偏振 - 维基百科，自由的百科全书

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</a> <button aria-controls="toc-理論概述-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> 开关理論概述子章节 </button> <ul id="toc-理論概述-sublist" class="vector-toc-list"> <li id="toc-橫電磁波" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#橫電磁波"> <div class="vector-toc-text"> 2.1 橫電磁波 </div> </a> <ul id="toc-橫電磁波-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-偏振態" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#偏振態"> <div class="vector-toc-text"> 2.2 偏振態 </div> </a> <ul id="toc-偏振態-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-非偏振光" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#非偏振光"> <div class="vector-toc-text"> 2.3 非偏振光 </div> </a> <ul id="toc-非偏振光-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-其它種類偏振" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#其它種類偏振"> <div class="vector-toc-text"> 2.4 其它種類偏振 </div> </a> <ul id="toc-其它種類偏振-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-數學表述" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#數學表述"> <div class="vector-toc-text"> 3 數學表述 </div> </a> <button aria-controls="toc-數學表述-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> 开关數學表述子章节 </button> <ul id="toc-數學表述-sublist" class="vector-toc-list"> <li id="toc-偏振橢圓" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#偏振橢圓"> <div class="vector-toc-text"> 3.1 偏振橢圓 </div> </a> <ul id="toc-偏振橢圓-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-瓊斯向量與瓊斯矩陣" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#瓊斯向量與瓊斯矩陣"> <div class="vector-toc-text"> 3.2 瓊斯向量與瓊斯矩陣 </div> </a> <ul id="toc-瓊斯向量與瓊斯矩陣-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-斯托克斯參數與穆勒矩陣" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#斯托克斯參數與穆勒矩陣"> <div class="vector-toc-text"> 3.3 斯托克斯參數與穆勒矩陣 </div> </a> <ul id="toc-斯托克斯參數與穆勒矩陣-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-偏振測量技術" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#偏振測量技術"> <div class="vector-toc-text"> 4 偏振測量技術 </div> </a> <button aria-controls="toc-偏振測量技術-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> 开关偏振測量技術子章节 </button> <ul id="toc-偏振測量技術-sublist" class="vector-toc-list"> <li id="toc-測量應力" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#測量應力"> <div class="vector-toc-text"> 4.1 測量應力 </div> </a> <ul id="toc-測量應力-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-橢圓偏振測量術" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#橢圓偏振測量術"> <div class="vector-toc-text"> 4.2 橢圓偏振測量術 </div> </a> <ul id="toc-橢圓偏振測量術-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-地質學" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#地質學"> <div class="vector-toc-text"> 4.3 地質學 </div> </a> <ul id="toc-地質學-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-地震學" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#地震學"> <div class="vector-toc-text"> 4.4 地震學 </div> </a> <ul id="toc-地震學-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-化學" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#化學"> <div class="vector-toc-text"> 4.5 化學 </div> </a> <ul id="toc-化學-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-天文學" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#天文學"> <div class="vector-toc-text"> 4.6 天文學 </div> </a> <ul id="toc-天文學-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-重要應用" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#重要應用"> <div