332809-.4189472-1.0072069l-4.5763192-4.57631922c-.2038461-.20384606-.718603-.41894717-1.0001312-.41894717zm-1.5046024 4c.27614237 0 .5.21637201.5.49209595v6.14827645l1.7462789-1.77990922c.1933927-.1971171.5125222-.19455839.7001689-.0069117.1932998.19329992.1910058.50899492-.0027774.70277812l-2.59089271 2.5908927c-.19483374.1948337-.51177825.1937771-.70556873-.0000133l-2.59099079-2.5909908c-.19484111-.1948411-.19043735-.5151448-.00279066-.70279146.19329987-.19329987.50465175-.19237083.70018565.00692852l1.74638684 1.78001764v-6.14827695c0-.27177709.23193359-.49209595.5-.49209595z" fill-rule="evenodd"/></symbol><symbol id="icon-download" viewBox="0 0 16 16"><path d="m12.9975267 12.999368c.5467123 0 1.0024733.4478567 1.0024733 1.000316 0 .5563109-.4488226 1.000316-1.0024733 1.000316h-9.99505341c-.54671233 0-1.00247329-.4478567-1.00247329-1.000316 0-.5563109.44882258-1.000316 1.00247329-1.000316zm-4.9975267-11.999368c.55228475 0 1 .44497754 1 .99589209v6.80214418l2.4816273-2.48241149c.3928222-.39294628 1.0219732-.4006883 1.4030652-.01947579.3911302.39125371.3914806 1.02525073-.0001404 1.41699553l-4.17620792 4.17752758c-.39120769.3913313-1.02508144.3917306-1.41671995-.0000316l-4.17639421-4.17771394c-.39122513-.39134876-.39767006-1.01940351-.01657797-1.40061601.39113012-.39125372 1.02337105-.3931606 1.41951349.00310701l2.48183446 2.48261871v-6.80214418c0-.55001601.44386482-.99589209 1-.99589209z" fill-rule="evenodd"/></symbol><symbol id="icon-editors" viewBox="0 0 18 18"><path d="m8.72592184 2.54588137c-.48811714-.34391207-1.08343326-.54588137-1.72592184-.54588137-1.65685425 0-3 1.34314575-3 3 0 1.02947485.5215457 1.96853646 1.3698342 2.51900785l.6301658.40892721v1.02400182l-.79002171.32905522c-1.93395773.8055207-3.20997829 2.7024791-3.20997829 4.8180274v.9009805h-1v-.9009805c0-2.5479714 1.54557359-4.79153984 3.82548288-5.7411543-1.09870406-.71297106-1.82548288-1.95054399-1.82548288-3.3578652 0-2.209139 1.790861-4 4-4 1.09079823 0 2.07961816.43662103 2.80122451 1.1446278-.37707584.09278571-.7373238.22835063-1.07530267.40125357zm-2.72592184 14.45411863h-1v-.9009805c0-2.5479714 1.54557359-4.7915398 3.82548288-5.7411543-1.09870406-.71297106-1.82548288-1.95054399-1.82548288-3.3578652 0-2.209139 1.790861-4 4-4s4 1.790861 4 4c0 1.40732121-.7267788 2.64489414-1.8254829 3.3578652 2.2799093.9496145 3.8254829 3.1931829 3.8254829 5.7411543v.9009805h-1v-.9009805c0-2.1155483-1.2760206-4.0125067-3.2099783-4.8180274l-.7900217-.3290552v-1.02400184l.6301658-.40892721c.8482885-.55047139 1.3698342-1.489533 1.3698342-2.51900785 0-1.65685425-1.3431458-3-3-3-1.65685425 0-3 1.34314575-3 3 0 1.02947485.5215457 1.96853646 1.3698342 2.51900785l.6301658.40892721v1.02400184l-.79002171.3290552c-1.93395773.8055207-3.20997829 2.7024791-3.20997829 4.8180274z" fill-rule="evenodd"/></symbol><symbol id="icon-email" viewBox="0 0 18 18"><path d="m16.0049107 2c1.1018574 0 1.9950893.89706013 1.9950893 2.00585866v9.98828264c0 1.1078052-.8926228 2.0058587-1.9950893 2.0058587h-14.00982141c-1.10185739 0-1.99508929-.8970601-1.99508929-2.0058587v-9.98828264c0-1.10780515.8926228-2.00585866 1.99508929-2.00585866zm0 1h-14.00982141c-.54871518 0-.99508929.44887827-.99508929 1.00585866v9.98828264c0 .5572961.44630695 1.0058587.99508929 1.0058587h14.00982141c.5487152 0 .9950893-.4488783.9950893-1.0058587v-9.98828264c0-.55729607-.446307-1.00585866-.9950893-1.00585866zm-.0049107 2.55749512v1.44250488l-7 4-7-4v-1.44250488l7 4z" fill-rule="evenodd"/></symbol><symbol id="icon-error" viewBox="0 0 18 18"><path d="m9 0c4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9zm2.8630343 4.71100931-2.8630343 2.86303426-2.86303426-2.86303426c-.39658757-.39658757-1.03281091-.39438847-1.4265779-.00062147-.39651227.39651226-.39348876 1.03246767.00062147 1.4265779l2.86303426 2.86303426-2.86303426 2.8630343c-.39658757.3965875-.39438847 1.0328109-.00062147 1.4265779.39651226.3965122 1.03246767.3934887 1.4265779-.0006215l2.86303426-2.8630343 2.8630343 2.8630343c.3965875.3965876 1.0328109.3943885 1.4265779.0006215.3965122-.3965123.3934887-1.0324677-.0006215-1.4265779l-2.8630343-2.8630343 2.8630343-2.86303426c.3965876-.39658757.3943885-1.03281091.0006215-1.4265779-.3965123-.39651227-1.0324677-.39348876-1.4265779.00062147z" fill-rule="evenodd"/></symbol><symbol id="icon-ethics" viewBox="0 0 18 18"><path d="m6.76384967 1.41421356.83301651-.8330165c.77492941-.77492941 2.03133823-.77492941 2.80626762 0l.8330165.8330165c.3750728.37507276.8837806.58578644 1.4142136.58578644h1.3496361c1.1045695 0 2 .8954305 2 2v1.34963611c0 .53043298.2107137 1.03914081.5857864 1.41421356l.8330165.83301651c.7749295.77492941.7749295 2.03133823 0 2.80626762l-.8330165.8330165c-.3750727.3750728-.5857864.8837806-.5857864 1.4142136v1.3496361c0 1.1045695-.8954305 2-2 2h-1.3496361c-.530433 0-1.0391408.2107137-1.4142136.5857864l-.8330165.8330165c-.77492939.7749295-2.03133821.7749295-2.80626762 0l-.83301651-.8330165c-.37507275-.3750727-.88378058-.5857864-1.41421356-.5857864h-1.34963611c-1.1045695 0-2-.8954305-2-2v-1.3496361c0-.530433-.21071368-1.0391408-.58578644-1.4142136l-.8330165-.8330165c-.77492941-.77492939-.77492941-2.03133821 0-2.80626762l.8330165-.83301651c.37507276-.37507275.58578644-.88378058.58578644-1.41421356v-1.34963611c0-1.1045695.8954305-2 2-2h1.34963611c.53043298 0 1.03914081-.21071368 1.41421356-.58578644zm-1.41421356 1.58578644h-1.34963611c-.55228475 0-1 .44771525-1 1v1.34963611c0 .79564947-.31607052 1.55871121-.87867966 2.12132034l-.8330165.83301651c-.38440512.38440512-.38440512 1.00764896 0 1.39205408l.8330165.83301646c.56260914.5626092.87867966 1.3256709.87867966 2.1213204v1.3496361c0 .5522847.44771525 1 1 1h1.34963611c.79564947 0 1.55871121.3160705 2.12132034.8786797l.83301651.8330165c.38440512.3844051 1.00764896.3844051 1.39205408 0l.83301646-.8330165c.5626092-.5626092 1.3256709-.8786797 2.1213204-.8786797h1.3496361c.5522847 0 1-.4477153 1-1v-1.3496361c0-.7956495.3160705-1.5587112.8786797-2.1213204l.8330165-.83301646c.3844051-.38440512.3844051-1.00764896 0-1.39205408l-.8330165-.83301651c-.5626092-.56260913-.8786797-1.32567087-.8786797-2.12132034v-1.34963611c0-.55228475-.4477153-1-1-1h-1.3496361c-.7956495 