class="vector-toc-text"> 5 重要應用 </div> </a> <button aria-controls="toc-重要應用-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> 开关重要應用子章节 </button> <ul id="toc-重要應用-sublist" class="vector-toc-list"> <li id="toc-偏光太陽鏡" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#偏光太陽鏡"> <div class="vector-toc-text"> 5.1 偏光太陽鏡 </div> </a> <ul id="toc-偏光太陽鏡-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-天空中的偏振光" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#天空中的偏振光"> <div class="vector-toc-text"> 5.2 天空中的偏振光 </div> </a> <ul id="toc-天空中的偏振光-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-液晶顯示器" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#液晶顯示器"> <div class="vector-toc-text"> 5.3 液晶顯示器 </div> </a> <ul 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id="toc-註釋" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#註釋"> <div class="vector-toc-text"> 7 註釋 </div> </a> <ul id="toc-註釋-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參考文獻" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參考文獻"> <div class="vector-toc-text"> 8 參考文獻 </div> </a> <ul id="toc-參考文獻-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="开关目录" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > 开关目录 </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">偏振</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="前往另一种语言写成的文章。57种语言可用" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-57" aria-hidden="true" > 57种语言 </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%A8%E1%89%A5%E1%88%AD%E1%88%83%E1%8A%95_%E1%8B%8B%E1%88%88%E1%89%B3" title="የብርሃን ዋለታ – 阿姆哈拉语" lang="am" hreflang="am" data-title="የብርሃን ዋለታ" data-language-autonym="አማርኛ" data-language-local-name="阿姆哈拉语" class="interlanguage-link-target">አማርኛ</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D8%B3%D8%AA%D9%82%D8%B7%D8%A7%D8%A8_(%D9%81%D9%8A%D8%B2%D9%8A%D8%A7%D8%A1)" title="استقطاب (فيزياء) – 阿拉伯语" lang="ar" hreflang="ar" data-title="استقطاب (فيزياء)" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Polarizaci%C3%B3n_electromagn%C3%A9tica" title="Polarización electromagnética – 阿斯图里亚斯语" lang="ast" hreflang="ast" data-title="Polarización electromagnética" data-language-autonym="Asturianu" data-language-local-name="阿斯图里亚斯语" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%B0%D0%BB%D1%8F%D1%80%D1%8B%D0%B7%D0%B0%D1%86%D1%8B%D1%8F_%D1%81%D0%B2%D1%8F%D1%82%D0%BB%D0%B0" title="Палярызацыя святла – 白俄罗斯语" lang="be" hreflang="be" data-title="Палярызацыя святла" data-language-autonym="Беларуская" data-language-local-name="白俄罗斯语" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D1%8F%D1%80%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F_(%D0%B2%D1%8A%D0%BB%D0%BD%D0%B8)" title="Поляризация (вълни) – 保加利亚语" lang="bg" hreflang="bg" data-title="Поляризация (вълни)" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%AE%E0%A6%AC%E0%A6%B0%E0%A7%8D%E0%A6%A4%E0%A6%A8" title="সমবর্তন – 孟加拉语" lang="bn" hreflang="bn" data-title="সমবর্তন" data-language-autonym="বাংলা" data-language-local-name="孟加拉语" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Polaritzaci%C3%B3_electromagn%C3%A8tica" title="Polarització electromagnètica – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Polarització electromagnètica" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Polarizace_(elektrodynamika)" title="Polarizace (elektrodynamika) – 捷克语" lang="cs" hreflang="cs" data-title="Polarizace (elektrodynamika)" data-language-autonym="Čeština" data-language-local-name="捷克语" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Polarisering_(tv%C3%A6rb%C3%B8lge)" title="Polarisering (tværbølge) – 丹麦语" lang="da" hreflang="da" data-title="Polarisering (tværbølge)" data-language-autonym="Dansk" data-language-local-name="丹麦语" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Polarisation" title="Polarisation – 德语" lang="de" hreflang="de" data-title="Polarisation" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CF%8C%CE%BB%CF%89%CF%83%CE%B7" title="Πόλωση – 希腊语" lang="el" hreflang="el" data-title="Πόλωση" data-language-autonym="Ελληνικά" data-language-local-name="希腊语" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Polarization_(waves)" title="Polarization (waves) – 英语" lang="en" hreflang="en" data-title="Polarization (waves)" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target">English</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Polarizado" title="Polarizado – 世界语" lang="eo" hreflang="eo" data-title="Polarizado" data-language-autonym="Esperanto" data-language-local-name="世界语" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Polarizaci%C3%B3n_electromagn%C3%A9tica" title="Polarización electromagnética – 西班牙语" lang="es" hreflang="es" data-title="Polarización electromagnética" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Polarisatsioon" title="Polarisatsioon – 爱沙尼亚语" lang="et" hreflang="et" data-title="Polarisatsioon" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Polarizazio_(uhinak)" title="Polarizazio (uhinak) – 巴斯克语" lang="eu" hreflang="eu" data-title="Polarizazio (uhinak)" data-language-autonym="Euskara" data-language-local-name="巴斯克语" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%82%D8%B7%D8%A8%D8%B4_(%D9%85%D9%88%D8%AC%E2%80%8C%D9%87%D8%A7)" title="قطبش (موج‌ها) – 波斯语" lang="fa" hreflang="fa" data-title="قطبش (موج‌ها)" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Polarisaatio" title="Polarisaatio – 芬兰语" lang="fi" hreflang="fi" data-title="Polarisaatio" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Polarisation_(optique)" title="Polarisation (optique) – 法语" lang="fr" hreflang="fr" data-title="Polarisation (optique)" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Polar%C3%BA" title="Polarú – 爱尔兰语" lang="ga" hreflang="ga" data-title="Polarú" data-language-autonym="Gaeilge" data-language-local-name="爱尔兰语" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Polarizaci%C3%B3n" title="Polarización – 加利西亚语" lang="gl" hreflang="gl" data-title="Polarización" data-language-autonym="Galego" data-language-local-name="加利西亚语" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%99%D7%98%D7%95%D7%91" title="קיטוב – 希伯来语" lang="he" hreflang="he" data-title="קיטוב" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A7%E0%A5%8D%E0%A4%B0%E0%A5%81%E0%A4%B5%E0%A4%A3_(%E0%A4%B5%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%A4%E0%A4%9A%E0%A5%81%E0%A4%AE%E0%A5%8D%E0%A4%AC%E0%A4%95%E0%A5%80%E0%A4%AF)" title="ध्रुवण (विद्युतचुम्बकीय) – 印地语" lang="hi" hreflang="hi" data-title="ध्रुवण (विद्युतचुम्बकीय)" data-language-autonym="हिन्दी" data-language-local-name="印地语" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Polarizirana_svjetlost" title="Polarizirana svjetlost – 克罗地亚语" lang="hr" hreflang="hr" data-title="Polarizirana