0-1.5587112-.31607052-2.1213204-.87867966l-.83301646-.8330165c-.38440512-.38440512-1.00764896-.38440512-1.39205408 0l-.83301651.8330165c-.56260913.56260914-1.32567087.87867966-2.12132034.87867966zm3.58698944 11.4960218c-.02081224.002155-.04199226.0030286-.06345763.002542-.98766446-.0223875-1.93408568-.3063547-2.75885125-.8155622-.23496767-.1450683-.30784554-.4531483-.16277726-.688116.14506827-.2349677.45314827-.3078455.68811595-.1627773.67447084.4164161 1.44758575.6483839 2.25617384.6667123.01759529.0003988.03495764.0017019.05204365.0038639.01713363-.0017748.03452416-.0026845.05212715-.0026845 2.4852814 0 4.5-2.0147186 4.5-4.5 0-1.04888973-.3593547-2.04134635-1.0074477-2.83787157-.1742817-.21419731-.1419238-.5291218.0722736-.70340353.2141973-.17428173.5291218-.14192375.7034035.07227357.7919032.97327203 1.2317706 2.18808682 1.2317706 3.46900153 0 3.0375661-2.4624339 5.5-5.5 5.5-.02146768 0-.04261937-.0013529-.06337445-.0039782zm1.57975095-10.78419583c.2654788.07599731.419084.35281842.3430867.61829728-.0759973.26547885-.3528185.419084-.6182973.3430867-.37560116-.10752146-.76586237-.16587951-1.15568824-.17249193-2.5587807-.00064534-4.58547766 2.00216524-4.58547766 4.49928198 0 .62691557.12797645 1.23496.37274865 1.7964426.11035133.2531347-.0053975.5477984-.25853224.6581497-.25313473.1103514-.54779841-.0053975-.65814974-.2585322-.29947131-.6869568-.45606667-1.43097603-.45606667-2.1960601 0-3.05211432 2.47714695-5.50006595 5.59399617-5.49921198.48576182.00815502.96289603.0795037 1.42238033.21103795zm-1.9766658 6.41091303 2.69835-2.94655317c.1788432-.21040373.4943901-.23598862.7047939-.05714545.2104037.17884318.2359886.49439014.0571454.70479387l-3.01637681 3.34277395c-.18039088.1999106-.48669547.2210637-.69285412.0478478l-1.93095347-1.62240047c-.21213845-.17678204-.24080048-.49206439-.06401844-.70420284.17678204-.21213844.49206439-.24080048.70420284-.06401844z" fill-rule="evenodd"/></symbol><symbol id="icon-expand"><path d="M7.498 11.918a.997.997 0 0 0-.003-1.411.995.995 0 0 0-1.412-.003l-4.102 4.102v-3.51A1 1 0 0 0 .98 10.09.992.992 0 0 0 0 11.092V17c0 .554.448 1.002 1.002 1.002h5.907c.554 0 1.002-.45 1.002-1.003 0-.539-.45-.978-1.006-.978h-3.51zm3.005-5.835a.997.997 0 0 0 .003 1.412.995.995 0 0 0 1.411.003l4.103-4.103v3.51a1 1 0 0 0 1.001 1.006A.992.992 0 0 0 18 6.91V1.002A1 1 0 0 0 17 0h-5.907a1.003 1.003 0 0 0-1.002 1.003c0 .539.45.978 1.006.978h3.51z" fill-rule="evenodd"/></symbol><symbol id="icon-explore" viewBox="0 0 18 18"><path d="m9 17c4.418278 0 8-3.581722 8-8s-3.581722-8-8-8-8 3.581722-8 8 3.581722 8 8 8zm0 1c-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9 4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9zm0-2.5c-.27614237 0-.5-.2238576-.5-.5s.22385763-.5.5-.5c2.969509 0 5.400504-2.3575119 5.497023-5.31714844.0090007-.27599565.2400359-.49243782.5160315-.48343711.2759957.0090007.4924378.2400359.4834371.51603155-.114093 3.4985237-2.9869632 6.284554-6.4964916 6.284554zm-.29090657-12.99359748c.27587424-.01216621.50937715.20161139.52154336.47748563.01216621.27587423-.20161139.50937715-.47748563.52154336-2.93195733.12930094-5.25315116 2.54886451-5.25315116 5.49456849 0 .27614237-.22385763.5-.5.5s-.5-.22385763-.5-.5c0-3.48142406 2.74307146-6.34074398 6.20909343-6.49359748zm1.13784138 8.04763908-1.2004882-1.20048821c-.19526215-.19526215-.19526215-.51184463 0-.70710678s.51184463-.19526215.70710678 0l1.20048821 1.2004882 1.6006509-4.00162734-4.50670359 1.80268144-1.80268144 4.50670359zm4.10281269-6.50378907-2.6692597 6.67314927c-.1016411.2541026-.3029834.4554449-.557086.557086l-6.67314927 2.6692597 2.66925969-6.67314926c.10164107-.25410266.30298336-.45544495.55708602-.55708602z" fill-rule="evenodd"/></symbol><symbol id="icon-filter" viewBox="0 0 16 16"><path d="m14.9738641 0c.5667192 0 1.0261359.4477136 1.0261359 1 0 .24221858-.0902161.47620768-.2538899.65849851l-5.6938314 6.34147206v5.49997973c0 .3147562-.1520673.6111434-.4104543.7999971l-2.05227171 1.4999945c-.45337535.3313696-1.09655869.2418269-1.4365902-.1999993-.13321514-.1730955-.20522717-.3836284-.20522717-.5999978v-6.99997423l-5.69383133-6.34147206c-.3731872-.41563511-.32996891-1.0473954.09653074-1.41107611.18705584-.15950448.42716133-.2474224.67571519-.2474224zm-5.9218641 8.5h-2.105v6.491l.01238459.0070843.02053271.0015705.01955278-.0070558 2.0532976-1.4990996zm-8.02585008-7.5-.01564945.00240169 5.83249953 6.49759831h2.313l5.836-6.499z"/></symbol><symbol id="icon-home" viewBox="0 0 18 18"><path d="m9 5-6 6v5h4v-4h4v4h4v-5zm7 6.5857864v4.4142136c0 .5522847-.4477153 1-1 1h-5v-4h-2v4h-5c-.55228475 0-1-.4477153-1-1v-4.4142136c-.25592232 0-.51184464-.097631-.70710678-.2928932l-.58578644-.5857864c-.39052429-.3905243-.39052429-1.02368929 0-1.41421358l8.29289322-8.29289322 8.2928932 8.29289322c.3905243.39052429.3905243 1.02368928 0 1.41421358l-.5857864.5857864c-.1952622.1952622-.4511845.2928932-.7071068.2928932zm-7-9.17157284-7.58578644 7.58578644.58578644.5857864 7-6.99999996 7 6.99999996.5857864-.5857864z" fill-rule="evenodd"/></symbol><symbol id="icon-image" viewBox="0 0 18 18"><path d="m10.0046024 0c.5497429 0 1.3179837.32258606 1.707238.71184039l4.5763192 4.57631922c.3931386.39313859.7118404 1.16760135.7118404 1.71431368v8.98899651c0 1.1092806-.8945138 2.0085302-1.9940603 2.0085302h-12.01187942c-1.10128908 0-1.99406028-.8926228-1.99406028-1.9950893v-14.00982141c0-1.10185739.88743329-1.99508929 1.99961498-1.99508929zm-3.49645283 10.1752453-3.89407257 6.7495552c.11705545.048464.24538859.0751995.37998328.0751995h10.60290092l-2.4329715-4.2154691-1.57494129 2.7288098zm8.49779013 6.8247547c.5463747 0 .9940603-.4506622.9940603-1.0085302v-8.98899651c0-.28393444-.2150684-.80332809-.4189472-1.0072069l-4.5763192-4.57631922c-.2038461-.20384606-.718603-.41894717-1.0001312-.41894717h-7.00498742c-.55709576 0-.99961498.44271433-.99961498.99508929v13.98991071l4.50814957-7.81026689 3.08089884 5.33809539 1.57494129-2.7288097 3.5875735 6.2159812zm-3.0059397-11c1.1045695 0 2 .8954305 2 2s-.8954305 2-2 2-2-.8954305-2-2 .8954305-2 2-2zm0 1c-.5522847 0-1 .44771525-1 1s.4477153 1 1 1 1-.44771525 1-1-.4477153-1-1-1z" fill-rule="evenodd"/></symbol><symbol id="icon-info" viewBox="0 0 18 18"><path d="m9 0c4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9zm0 