svjetlost" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Polariz%C3%A1ci%C3%B3" title="Polarizáció – 匈牙利语" lang="hu" hreflang="hu" data-title="Polarizáció" data-language-autonym="Magyar" data-language-local-name="匈牙利语" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%AC%D5%AB%D6%84%D5%B6%D5%A5%D6%80%D5%AB_%D5%A2%D6%87%D5%A5%D5%BC%D5%A1%D6%81%D5%B8%D6%82%D5%B4" title="Ալիքների բևեռացում – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Ալիքների բևեռացում" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Polarisasi_(gelombang)" title="Polarisasi (gelombang) – 印度尼西亚语" lang="id" hreflang="id" data-title="Polarisasi (gelombang)" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Polarizzazione_della_radiazione_elettromagnetica" title="Polarizzazione della radiazione elettromagnetica – 意大利语" lang="it" hreflang="it" data-title="Polarizzazione della radiazione elettromagnetica" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%81%8F%E5%85%89" title="偏光 – 日语" lang="ja" hreflang="ja" data-title="偏光" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8E%B8%EA%B4%91" title="편광 – 韩语" lang="ko" hreflang="ko" data-title="편광" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Poliarizacija" title="Poliarizacija – 立陶宛语" lang="lt" hreflang="lt" data-title="Poliarizacija" data-language-autonym="Lietuvių" data-language-local-name="立陶宛语" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D0%B0%D1%80%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%98%D0%B0_(%D0%B1%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B8)" title="Поларизација (бранови) – 马其顿语" lang="mk" hreflang="mk" data-title="Поларизација (бранови)" data-language-autonym="Македонски" data-language-local-name="马其顿语" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%A7%E0%A5%8D%E0%A4%B0%E0%A5%81%E0%A4%B5%E0%A4%BF%E0%A4%95%E0%A4%B0%E0%A4%A3_(%E0%A4%A4%E0%A4%B0%E0%A4%99)" title="ध्रुविकरण (तरङ) – 尼泊尔语" lang="ne" hreflang="ne" data-title="ध्रुविकरण (तरङ)" data-language-autonym="नेपाली" data-language-local-name="尼泊尔语" class="interlanguage-link-target">नेपाली</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Polarisatie_(elektromagnetisme)" title="Polarisatie (elektromagnetisme) – 荷兰语" lang="nl" hreflang="nl" data-title="Polarisatie (elektromagnetisme)" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Elektromagnetisk_polarisering" title="Elektromagnetisk polarisering – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Elektromagnetisk polarisering" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Polarisering_(elektromagnetisme)" title="Polarisering (elektromagnetisme) – 书面挪威语" lang="nb" hreflang="nb" data-title="Polarisering (elektromagnetisme)" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Polaryzacja_fali" title="Polaryzacja fali – 波兰语" lang="pl" hreflang="pl" data-title="Polaryzacja fali" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Polarisassion" title="Polarisassion – 皮埃蒙特文" lang="pms" hreflang="pms" data-title="Polarisassion" data-language-autonym="Piemontèis" data-language-local-name="皮埃蒙特文" class="interlanguage-link-target">Piemontèis</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Polariza%C3%A7%C3%A3o_eletromagn%C3%A9tica" title="Polarização eletromagnética – 葡萄牙语" lang="pt" hreflang="pt" data-title="Polarização eletromagnética" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Polarizare_(unde)" title="Polarizare (unde) – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Polarizare (unde)" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D1%8F%D1%80%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F_%D0%B2%D0%BE%D0%BB%D0%BD" title="Поляризация волн – 俄语" lang="ru" hreflang="ru" data-title="Поляризация волн" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D0%B0%D1%80%D1%96%D0%B7%D0%B0%D1%86%D1%96%D1%8F_(%D0%B5%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D0%B4%D1%96%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0)" title="Поларізація (електродінаміка) – 盧森尼亞文" lang="rue" hreflang="rue" data-title="Поларізація (електродінаміка)" data-language-autonym="Русиньскый" data-language-local-name="盧森尼亞文" class="interlanguage-link-target">Русиньскый</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Polarizacija_svjetlosti" title="Polarizacija svjetlosti – 塞尔维亚-克罗地亚语" lang="sh" hreflang="sh" data-title="Polarizacija svjetlosti" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞尔维亚-克罗地亚语" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Polarization" title="Polarization – Simple English" lang="en-simple" hreflang="en-simple" data-title="Polarization" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Polarizacija_valovanja" title="Polarizacija valovanja – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Polarizacija valovanja" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Polarizovana_svetlost" title="Polarizovana svetlost – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Polarizovana svetlost" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Polarisering_(elektromagnetism)" title="Polarisering (elektromagnetism) – 瑞典语" lang="sv" hreflang="sv" data-title="Polarisering (elektromagnetism)" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AF%81%E0%AE%B0%E0%AF%81%E0%AE%B5%E0%AE%AE%E0%AF%81%E0%AE%A9%E0%AF%88%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81" title="துருவமுனைப்பு – 泰米尔语" lang="ta" hreflang="ta" data-title="துருவமுனைப்பு" data-language-autonym="தமிழ்" data-language-local-name="泰米尔语" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%A7%E0%B1%8D%E0%B0%B0%E0%B1%81%E0%B0%B5%E0%B0%A3%E0%B0%A4_(%E0%B0%A4%E0%B0%B0%E0%B0%82%E0%B0%97%E0%B0%BE%E0%B0%B2%E0%B1%81)" title="ధ్రువణత (తరంగాలు) – 泰卢固语" lang="te" hreflang="te" data-title="ధ్రువణత (తరంగాలు)" data-language-autonym="తెలుగు" data-language-local-name="泰卢固语" class="interlanguage-link-target">తెలుగు</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%82%E0%B8%9E%E0%B8%A5%E0%B8%B2%E0%B9%84%E0%B8%A3%E0%B9%80%E0%B8%8B%E0%B8%8A%E0%B8%B1%E0%B8%99" title="โพลาไรเซชัน – 泰语" lang="th" hreflang="th" data-title="โพลาไรเซชัน" data-language-autonym="ไทย" data-language-local-name="泰语" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Polarizasyon" title="Polarizasyon – 土耳其语" lang="tr" hreflang="tr" data-title="Polarizasyon" data-language-autonym="Türkçe" data-language-local-name="土耳其语" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%94%D1%83%D0%BB%D0%BA%D1%8B%D0%BD%D0%BD%D0%B0%D1%80_%D0%BF%D0%BE%D0%BB%D1%8F%D1%80%D0%BB%D0%B0%D1%88%D1%83" title="Дулкыннар полярлашу – 鞑靼语" lang="tt" hreflang="tt" data-title="Дулкыннар полярлашу" data-language-autonym="Татарча / tatarça" data-language-local-name="鞑靼语" class="interlanguage-link-target">Татарча / tatarça</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D1%8F%D1%80%D0%B8%D0%B7%D0%B0%D1%86%D1%96%D1%8F_%D1%85%D0%B2%D0%B8%D0%BB%D1%8C" title="Поляризація хвиль – 乌克兰语" lang="uk" hreflang="uk" data-title="Поляризація хвиль" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Yorug%CA%BBlikning_qutblanishi" title="Yorugʻlikning qutblanishi – 乌兹别克语" lang="uz" hreflang="uz" data-title="Yorugʻlikning qutblanishi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="乌兹别克语" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A2n_c%E1%BB%B1c" title="Phân cực – 越南语" lang="vi" hreflang="vi" data-title="Phân cực" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%81%8F%E6%8C%AF" title="偏振 – 粤语" lang="yue" hreflang="yue" data-title="偏振" data-language-autonym="粵語" data-language-local-name="粤语" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Ukuluthuzeka_(amaza)" title="Ukuluthuzeka (amaza) – 祖鲁语" lang="zu" hreflang="zu" data-title="Ukuluthuzeka (amaza)" data-language-autonym="IsiZulu" data-language-local-name="祖鲁语" class="interlanguage-link-target">IsiZulu</a></li> </ul> <div class="after-portlet after-portlet-lang"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q193760#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</a></div> </div> </div> </div> </header> <div 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aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> <div id="mw-indicator-GA" class="mw-indicator"><div class="mw-parser-output"><a href="/wiki/Wikipedia:%E4%BC%98%E8%89%AF%E6%9D%A1%E7%9B%AE" title="这是一篇优良条目，点击此处获取更多信息。"><img alt="这是一篇优良条目，点击此处获取更多信息。" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Symbol_support_vote.svg/24px-Symbol_support_vote.svg.png" decoding="async" width="24" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Symbol_support_vote.svg/36px-Symbol_support_vote.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/Symbol_support_vote.svg/48px-Symbol_support_vote.svg.png 2x" data-file-width="180" data-file-height="185" /></a></div></div> <div id="mw-indicator-noteTA-5ff6fd68" class="mw-indicator"><div class="mw-parser-output"><img alt="本页使用了标题或全文手工转换" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/35px-Zh_conversion_icon_m.svg.png" decoding="async" width="35" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/53px-Zh_conversion_icon_m.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/70px-Zh_conversion_icon_m.svg.png 2x" data-file-width="32" data-file-height="20" /></div></div> </div> <div id="siteSub" class="noprint">维基百科，自由的百科全书</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><div id="noteTA-5ff6fd68" class="noteTA"><div class="noteTA-group"><div data-noteta-group-source="module" data-noteta-group="Physics"></div></div></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Polarizacio.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Polarizacio.jpg/220px-Polarizacio.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Polarizacio.jpg/330px-Polarizacio.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Polarizacio.jpg/440px-Polarizacio.jpg 2x" data-file-width="1280" data-file-height="1280" /></a><figcaption>橡膠細線的圓偏振運動，在經過一條狹縫之後，改變為線偏振運動。</figcaption></figure> 偏振（英語：polarization）指的是<a href="/wiki/%E6%A8%AA%E6%B3%A2" title="横波">横波</a>能夠朝著不同方向<a href="/wiki/%E6%8C%AF%E8%8D%A1" title="振荡">振盪</a>的性質。例如<a href="/wiki/%E9%9B%BB%E7%A3%81%E6%B3%A2" class="mw-redirect" title="電磁波">電磁波</a>、<a href="/wiki/%E5%BC%95%E5%8A%9B%E6%B3%A2" title="引力波">引力波</a>都會展示出偏振現象。