7h-1.5l-.11662113.00672773c-.49733868.05776511-.88337887.48043643-.88337887.99327227 0 .47338693.32893365.86994729.77070917.97358929l.1126697.01968298.11662113.00672773h.5v3h-.5l-.11662113.0067277c-.42082504.0488782-.76196299.3590206-.85696816.7639815l-.01968298.1126697-.00672773.1166211.00672773.1166211c.04887817.4208251.35902055.761963.76398144.8569682l.1126697.019683.11662113.0067277h3l.1166211-.0067277c.4973387-.0577651.8833789-.4804365.8833789-.9932723 0-.4733869-.3289337-.8699473-.7707092-.9735893l-.1126697-.019683-.1166211-.0067277h-.5v-4l-.00672773-.11662113c-.04887817-.42082504-.35902055-.76196299-.76398144-.85696816l-.1126697-.01968298zm0-3.25c-.69035594 0-1.25.55964406-1.25 1.25s.55964406 1.25 1.25 1.25 1.25-.55964406 1.25-1.25-.55964406-1.25-1.25-1.25z" fill-rule="evenodd"/></symbol><symbol id="icon-institution" viewBox="0 0 18 18"><path d="m7 16.9998189v-2.0003623h4v2.0003623h2v-3.0005434h-8v3.0005434zm-3-10.00181122h-1.52632364c-.27614237 0-.5-.22389817-.5-.50009056 0-.13995446.05863589-.27350497.16166338-.36820841l1.23156713-1.13206327h-2.36690687v12.00217346h3v-2.0003623h-3v-1.0001811h3v-1.0001811h1v-4.00072448h-1zm10 0v2.00036224h-1v4.00072448h1v1.0001811h3v1.0001811h-3v2.0003623h3v-12.00217346h-2.3695309l1.2315671 1.13206327c.2033191.186892.2166633.50325042.0298051.70660631-.0946863.10304615-.2282126.16169266-.3681417.16169266zm3-3.00054336c.5522847 0 1 .44779634 1 1.00018112v13.00235456h-18v-13.00235456c0-.55238478.44771525-1.00018112 1-1.00018112h3.45499992l4.20535144-3.86558216c.19129876-.17584288.48537447-.17584288.67667324 0l4.2053514 3.86558216zm-4 3.00054336h-8v1.00018112h8zm-2 6.00108672h1v-4.00072448h-1zm-1 0v-4.00072448h-2v4.00072448zm-3 0v-4.00072448h-1v4.00072448zm8-4.00072448c.5522847 0 1 .44779634 1 1.00018112v2.00036226h-2v-2.00036226c0-.55238478.4477153-1.00018112 1-1.00018112zm-12 0c.55228475 0 1 .44779634 1 1.00018112v2.00036226h-2v-2.00036226c0-.55238478.44771525-1.00018112 1-1.00018112zm5.99868798-7.81907007-5.24205601 4.81852671h10.48411203zm.00131202 3.81834559c-.55228475 0-1-.44779634-1-1.00018112s.44771525-1.00018112 1-1.00018112 1 .44779634 1 1.00018112-.44771525 1.00018112-1 1.00018112zm-1 11.00199236v1.0001811h2v-1.0001811z" fill-rule="evenodd"/></symbol><symbol id="icon-location" viewBox="0 0 18 18"><path d="m9.39521328 16.2688008c.79596342-.7770119 1.59208152-1.6299956 2.33285652-2.5295081 1.4020032-1.7024324 2.4323601-3.3624519 2.9354918-4.871847.2228715-.66861448.3364384-1.29323246.3364384-1.8674457 0-3.3137085-2.6862915-6-6-6-3.36356866 0-6 2.60156856-6 6 0 .57421324.11356691 1.19883122.3364384 1.8674457.50313169 1.5093951 1.53348863 3.1694146 2.93549184 4.871847.74077492.8995125 1.53689309 1.7524962 2.33285648 2.5295081.13694479.1336842.26895677.2602648.39521328.3793207.12625651-.1190559.25826849-.2456365.39521328-.3793207zm-.39521328 1.7311992s-7-6-7-11c0-4 3.13400675-7 7-7 3.8659932 0 7 3.13400675 7 7 0 5-7 11-7 11zm0-8c-1.65685425 0-3-1.34314575-3-3s1.34314575-3 3-3c1.6568542 0 3 1.34314575 3 3s-1.3431458 3-3 3zm0-1c1.1045695 0 2-.8954305 2-2s-.8954305-2-2-2-2 .8954305-2 2 .8954305 2 2 2z" fill-rule="evenodd"/></symbol><symbol id="icon-minus" viewBox="0 0 16 16"><path d="m2.00087166 7h11.99825664c.5527662 0 1.0008717.44386482 1.0008717 1 0 .55228475-.4446309 1-1.0008717 1h-11.99825664c-.55276616 0-1.00087166-.44386482-1.00087166-1 0-.55228475.44463086-1 1.00087166-1z" fill-rule="evenodd"/></symbol><symbol id="icon-newsletter" viewBox="0 0 18 18"><path d="m9 11.8482489 2-1.1428571v-1.7053918h-4v1.7053918zm-3-1.7142857v-2.1339632h6v2.1339632l3-1.71428574v-6.41967746h-12v6.41967746zm10-5.3839632 1.5299989.95624934c.2923814.18273835.4700011.50320827.4700011.8479983v8.44575236c0 1.1045695-.8954305 2-2 2h-14c-1.1045695 0-2-.8954305-2-2v-8.44575236c0-.34479003.1776197-.66525995.47000106-.8479983l1.52999894-.95624934v-2.75c0-.55228475.44771525-1 1-1h12c.5522847 0 1 .44771525 1 1zm0 1.17924764v3.07075236l-7 4-7-4v-3.07075236l-1 .625v8.44575236c0 .5522847.44771525 1 1 1h14c.5522847 0 1-.4477153 1-1v-8.44575236zm-10-1.92924764h6v1h-6zm-1 2h8v1h-8z" fill-rule="evenodd"/></symbol><symbol id="icon-orcid" viewBox="0 0 18 18"><path d="m9 1c4.418278 0 8 3.581722 8 8s-3.581722 8-8 8-8-3.581722-8-8 3.581722-8 8-8zm-2.90107518 5.2732337h-1.41865256v7.1712107h1.41865256zm4.55867178.02508949h-2.99247027v7.14612121h2.91062487c.7673039 0 1.4476365-.1483432 2.0410182-.445034s1.0511995-.7152915 1.3734671-1.2558144c.3222677-.540523.4833991-1.1603247.4833991-1.85942385 0-.68545815-.1602789-1.30270225-.4808414-1.85175082-.3205625-.54904856-.7707074-.97532211-1.3504481-1.27883343-.5797408-.30351132-1.2413173-.45526471-1.9847495-.45526471zm-.1892674 1.07933542c.7877654 0 1.4143875.22336734 1.8798852.67010873.4654977.44674138.698243 1.05546001.698243 1.82617415 0 .74343221-.2310402 1.34447791-.6931277 1.80315511-.4620874.4586773-1.0750688.6880124-1.8389625.6880124h-1.46810075v-4.98745039zm-5.08652545-3.71099194c-.21825533 0-.410525.08444276-.57681478.25333081-.16628977.16888806-.24943341.36245684-.24943341.58071218 0 .22345188.08314364.41961891.24943341.58850696.16628978.16888806.35855945.25333082.57681478.25333082.233845 0 .43390938-.08314364.60019916-.24943342.16628978-.16628977.24943342-.36375592.24943342-.59240436 0-.233845-.08314364-.43131115-.24943342-.59240437s-.36635416-.24163862-.60019916-.24163862z" fill-rule="evenodd"/></symbol><symbol id="icon-plus" viewBox="0 0 16 16"><path d="m2.00087166 7h4.99912834v-4.99912834c0-.55276616.44386482-1.00087166 1-1.00087166.55228475 0 1 .44463086 1 1.00087166v4.99912834h4.9991283c.5527662 0 1.0008717.44386482 1.0008717 1 0 .55228475-.4446309 1-1.0008717 1h-4.9991283v4.9991283c0 .5527662-.44386482 1.0008717-1 1.0008717-.55228475 0-1-.4446309-1-1.0008717v-4.9991283h-4.99912834c-.55276616 0-1.00087166-.44386482-1.00087166-1 0-.55228475.44463086-1 1.00087166-1z" fill-rule="evenodd"/></symbol><symbol id="icon-print" viewBox="0 0 18 18"><path d="m16.0049107 5h-14.00982141c-.54941618 0-.99508929.4467783-.99508929.99961498v6.00077002c0 .5570958.44271433.999615.99508929.999615h1.00491071v-3h12v3h1.0049107c.5494162 0 .9950893-.4467783.9950893-.999615v-6.00077002c0-.55709576-.4427143-.99961498-.9950893-.99961498zm-2.0049107-1v-2.00208688c0-.54777062-.4519464-.99791312-1.0085302-.99791312h-7.9829396c-.55661731 0-1.0085302.44910695-1.0085302.99791312v2.00208688zm1 10v2.0018986c0 1.103521-.9019504 1.9981014-2.0085302 1.9981014h-7.9829396c-1.1092806 0-2.0085302-.8867064-2.0085302-1.9981014v-2.0018986h-1.00491071c-1.10185739 0-1.99508929-.8874333-1.99508929-1.999615v-6.00077002c0-1.10435686.8926228-1.99961498 1.99508929-1.99961498h1.00491071v-2.00208688c0-1.10341695.90195036-1.99791312 2.0085302-1.99791312h7.9829396c1.1092806 0 2.0085302.89826062 2.0085302 1.99791312v2.00208688h1.0049107c1.1018574 0 1.9950893.88743329 1.9950893 1.99961498v6.00077002c0 1.1043569-.8926228 1.999615-1.9950893 1.999615zm-1-3h-10v5.0018986c0 .5546075.44702548.9981014 1.0085302.9981014h7.9829396c.5565964 0 1.0085302-.4491701 1.0085302-.9981014zm-9 1h8v1h-8zm0 2h5v1h-5zm9-5c-.5522847 0-1-.44771525-1-1s.4477153-1 1-1 1 .44771525 1 1-.4477153 1-1 1z" fill-rule="evenodd"/></symbol><symbol id="icon-search" viewBox="0 0 22 22"><path d="M21.697 20.261a1.028 1.028 0 01.01 1.448 1.034 1.034 0 01-1.448-.01l-4.267-4.267A9.812 9.811 0 010 9.812a9.812 9.811 0 1117.43 6.182zM9.812 18.222A8.41 8.41 0 109.81 1.403a8.41 8.41 0 000 16.82z" fill-rule="evenodd"/></symbol><symbol id="icon-social-facebook" viewBox="0 0 24 24"><path d="m6.00368507 20c-1.10660471 0-2.00368507-.8945138-2.00368507-1.9940603v-12.01187942c0-1.10128908.89451376-1.99406028 1.99406028-1.99406028h12.01187942c1.1012891 0 1.9940603.89451376 1.9940603 1.99406028v12.01187942c0 1.1012891-.88679 1.9940603-2.0032184 1.9940603h-2.9570132v-6.1960818h2.0797387l.3114113-2.414723h-2.39115v-1.54164807c0-.69911803.1941355-1.1755439 1.1966615-1.1755439l1.2786739-.00055875v-2.15974763l-.2339477-.02492088c-.3441234-.03134957-.9500153-.07025255-1.6293054-.07025255-1.8435726 0-3.1057323 1.12531866-3.1057323 3.19187953v1.78079225h-2.0850778v2.414723h2.0850778v6.1960818z" fill-rule="evenodd"/></symbol><symbol id="icon-social-twitter" viewBox="0 0 24 24"><path d="m18.8767135 6.87445248c.7638174-.46908424 1.351611-1.21167363 1.6250764-2.09636345-.7135248.43394112-1.50406.74870123-2.3464594.91677702-.6695189-.73342162-1.6297913-1.19486605-2.6922204-1.19486605-2.0399895 0-3.6933555 1.69603749-3.6933555 3.78628909 0 .29642457.0314329.58673729.0942985.8617704-3.06469922-.15890802-5.78835241-1.66547825-7.60988389-3.9574208-.3174714.56076194-.49978171 1.21167363-.49978171 1.90536824 0 1.31404706.65223085 2.47224203 1.64236444 3.15218497-.60350999-.0198635-1.17401554-.1925232-1.67222562-.47366811v.04583885c0 1.83355406 1.27302891 3.36609966 2.96411421 3.71294696-.31118484.0886217-.63651445.1329326-.97441718.1329326-.2357461 0-.47149219-.0229194-.69466516-.0672303.47149219 1.5065703 1.83253297 2.6036468 3.44975116 2.632678-1.2651707 1.0160946-2.85724264 1.6196394-4.5891906 1.6196394-.29861172 0-.59093688-.0152796-.88011875-.0504227 1.63450624 1.0726291 3.57548241 1.6990934 5.66104951 1.6990934 6.79263079 0 10.50641749-5.7711113 10.50641749-10.7751859l-.0094298-.48894775c.7229547-.53478659 1.3516109-1.20250585 1.8419628-1.96190282-.6632323.30100846-1.3751855.50422736-2.1217148.59590507z" fill-rule="evenodd"/></symbol><symbol id="icon-social-youtube" viewBox="0 0 24 24"><path d="m10.1415 14.3973208-.0005625-5.19318431 4.863375 2.60554491zm9.963-7.92753362c-.6845625-.73643756-1.4518125-.73990314-1.803375-.7826454-2.518875-.18714178-6.2971875-.18714178-6.2971875-.18714178-.007875 0-3.7861875 0-6.3050625.18714178-.352125.04274226-1.1188125.04620784-1.8039375.7826454-.5394375.56084773-.7149375 1.8344515-.7149375 1.8344515s-.18 1.49597903-.18 2.99138042v1.4024082c0 1.495979.18 2.9913804.18 2.9913804s.1755 1.2736038.7149375 1.8344515c.685125.7364376 1.5845625.7133337 1.9850625.7901542 1.44.1420891 6.12.1859866 6.12.1859866s3.78225-.005776 6.301125-.1929178c.3515625-.0433198 1.1188125-.0467854 1.803375-.783223.5394375-.5608477.7155-1.8344515.7155-1.8344515s.18-1.4954014.18-2.9913804v-1.4024082c0-1.49540139-.18-2.99138042-.18-2.99138042s-.1760625-1.27360377-.7155-1.8344515z" fill-rule="evenodd"/></symbol><symbol id="icon-subject-medicine" viewBox="0 0 18 18"><path d="m12.5 8h-6.5c-1.65685425 0-3 1.34314575-3 3v1c0 1.6568542 1.34314575 3 3 3h1v-2h-.5c-.82842712 0-1.5-.6715729-1.5-1.5s.67157288-1.5 1.5-1.5h1.5 2 1 2c1.6568542 0 3-1.34314575 3-3v-1c0-1.65685425-1.3431458-3-3-3h-2v2h1.5c.8284271 0 1.5.67157288 1.5 1.5s-.6715729 1.5-1.5 1.5zm-5.5-1v-1h-3.5c-1.38071187 0-2.5-1.11928813-2.5-2.5s1.11928813-2.5 2.5-2.5h1.02786405c.46573528 0 .92507448.10843528 1.34164078.31671843l1.13382424.56691212c.06026365-1.05041141.93116291-1.88363055 1.99667093-1.88363055 1.1045695 0 2 .8954305 2 2h2c2.209139 0 4 1.790861 4 4v1c0 2.209139-1.790861 4-4 4h-2v1h2c1.1045695 0 2 .8954305 2 2s-.8954305 2-2 2h-2c0 1.1045695-.8954305 2-2 2s-2-.8954305-2-2h-1c-2.209139 0-4-1.790861-4-4v-1c0-2.209139 1.790861-4 4-4zm0-2v-2.05652691c-.14564246-.03538148-.28733393-.08714006-.42229124-.15461871l-1.15541752-.57770876c-.27771087-.13885544-.583937-.21114562-.89442719-.21114562h-1.02786405c-.82842712 0-1.5.67157288-1.5 1.5s.67157288 1.5 1.5 1.5zm4 1v1h1.5c.2761424 0 .5-.22385763.5-.5s-.2238576-.5-.5-.5zm-1 1v-5c0-.55228475-.44771525-1-1-1s-1 .44771525-1 1v5zm-2 4v5c0 .5522847.44771525 1 1 1s1-.4477153 1-1v-5zm3 2v2h2c.5522847 0 1-.4477153 1-1s-.4477153-1-1-1zm-4-1v-1h-.5c-.27614237 0-.5.2238576-.5.5s.22385763.5.5.5zm-3.5-9h1c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-1c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5z" fill-rule="evenodd"/></symbol><symbol id="icon-success" viewBox="0 0 18 18"><path d="m9 0c4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9zm3.4860198 4.98163161-4.71802968 5.50657859-2.62834168-2.02300024c-.42862421-.36730544-1.06564993-.30775346-1.42283677.13301307-.35718685.44076653-.29927542 1.0958383.12934879 1.46314377l3.40735508 2.7323063c.42215801.3385221 1.03700951.2798252 1.38749189-.1324571l5.38450527-6.33394549c.3613513-.43716226.3096573-1.09278382-.115462-1.46437175-.4251192-.37158792-1.0626796-.31842941-1.4240309.11873285z" fill-rule="evenodd"/></symbol><symbol id="icon-table" viewBox="0 0 18 18"><path d="m16.0049107 2c1.1018574 0 1.9950893.89706013 1.9950893 2.00585866v9.98828264c0 1.1078052-.8926228 2.0058587-1.9950893 2.0058587l-4.0059107-.001.001.001h-1l-.001-.001h-5l.001.001h-1l-.001-.001-3.00391071.001c-1.10185739 0-1.99508929-.8970601-1.99508929-2.0058587v-9.98828264c0-1.10780515.8926228-2.00585866 1.99508929-2.00585866zm-11.0059107 5h-3.999v6.9941413c0 .5572961.44630695 1.0058587.99508929 1.0058587h3.00391071zm6 0h-5v8h5zm5.0059107-4h-4.0059107v3h5.001v1h-5.001v7.999l4.0059107.001c.5487152 0 .9950893-.4488783.9950893-1.0058587v-9.98828264c0-.55729607-.446307-1.00585866-.9950893-1.00585866zm-12.5049107 9c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-1c-.27614237 0-.5-.2238576-.5-.5s.22385763-.5.5-.5zm12 0c.2761424 0 .5.2238576.5.5s-.2238576.5-.5.5h-2c-.2761424 0-.5-.2238576-.5-.5s.2238576-.5.5-.5zm-6 0c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-2c-.27614237 0-.5-.2238576-.5-.5s.22385763-.5.5-.5zm-6-2c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-1c-.27614237 0-.5-.2238576-.5-.5s.22385763-.5.5-.5zm12 0c.2761424 0 .5.2238576.5.5s-.2238576.5-.5.5h-2c-.2761424 0-.5-.2238576-.5-.5s.2238576-.5.5-.5zm-6 0c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-2c-.27614237 0-.5-.2238576-.5-.5s.22385763-.5.5-.5zm-6-2c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-1c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm12 0c.2761424 0 .5.22385763.5.5s-.2238576.5-.5.5h-2c-.2761424 0-.5-.22385763-.5-.5s.2238576-.5.5-.5zm-6 0c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-2c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm1.499-5h-5v3h5zm-6 0h-3.00391071c-.54871518 0-.99508929.44887827-.99508929 1.00585866v1.99414134h3.999z" fill-rule="evenodd"/></symbol><symbol id="icon-tick-circle" viewBox="0 0 24 24"><path d="m12 2c5.5228475 0 10 4.4771525 10 10s-4.4771525 10-10 10-10-4.4771525-10-10 4.4771525-10 10-10zm0 1c-4.97056275 0-9 4.02943725-9 9 0 4.9705627 4.02943725 9 9 9 4.9705627 0 9-4.0294373 9-9 0-4.97056275-4.0294373-9-9-9zm4.2199868 5.36606669c.3613514-.43716226.9989118-.49032077 1.424031-.11873285s.4768133 1.02720949.115462 1.46437175l-6.093335 6.94397871c-.3622945.4128716-.9897871.4562317-1.4054264.0971157l-3.89719065-3.3672071c-.42862421-.3673054-.48653564-1.0223772-.1293488-1.4631437s.99421256-.5003185 1.42283677-.1330131l3.11097438 2.6987741z" fill-rule="evenodd"/></symbol><symbol id="icon-tick" viewBox="0 0 16 16"><path d="m6.76799012 9.21106946-3.1109744-2.58349728c-.42862421-.35161617-1.06564993-.29460792-1.42283677.12733148s-.29927541 1.04903009.1293488 1.40064626l3.91576307 3.23873978c.41034319.3393961 1.01467563.2976897 1.37450571-.0948578l6.10568327-6.660841c.3613513-.41848908.3096572-1.04610608-.115462-1.4018218-.4251192-.35571573-1.0626796-.30482786-1.424031.11366122z" fill-rule="evenodd"/></symbol><symbol id="icon-update" viewBox="0 0 18 18"><path d="m1 13v1c0 .5522847.44771525 1 1 1h14c.5522847 0 1-.4477153 1-1v-1h-1v-10h-14v10zm16-1h1v2c0 1.1045695-.8954305 2-2 2h-14c-1.1045695 0-2-.8954305-2-2v-2h1v-9c0-.55228475.44771525-1 1-1h14c.5522847 0 1 .44771525 1 1zm-1 0v1h-4.5857864l-1 1h-2.82842716l-1-1h-4.58578644v-1h5l1 1h2l1-1zm-13-8h12v7h-12zm1 1v5h10v-5zm1 1h4v1h-4zm0 2h4v1h-4z" fill-rule="evenodd"/></symbol><symbol id="icon-upload" viewBox="0 0 18 18"><path d="m10.0046024 0c.5497429 0 1.3179837.32258606 1.707238.71184039l4.5763192 4.57631922c.3931386.39313859.7118404 1.16760135.7118404 1.71431368v8.98899651c0 1.1092806-.8945138 2.0085302-1.9940603 2.0085302h-12.01187942c-1.10128908 0-1.99406028-.8926228-1.99406028-1.9950893v-14.00982141c0-1.10185739.88743329-1.99508929 1.99961498-1.99508929zm0 1h-7.00498742c-.55709576 0-.99961498.44271433-.99961498.99508929v14.00982141c0 .5500396.44491393.9950893.99406028.9950893h12.01187942c.5463747 0 .9940603-.4506622.9940603-1.0085302v-8.98899651c0-.28393444-.2150684-.80332809-.4189472-1.0072069l-4.5763192-4.57631922c-.2038461-.20384606-.718603-.41894717-1.0001312-.41894717zm-1.85576936 4.14572769c.19483374-.19483375.51177826-.19377714.70556874.00001334l2.59099082 2.59099079c.1948411.19484112.1904373.51514474.0027906.70279143-.1932998.19329987-.5046517.19237083-.7001856-.00692852l-1.74638687-1.7800176v6.14827687c0 .2717771-.23193359.492096-.5.492096-.27614237 0-.5-.216372-.5-.492096v-6.14827641l-1.74627892 1.77990922c-.1933927.1971171-.51252214.19455839-.70016883.0069117-.19329987-.19329988-.19100584-.50899493.00277731-.70277808z" fill-rule="evenodd"/></symbol><symbol id="icon-video" viewBox="0 0 18 18"><path d="m16.0049107 2c1.1018574 0 1.9950893.89706013 1.9950893 2.00585866v9.98828264c0 1.1078052-.8926228 2.0058587-1.9950893 2.0058587h-14.00982141c-1.10185739 0-1.99508929-.8970601-1.99508929-2.0058587v-9.98828264c0-1.10780515.8926228-2.00585866 1.99508929-2.00585866zm0 1h-14.00982141c-.54871518 0-.99508929.44887827-.99508929 1.00585866v9.98828264c0 .5572961.44630695 1.0058587.99508929 1.0058587h14.00982141c.5487152 0 .9950893-.4488783.9950893-1.0058587v-9.98828264c0-.55729607-.446307-1.00585866-.9950893-1.00585866zm-8.30912922 2.24944486 4.60460462 2.73982242c.9365543.55726659.9290753 1.46522435 0 2.01804082l-4.60460462 2.7398224c-.93655425.5572666-1.69578148.1645632-1.69578148-.8937585v-5.71016863c0-1.05087579.76670616-1.446575 1.69578148-.89375851zm-.67492769.96085624v5.5750128c0 .2995102-.10753745.2442517.16578928.0847713l4.58452283-2.67497259c.3050619-.17799716.3051624-.21655446 0-.39461026l-4.58452283-2.67497264c-.26630747-.15538481-.16578928-.20699944-.16578928.08477139z" fill-rule="evenodd"/></symbol><symbol id="icon-warning" viewBox="0 0 18 18"><path d="m9 11.75c.69035594 0 1.25.5596441 1.25 1.25s-.55964406 1.25-1.25 1.25-1.25-.5596441-1.25-1.25.55964406-1.25 1.25-1.25zm.41320045-7.75c.55228475 0 1.00000005.44771525 1.00000005 1l-.0034543.08304548-.3333333 4c-.043191.51829212-.47645714.91695452-.99654578.91695452h-.15973424c-.52008864 0-.95335475-.3986624-.99654576-.91695452l-.33333333-4c-.04586475-.55037702.36312325-1.03372649.91350028-1.07959124l.04148683-.00259031zm-.41320045 14c-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9 4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9z" fill-rule="evenodd"/></symbol><symbol id="icon-checklist-banner" viewBox="0 0 56.69 56.69"><path style="fill:none" d="M0 