纵波则不會展示出偏振現象，例如傳播於氣體或液體的<a href="/wiki/%E8%81%B2%E6%B3%A2" class="mw-redirect" title="聲波">聲波</a>，其只會朝著傳播方向振盪。如右圖所示，緊拉的細線可以展示出線偏振現象與圓偏振現象。 電磁波的<a href="/wiki/%E9%9B%BB%E5%A0%B4" title="電場">電場</a>與<a href="/wiki/%E7%A3%81%E5%A0%B4" title="磁場">磁場</a>彼此相互垂直。按照常規，電磁波的偏振方向指的是電場的偏振方向。在<a href="/wiki/%E8%87%AA%E7%94%B1%E7%A9%BA%E9%96%93" title="自由空間">自由空間</a>裏，電磁波是以<a href="/wiki/%E6%A8%AA%E6%B3%A2" title="横波">橫波</a>方式傳播，即電場與磁場又都垂直於電磁波的傳播方向。理論而言，只要垂直於傳播方向的方向，振盪的電場可以呈任意方向。假若電場的振盪只朝著單獨一個方向，則稱此為「線偏振」或「平面偏振」；假若電場的振盪方向是以電磁波的波頻率進行旋轉動作，並且電場向量的矢端隨著時間流意勾繪出圓型，則稱此為「圓偏振」；假若勾繪出橢圓型，則稱此為「橢圓偏振」；對於這兩個案例，又可按照在任意位置朝著源頭望去，電場隨時間流易而旋轉的<a href="/wiki/%E9%A0%86%E6%99%82%E9%87%9D%E6%96%B9%E5%90%91" title="順時針方向">順時針方向</a>、<a href="/wiki/%E9%80%86%E6%99%82%E9%87%9D%E6%96%B9%E5%90%91" title="逆時針方向">逆時針方向</a>，將圓偏振細分為「右旋圓偏振」、「左旋圓偏振」，將橢圓偏振細分為「右旋橢圓偏振」、「左旋橢圓偏振」；這性質稱為<a href="/wiki/%E6%89%8B%E5%BE%B5%E6%80%A7" title="手徵性">手徵性</a>。<a href="#cite_note-Hecht2002-1">[1]</a>:327-328 光波是一種電磁波。很多常見的光學物質都具有<a href="/wiki/%E5%90%84%E5%90%91%E5%90%8C%E6%80%A7" title="各向同性">各向同性</a>，例如<a href="/wiki/%E7%8E%BB%E7%92%83" title="玻璃">玻璃</a>。這些物質會維持波的偏振態不變，不會因偏振態的不同而展現出不同的物理行為。可是，有些重要的<a href="/wiki/%E5%8F%8C%E6%8A%98%E5%B0%84" title="双折射">雙折射</a>物質或<a href="/wiki/%E6%97%8B%E5%85%89%E6%80%A7" class="mw-redirect" title="旋光性">光學活性</a>物質具有<a href="/wiki/%E5%90%84%E5%90%91%E5%BC%82%E6%80%A7" title="各向异性">各向異性</a>。因此，偏振方向的不同，波的傳播狀況也不同，或者，波的偏振方向會被改變。<a href="/wiki/%E8%B5%B7%E5%81%8F%E5%99%A8" class="mw-redirect" title="起偏器">起偏器</a>是一種<a href="/wiki/%E6%BB%A4%E5%85%89%E5%99%A8" title="滤光器">光學濾波器</a>，只能讓朝著某特定方向偏振的光波通過，因此，可以將非偏振光變為偏振光。 在涉及到橫波傳播的科學領域，例如<a href="/wiki/%E5%85%89%E5%AD%B8" class="mw-redirect" title="光學">光學</a>、<a href="/wiki/%E5%9C%B0%E9%9C%87%E5%AD%B8" class="mw-redirect" title="地震學">地震學</a>、<a href="/wiki/%E7%84%A1%E7%B7%9A%E9%9B%BB" class="mw-redirect" title="無線電">無線電學</a>、<a href="/wiki/%E5%BE%AE%E6%B3%A2" title="微波">微波學</a>等等，偏振是很重要的參數。<a href="/wiki/%E6%BF%80%E5%85%89" title="激光">激光</a>、<a href="/wiki/%E5%85%89%E7%BA%A4%E9%80%9A%E4%BF%A1" class="mw-redirect" title="光纤通信">光纖通信</a>、<a href="/wiki/%E7%84%A1%E7%B7%9A%E9%80%9A%E4%BF%A1" class="mw-redirect" title="無線通信">無線通信</a>、<a href="/wiki/%E9%9B%B7%E9%81%94" class="mw-redirect" title="雷達">雷達</a>等等應用科技，都需要完善處理偏振問題。 <a href="/wiki/%E9%9B%BB%E6%A5%B5%E5%8C%96" title="電極化">極化</a>的英文原文也是「polarization」，在英文文獻裏，偏振與極化兩個術語通用，都是使用同一個詞彙來表達，只有在中文文獻裏，才有不同的用法。一般來說，偏振指的是任何波動朝著某特定方向振盪的性質，而極化指的是各個帶電粒子因正負電荷在空間裡分離而產生的現象。 <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="歷史">歷史</h2>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=1" title="编辑章节：歷史">编辑</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Etienne-Louis_Malus.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Etienne-Louis_Malus.jpg/200px-Etienne-Louis_Malus.jpg" decoding="async" width="200" height="271" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Etienne-Louis_Malus.jpg/300px-Etienne-Louis_Malus.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Etienne-Louis_Malus.jpg/400px-Etienne-Louis_Malus.jpg 2x" data-file-width="612" data-file-height="830" /></a><figcaption>艾蒂安-路易·馬呂斯</figcaption></figure> 丹麥科學家<a href="/wiki/%E6%8B%89%E6%96%AF%E7%A9%86%C2%B7%E5%B7%B4%E5%A4%9A%E6%9E%97" title="拉斯穆·巴多林">拉斯穆·巴多林</a>於1669年發現了光束通過<a href="/wiki/%E5%86%B0%E6%B4%B2%E7%9F%B3" class="mw-redirect" title="冰洲石">冰洲石</a>（Iceland spar）時會出現<a href="/wiki/%E5%8F%8C%E6%8A%98%E5%B0%84" title="双折射">雙折射</a>現象，假設照射光束於冰洲石，則這光束會被折射為兩道光束，一道光束遵守普通的折射定律，稱為「尋常光」，另外一道光束不遵守普通的折射定律，稱為「非常光」。