0h56.69v56.69H0z"/><clipPath id="b"><use xlink:href="#a" style="overflow:visible"/></clipPath><path d="M21.14 34.46c0-6.77 5.48-12.26 12.24-12.26s12.24 5.49 12.24 12.26-5.48 12.26-12.24 12.26c-6.76-.01-12.24-5.49-12.24-12.26zm19.33 10.66 10.23 9.22s1.21 1.09 2.3-.12l2.09-2.32s1.09-1.21-.12-2.3l-10.23-9.22m-19.29-5.92c0-4.38 3.55-7.94 7.93-7.94s7.93 3.55 7.93 7.94c0 4.38-3.55 7.94-7.93 7.94-4.38-.01-7.93-3.56-7.93-7.94zm17.58 12.99 4.14-4.81" style="clip-path:url(#b);fill:none;stroke:#01324b;stroke-width:2;stroke-linecap:round"/><path d="M8.26 9.75H28.6M8.26 15.98H28.6m-20.34 6.2h12.5m14.42-5.2V4.86s0-2.93-2.93-2.93H4.13s-2.93 0-2.93 2.93v37.57s0 2.93 2.93 2.93h15.01M8.26 9.75H28.6M8.26 15.98H28.6m-20.34 6.2h12.5" style="clip-path:url(#b);fill:none;stroke:#01324b;stroke-width:2;stroke-linecap:round;stroke-linejoin:round"/></symbol><symbol id="icon-chevron-down" viewBox="0 0 16 16"><path d="m5.58578644 3-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z" fill-rule="evenodd" transform="matrix(0 1 -1 0 11 1)"/></symbol><symbol id="icon-eds-i-arrow-right-medium" viewBox="0 0 24 24"><path d="m12.728 3.293 7.98 7.99a.996.996 0 0 1 .281.561l.011.157c0 .32-.15.605-.384.788l-7.908 7.918a1 1 0 0 1-1.416-1.414L17.576 13H4a1 1 0 0 1 0-2h13.598l-6.285-6.293a1 1 0 0 1-.082-1.32l.083-.095a1 1 0 0 1 1.414.001Z"/></symbol><symbol id="icon-eds-i-chevron-down-medium" viewBox="0 0 16 16"><path d="m2.00087166 7h4.99912834v-4.99912834c0-.55276616.44386482-1.00087166 1-1.00087166.55228475 0 1 .44463086 1 1.00087166v4.99912834h4.9991283c.5527662 0 1.0008717.44386482 1.0008717 1 0 .55228475-.4446309 1-1.0008717 1h-4.9991283v4.9991283c0 .5527662-.44386482 1.0008717-1 1.0008717-.55228475 0-1-.4446309-1-1.0008717v-4.9991283h-4.99912834c-.55276616 0-1.00087166-.44386482-1.00087166-1 0-.55228475.44463086-1 1.00087166-1z" fill-rule="evenodd"/></symbol><symbol id="icon-eds-i-chevron-down-small" viewBox="0 0 16 16"><path d="M13.692 5.278a1 1 0 0 1 .03 1.414L9.103 11.51a1.491 1.491 0 0 1-2.188.019L2.278 6.692a1 1 0 0 1 1.444-1.384L8 9.771l4.278-4.463a1 1 0 0 1 1.318-.111l.096.081Z"/></symbol><symbol id="icon-eds-i-chevron-right-medium" viewBox="0 0 10 10"><path d="m5.96738168 4.70639573 2.39518594-2.41447274c.37913917-.38219212.98637524-.38972225 1.35419292-.01894278.37750606.38054586.37784436.99719163-.00013556 1.37821513l-4.03074001 4.06319683c-.37758093.38062133-.98937525.38100976-1.367372-.00003075l-4.03091981-4.06337806c-.37759778-.38063832-.38381821-.99150444-.01600053-1.3622839.37750607-.38054587.98772445-.38240057 1.37006824.00302197l2.39538588 2.4146743.96295325.98624457z" fill-rule="evenodd" transform="matrix(0 -1 1 0 0 10)"/></symbol><symbol id="icon-eds-i-chevron-right-small" viewBox="0 0 10 10"><path d="m5.96738168 4.70639573 2.39518594-2.41447274c.37913917-.38219212.98637524-.38972225 1.35419292-.01894278.37750606.38054586.37784436.99719163-.00013556 1.37821513l-4.03074001 4.06319683c-.37758093.38062133-.98937525.38100976-1.367372-.00003075l-4.03091981-4.06337806c-.37759778-.38063832-.38381821-.99150444-.01600053-1.3622839.37750607-.38054587.98772445-.38240057 1.37006824.00302197l2.39538588 2.4146743.96295325.98624457z" fill-rule="evenodd" transform="matrix(0 -1 1 0 0 10)"/></symbol><symbol id="icon-eds-i-chevron-up-medium" viewBox="0 0 16 16"><path d="m2.00087166 7h11.99825664c.5527662 0 1.0008717.44386482 1.0008717 1 0 .55228475-.4446309 1-1.0008717 1h-11.99825664c-.55276616 0-1.00087166-.44386482-1.00087166-1 0-.55228475.44463086-1 1.00087166-1z" fill-rule="evenodd"/></symbol><symbol id="icon-eds-i-close-medium" viewBox="0 0 16 16"><path d="m2.29679575 12.2772478c-.39658757.3965876-.39438847 1.0328109-.00062148 1.4265779.39651227.3965123 1.03246768.3934888 1.42657791-.0006214l4.27724782-4.27724787 4.2772478 4.27724787c.3965876.3965875 1.0328109.3943884 1.4265779.0006214.3965123-.3965122.3934888-1.0324677-.0006214-1.4265779l-4.27724787-4.2772478 4.27724787-4.27724782c.3965875-.39658757.3943884-1.03281091.0006214-1.42657791-.3965122-.39651226-1.0324677-.39348875-1.4265779.00062148l-4.2772478 4.27724782-4.27724782-4.27724782c-.39658757-.39658757-1.03281091-.39438847-1.42657791-.00062148-.39651226.39651227-.39348875 1.03246768.00062148 1.42657791l4.27724782 4.27724782z" fill-rule="evenodd"/></symbol><symbol id="icon-eds-i-download-medium" viewBox="0 0 16 16"><path d="m12.9975267 12.999368c.5467123 0 1.0024733.4478567 1.0024733 1.000316 0 .5563109-.4488226 1.000316-1.0024733 1.000316h-9.99505341c-.54671233 0-1.00247329-.4478567-1.00247329-1.000316 0-.5563109.44882258-1.000316 1.00247329-1.000316zm-4.9975267-11.999368c.55228475 0 1 .44497754 1 .99589209v6.80214418l2.4816273-2.48241149c.3928222-.39294628 1.0219732-.4006883 1.4030652-.01947579.3911302.39125371.3914806 1.02525073-.0001404 1.41699553l-4.17620792 4.17752758c-.39120769.3913313-1.02508144.3917306-1.41671995-.0000316l-4.17639421-4.17771394c-.39122513-.39134876-.39767006-1.01940351-.01657797-1.40061601.39113012-.39125372 1.02337105-.3931606 1.41951349.00310701l2.48183446 2.48261871v-6.80214418c0-.55001601.44386482-.99589209 1-.99589209z" fill-rule="evenodd"/></symbol><symbol id="icon-eds-i-info-filled-medium" viewBox="0 0 18 18"><path d="m9 0c4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9zm0 7h-1.5l-.11662113.00672773c-.49733868.05776511-.88337887.48043643-.88337887.99327227 0 .47338693.32893365.86994729.77070917.97358929l.1126697.01968298.11662113.00672773h.5v3h-.5l-.11662113.0067277c-.42082504.0488782-.76196299.3590206-.85696816.7639815l-.01968298.1126697-.00672773.1166211.00672773.1166211c.04887817.4208251.35902055.761963.76398144.8569682l.1126697.019683.11662113.0067277h3l.1166211-.0067277c.4973387-.0577651.8833789-.4804365.8833789-.9932723 0-.4733869-.3289337-.8699473-.7707092-.9735893l-.1126697-.019683-.1166211-.0067277h-.5v-4l-.00672773-.11662113c-.04887817-.42082504-.35902055-.76196299-.76398144-.85696816l-.1126697-.01968298zm0-3.25c-.69035594 0-1.25.55964406-1.25 1.25s.55964406 1.25 1.25 1.25 1.25-.55964406 1.25-1.25-.55964406-1.25-1.25-1.25z" fill-rule="evenodd"/></symbol><symbol id="icon-eds-i-mail-medium" viewBox="0 0 24 24"><path d="m19.462 0c1.413 0 2.538 1.184 2.538 2.619v12.762c0 1.435-1.125 2.619-2.538 2.619h-16.924c-1.413 0-2.538-1.184-2.538-2.619v-12.762c0-1.435 1.125-2.619 2.538-2.619zm.538 5.158-7.378 6.258a2.549 2.549 0 0 1 -3.253-.008l-7.369-6.248v10.222c0 .353.253.619.538.619h16.924c.285 0 .538-.266.538-.619zm-.538-3.158h-16.924c-.264 0-.5.228-.534.542l8.65 7.334c.2.165.492.165.684.007l8.656-7.342-.001-.025c-.044-.3-.274-.516-.531-.516z"/></symbol><symbol id="icon-eds-i-menu-medium" viewBox="0 0 24 24"><path d="M21 4a1 1 0 0 1 0 2H3a1 1 0 1 1 0-2h18Zm-4 7a1 1 0 0 1 0 2H3a1 1 0 0 1 0-2h14Zm4 7a1 1 0 0 1 0 2H3a1 1 0 0 1 0-2h18Z"/></symbol><symbol id="icon-eds-i-search-medium" viewBox="0 0 24 24"><path d="M11 1c5.523 0 10 4.477 10 10 0 2.4-.846 4.604-2.256 6.328l3.963 3.965a1 1 0 0 1-1.414 1.414l-3.965-3.963A9.959 9.959 0 0 1 11 21C5.477 21 1 16.523 1 11S5.477 1 11 1Zm0 2a8 8 0 1 0 0 16 8 8 0 0 0 0-16Z"/></symbol><symbol id="icon-eds-i-user-single-medium" viewBox="0 0 24 24"><path d="M12 1a5 5 0 1 1 0 10 5 5 0 0 1 0-10Zm0 2a3 3 0 1 0 0 6 3 3 0 0 0 0-6Zm-.406 9.008a8.965 8.965 0 0 1 6.596 2.494A9.161 9.161 0 0 1 21 21.025V22a1 1 0 0 1-1 1H4a1 1 0 0 1-1-1v-.985c.05-4.825 3.815-8.777 8.594-9.007Zm.39 1.992-.299.006c-3.63.175-6.518 3.127-6.678 6.775L5 21h13.998l-.009-.268a7.157 7.157 0 0 0-1.97-4.573l-.214-.213A6.967 6.967 0 0 0 11.984 14Z"/></symbol><symbol id="icon-eds-i-warning-filled-medium" viewBox="0 0 18 18"><path d="m9 11.75c.69035594 0 1.25.5596441 1.25 1.25s-.55964406 1.25-1.25 1.25-1.25-.5596441-1.25-1.25.55964406-1.25 1.25-1.25zm.41320045-7.75c.55228475 0 1.00000005.44771525 1.00000005 1l-.0034543.08304548-.3333333 4c-.043191.51829212-.47645714.91695452-.99654578.91695452h-.15973424c-.52008864 0-.95335475-.3986624-.99654576-.91695452l-.33333333-4c-.04586475-.55037702.36312325-1.03372649.91350028-1.07959124l.04148683-.00259031zm-.41320045 14c-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9 4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9z" fill-rule="evenodd"/></symbol><symbol id="icon-expand-image" viewBox="0 0 18 18"><path d="m7.49754099 11.9178212c.38955542-.3895554.38761957-1.0207846-.00290473-1.4113089-.39324695-.3932469-1.02238878-.3918247-1.41130883-.0029047l-4.10273549 4.1027355.00055454-3.5103985c.00008852-.5603185-.44832171-1.006032-1.00155062-1.0059446-.53903074.0000852-.97857527.4487442-.97866268 1.0021075l-.00093318 5.9072465c-.00008751.553948.44841131 1.001882 1.00174994 1.0017946l5.906983-.0009331c.5539233-.0000875 1.00197907-.4486389 1.00206646-1.0018679.00008515-.5390307-.45026621-.9784332-1.00588841-.9783454l-3.51010549.0005545zm3.00571741-5.83449376c-.3895554.38955541-.3876196 1.02078454.0029047 1.41130883.393247.39324696 1.0223888.39182478 1.4113089.00290473l4.1027355-4.10273549-.0005546 3.5103985c-.0000885.56031852.4483217 1.006032 1.0015506 1.00594461.5390308-.00008516.9785753-.44874418.9786627-1.00210749l.0009332-5.9072465c.0000875-.553948-.4484113-1.00188204-1.0017499-1.00179463l-5.906983.00093313c-.5539233.00008751-1.0019791.44863892-1.0020665 1.00186784-.0000852.53903074.4502662.97843325 1.0058884.97834547l3.5101055-.00055449z" fill-rule="evenodd"/></symbol><symbol id="icon-github" viewBox="0 0 100 100"><path fill-rule="evenodd" clip-rule="evenodd" d="M48.854 0C21.839 0 0 22 0 49.217c0 21.756 13.993 40.172 33.405 46.69 2.427.49 3.316-1.059 3.316-2.362 0-1.141-.08-5.052-.08-9.127-13.59 2.934-16.42-5.867-16.42-5.867-2.184-5.704-5.42-7.17-5.42-7.17-4.448-3.015.324-3.015.324-3.015 4.934.326 7.523 5.052 7.523 5.052 4.367 7.496 11.404 5.378 14.235 4.074.404-3.178 1.699-5.378 3.074-6.6-10.839-1.141-22.243-5.378-22.243-24.283 0-5.378 1.94-9.778 5.014-13.2-.485-1.222-2.184-6.275.486-13.038 0 0 4.125-1.304 13.426 5.052a46.97 46.97 0 0 1 12.214-1.63c4.125 0 8.33.571 12.213 1.63 9.302-6.356 13.427-5.052 13.427-5.052 2.67 6.763.97 11.816.485 13.038 3.155 3.422 5.015 7.822 5.015 13.2 0 18.905-11.404 23.06-22.324 24.283 1.78 1.548 3.316 4.481 3.316 9.126 0 6.6-.08 11.897-.08 13.526 0 1.304.89 2.853 3.316 2.364 19.412-6.52 33.405-24.935 33.405-46.691C97.707 22 75.788 0 48.854 0z"/></symbol><symbol id="icon-springer-arrow-left"><path d="M15 7a1 1 0 000-2H3.385l2.482-2.482a.994.994 0 00.02-1.403 1.001 1.001 0 00-1.417 0L.294 5.292a1.001 1.001 0 000 1.416l4.176 4.177a.991.991 0 001.4.016 1 1 0 00-.003-1.42L3.385 7H15z"/></symbol><symbol id="icon-springer-arrow-right"><path d="M1 7a1 1 0 010-2h11.615l-2.482-2.482a.994.994 0 01-.02-1.403 1.001 1.001 0 011.417 0l4.176 4.177a1.001 1.001 0 010 1.416l-4.176 4.177a.991.991 0 01-1.4.016 1 1 0 01.003-1.42L12.615 7H1z"/></symbol><symbol id="icon-submit-open" viewBox="0 0 16 17"><path d="M12 0c1.10457 0 2 .895431 2 2v5c0 .276142-.223858.5-.5.5S13 7.276142 13 7V2c0-.512836-.38604-.935507-.883379-.993272L12 1H6v3c0 1.10457-.89543 2-2 2H1v8c0 .512836.38604.935507.883379.993272L2 15h6.5c.276142 0 .5.223858.5.5s-.223858.5-.5.5H2c-1.104569 0-2-.89543-2-2V5.828427c0-.530433.210714-1.039141.585786-1.414213L4.414214.585786C4.789286.210714 5.297994 0 5.828427 0H12Zm3.41 11.14c.250899.250899.250274.659726 0 .91-.242954.242954-.649606.245216-.9-.01l-1.863671-1.900337.001043 5.869492c0 .356992-.289839.637138-.647372.637138-.347077 0-.647371-.285256-.647371-.637138l-.001043-5.869492L9.5 12.04c-.253166.258042-.649726.260274-.9.01-.242954-.242954-.252269-.657731 0-.91l2.942184-2.951303c.250908-.250909.66127-.252277.91353-.000017L15.41 11.14ZM5 1.413 1.413 5H4c.552285 0 1-.447715 1-1V1.413ZM11 3c.276142 0 .5.223858.5.5s-.223858.5-.5.5H7.5c-.276142 0-.5-.223858-.5-.5s.223858-.5.5-.5H11Zm0 2c.276142 0 .5.223858.5.5s-.223858.5-.5.5H7.5c-.276142 0-.5-.223858-.5-.5s.223858-.5.5-.5H11Z" fill-rule="nonzero"/></symbol></svg> </div> </footer> <div class="c-site-messages message u-hide u-hide-print c-site-messages--nature-briefing c-site-messages--nature-briefing-email-variant c-site-messages--nature-briefing-redesign-2020 sans-serif " data-component-id="nature-briefing-banner" data-component-expirydays="30" data-component-trigger-scroll-percentage="15" data-track="in-view" data-track-action="in-view" data-track-category="nature briefing" data-track-label="Briefing banner visible: Flagship"> <div class="c-site-messages__banner-large"> <div class="c-site-messages__close-container"> <button class="c-site-messages__close" data-track="click" data-track-category="nature briefing" data-track-label="Briefing banner dismiss: Flagship"> <svg width="25px" height="25px" focusable="false" aria-hidden="true" viewBox="0 0 25 25" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <title>Close banner</title> <defs></defs> <g stroke="none" stroke-width="1" fill="none" fill-rule="evenodd"> <rect opacity="0" x="0" y="0" width="25" height="25"></rect> <path d="M6.29679575,16.2772478 C5.90020818,16.6738354 5.90240728,17.3100587 6.29617427,17.7038257 C6.69268654,18.100338 7.32864195,18.0973145 7.72275218,17.7032043 L12,13.4259564 L16.2772478,17.7032043 C16.6738354,18.0997918 17.3100587,18.0975927 17.7038257,17.7038257 C18.100338,17.3073135 18.0973145,16.671358 17.7032043,16.2772478 L13.4259564,12 L17.7032043,7.72275218 C18.0997918,7.32616461 18.0975927,6.68994127 17.7038257,6.29617427 C17.3073135,5.89966201 16.671358,5.90268552 16.2772478,6.29679575 L12,10.5740436 L7.72275218,6.29679575 C7.32616461,5.90020818 6.68994127,5.90240728 6.29617427,6.29617427 C5.89966201,6.69268654 5.90268552,7.32864195 6.29679575,7.72275218 L10.5740436,12 L6.29679575,16.2772478 Z" fill="#ffffff"></path> </g> </svg> <span class="visually-hidden">Close</span> </button> </div> <div class="c-site-messages__form-container"> <div class="grid grid-12 last"> <div class="grid grid-4"> <img alt="Nature Briefing" src="/static/images/logos/nature-briefing-logo-n150-white-d81c9da3ec.svg" width="250" height="40"> <p class="c-site-messages--nature-briefing__strapline extra-tight-line-height">Sign up for the <em>Nature Briefing</em> newsletter — what matters in science, free to your inbox daily.</p> </div> <div class="grid grid-8 last"> <form action="https://www.nature.com/briefing/briefing" method="post" data-location="banner" data-track="signup_nature_briefing_banner" data-track-action="transmit-form" data-track-category="nature briefing" data-track-label="Briefing banner submit: Flagship"> <input id="briefing-banner-signup-form-input-track-originReferralPoint" type="hidden" name="track_originReferralPoint" value="MainBriefingBanner"> <input id="briefing-banner-signup-form-input-track-formType" type="hidden" name="track_formType" value="DirectEmailBanner"> <input type="hidden" value="false" name="gdpr_tick" id="gdpr_tick_banner"> <input type="hidden" value="false" name="marketing" id="marketing_input_banner"> <input type="hidden" value="false" name="marketing_tick" id="marketing_tick_banner"> <input type="hidden" value="MainBriefingBanner" name="brieferEntryPoint" id="brieferEntryPoint_banner"> <label class="nature-briefing-banner__email-label" for="emailAddress">Email address</label> <div class="nature-briefing-banner__email-wrapper"> <input class="nature-briefing-banner__email-input box-sizing text14" type="email" id="emailAddress" name="emailAddress" value="" placeholder="e.g. jo.smith@university.ac.uk" required data-test-element="briefing-emailbanner-email-input"> <input type="hidden" value="true" name="N:nature_briefing_daily" id="defaultNewsletter_banner"> <button type="submit" class="nature-briefing-banner__submit-button box-sizing text14" data-test-element="briefing-emailbanner-signup-button">Sign up</button> </div> <div class="nature-briefing-banner__checkbox-wrapper grid grid-12 last"> <input class="nature-briefing-banner__checkbox-checkbox" id="gdpr-briefing-banner-checkbox" type="checkbox" name="gdpr" value="true" data-test-element="briefing-emailbanner-gdpr-checkbox" required> <label class="nature-briefing-banner__checkbox-label box-sizing text13 sans-serif block tighten-line-height" for="gdpr-briefing-banner-checkbox">I agree my information will be processed in accordance with the <em>Nature</em> and Springer Nature Limited <a href="https://www.nature.com/info/privacy">Privacy Policy</a>.</label> </div> </form> </div> </div> </div> </div> <div class="c-site-messages__banner-small"> <div class="c-site-messages__close-container"> <button class="c-site-messages__close" data-track="click" data-track-category="nature briefing" data-track-label="Briefing banner dismiss: Flagship"> <svg width="25px" height="25px" focusable="false" aria-hidden="true" viewBox="0 0 25 25" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <title>Close banner</title> <defs></defs> <g stroke="none" stroke-width="1" fill="none" fill-rule="evenodd"> <rect opacity="0" x="0" y="0" width="25" height="25"></rect> <path d="M6.29679575,16.2772478 C5.90020818,16.6738354 5.90240728,17.3100587 6.29617427,17.7038257 C6.69268654,18.100338 7.32864195,18.0973145 7.72275218,17.7032043 L12,13.4259564 L16.2772478,17.7032043 C16.6738354,18.0997918 17.3100587,18.0975927 17.7038257,17.7038257 C18.100338,17.3073135 18.0973145,16.671358 17.7032043,16.2772478 L13.4259564,12 L17.7032043,7.72275218 C18.0997918,7.32616461 18.0975927,6.68994127 17.7038257,6.29617427 C17.3073135,5.89966201 16.671358,5.90268552 16.2772478,6.29679575 L12,10.5740436 L7.72275218,6.29679575 C7.32616461,5.90020818 6.68994127,5.90240728 6.29617427,6.29617427 C5.89966201,6.69268654 5.90268552,7.32864195 6.29679575,7.72275218 L10.5740436,12 L6.29679575,16.2772478 Z" fill="#ffffff"></path> </g> </svg> <span class="visually-hidden">Close</span> </button> </div> <div class="c-site-messages__content text14"> <span class="c-site-messages--nature-briefing__strapline strong">Get the most important science stories of the day, free in your inbox.</span> <a class="nature-briefing__link text14 sans-serif" data-track="click" data-track-category="nature briefing" data-track-label="Small-screen banner CTA to site" data-test-element="briefing-banner-link" target="_blank" rel="noreferrer noopener" href="https://www.nature.com/briefing/signup/?brieferEntryPoint=MainBriefingBanner">Sign up for Nature Briefing </a> </div> </div> </div> <noscript> <img hidden src="https://verify.nature.com/verify/nature.png" width="0" height="0" style="display: none" alt=""> </noscript> <script src="//content.readcube.com/ping?doi=10.1038/s41566-021-00836-5&format=js&last_modified=2021-07-22" async></script> </body> </html>

CINXE.COM

Advances in Brillouin–Mandelstam light-scattering spectroscopy | Nature Photonics