巴多林無法解釋這現象的物理機制。<a href="#cite_note-Whittaker-2">[2]</a>:25後來，<a href="/wiki/%E5%85%8B%E9%87%8C%E6%96%AF%E8%92%82%E5%AE%89%C2%B7%E6%83%A0%E6%9B%B4%E6%96%AF" title="克里斯蒂安·惠更斯">克里斯蒂安·惠更斯</a>注意到這奇特現象，他在1690年著作《光論》的後半部裏，對這現象有很詳細的論述；他認為，由於空間可能存在有兩種不同物質，所以才會出現兩道光束，它們分別對應於兩個不同的<a href="/wiki/%E6%B3%A2%E5%89%8D" class="mw-redirect" title="波前">波前</a>以不同的速度傳播於空間，所以，這不是很不平常的現象，但是，惠更斯又發現，這兩道光束與原本光束的性質大不相同，將其中任何一道光束照射於第二塊冰洲石，則折射出來的兩道光束，其<a href="/wiki/%E8%BC%BB%E7%85%A7%E5%BA%A6" title="輻照度">輻照度</a>會因為繞著光束軸旋轉冰洲石而改變，有時候甚至只會剩成一道光束。惠更斯猜想光波是縱波，他想出的簡單波動理論不能對這現象給出解釋。<a href="/wiki/%E8%89%BE%E8%96%A9%E5%85%8B%C2%B7%E7%89%9B%E9%A0%93" class="mw-redirect" title="艾薩克·牛頓">艾薩克·牛頓</a>猜測，雙折射現象意味著組成光束的粒子具有側面（垂直於移動方向）性質。<a href="#cite_note-Whittaker-2">[2]</a>:25-28 1808年，<a href="/wiki/%E6%B3%95%E5%85%B0%E8%A5%BF%E5%AD%A6%E6%9C%AF%E9%99%A2" title="法兰西学术院">法蘭西學術院</a>提議，1810年物理獎比賽的題目為「對於雙折射給出數學理論，並且做實驗證實」。<a href="/wiki/%E8%89%BE%E8%92%82%E5%AE%89-%E8%B7%AF%E6%98%93%C2%B7%E9%A9%AC%E5%90%95%E6%96%AF" title="艾蒂安-路易·马吕斯">艾蒂安-路易·馬呂斯</a>決定參與競爭。他做實驗觀察，日光照射於<a href="/wiki/%E5%8D%A2%E6%A3%AE%E5%A0%A1%E5%AE%AB" title="卢森堡宫">盧森堡宮</a>的玻璃窗，然後被玻璃反射出來的光束，假若入射角度達到某特定數值，則這反射光與惠更斯觀察到的折射光具有類似的性質，他稱這性質為「偏振」性質。他猜想，組成光束的每一道光線都具有某種特別的不對稱性；當這些光線具有相同的不對稱性時，則光束具有偏振性；當這些光線的不對稱性分別機率地指向不同方向時，則光束具有非偏振性；當在這兩種案例之間時，則光束具有部分偏振性。不單是玻璃，任何透明的固體或液體都會產生這種現象。他又從實驗結果推論出<a href="/wiki/%E9%A9%AC%E5%90%95%E6%96%AF%E5%AE%9A%E5%BE%8B" title="马吕斯定律">馬呂斯定律</a>，定量地給出偏振光通過檢偏器後的<a href="/wiki/%E8%BC%BB%E7%85%A7%E5%BA%A6" title="輻照度">輻照度</a>，考慮到偏振方向與檢偏器傳輸軸方向之間的夾角角度。這實驗極具創意，又得到了很豐碩的重要成果，馬呂思因此榮獲1810年的物理獎。馬呂思對於偏振現象做出諸多貢獻，後人尊稱他為「偏振之父」。<a href="#cite_note-Driggers2003-3">[3]</a>:2050-2051<a href="#cite_note-BuchwaldFox2013-4">[4]</a>:448 後來，<a href="/wiki/%E5%A5%A7%E5%8F%A4%E6%96%AF%E4%B8%81%C2%B7%E8%8F%B2%E6%B6%85%E8%80%B3" class="mw-redirect" title="奧古斯丁·菲涅耳">奧古斯丁·菲涅耳</a>與<a href="/wiki/%E5%BC%97%E6%9C%97%E7%B4%A2%E7%93%A6%C2%B7%E9%98%BF%E6%8B%89%E6%88%88" title="弗朗索瓦·阿拉戈">弗朗索瓦·阿拉戈</a>合作研究偏振對於<a href="/wiki/%E6%A5%8A%E6%B0%8F%E5%B9%B2%E6%B6%89%E5%AF%A6%E9%A9%97" title="楊氏干涉實驗">楊氏干涉實驗</a>的影響，他們認為光波是縱波，呈縱向震盪，但是這縱波的概念無法合理解釋實驗結果。阿拉戈告訴<a href="/wiki/%E6%89%98%E9%A9%AC%E6%96%AF%C2%B7%E6%9D%A8" title="托马斯·杨">托馬斯·楊</a>這問題，托馬斯·楊大膽建議，假若光波是橫波，呈橫向震盪，則光波可以分解為兩個相互垂直的分量，或許這樣做可以對實驗結果給出解釋。果真，這建議清除了很多疑點。1817年，菲涅耳與阿拉戈將實驗結果定性總結為<a href="/wiki/%E8%8F%B2%E6%B6%85%E8%80%B3-%E9%98%BF%E6%8B%89%E6%88%88%E5%AE%9A%E5%BE%8B" title="菲涅耳-阿拉戈定律">菲涅耳-阿拉戈定律</a>，表述處於不同偏振態的光束彼此之間的干涉性質。之後，菲涅耳試圖進一步定量表述這實驗，他發展出的波動理論是一種振幅表述，主要是用光波的<a href="/wiki/%E6%8C%AF%E5%B9%85" title="振幅">振幅</a>與<a href="/wiki/%E7%9B%B8%E4%BD%8D" title="相位">相位</a>來作分析；振幅表述能夠定量地解釋偏振光的物理性質；但非偏振光或部分偏振光不具有穩定的振幅與相位，無法用振幅表述給予解釋。<a href="#cite_note-GoldsteinGoldstein2011-5">[5]</a>:xiii-xv<a href="#cite_note-BuchwaldFox2013-4">[4]</a>:466 1852年，<a href="/wiki/%E4%B9%94%E6%B2%BB%C2%B7%E6%96%AF%E6%89%98%E5%85%8B%E6%96%AF" title="乔治·斯托克斯">乔治·斯托克斯</a>提出一種強度表述，能夠描述偏振光、非偏振光與部分偏振光的物理行為；只需要使用四個參數，後來稱為<a href="/w/index.php?title=%E6%96%AF%E6%89%98%E5%85%8B%E6%96%AF%E5%8F%83%E6%95%B8&action=edit&redlink=1" class="new" title="斯托克斯參數（页面不存在）">斯托克斯參數</a>（英语：<a href="https://en.wikipedia.org/wiki/Stokes_parameters" class="extiw" title="en:Stokes parameters">Stokes parameters</a>）（Stokes parameters），就可以描述任何光束的偏振態，更重要地，這四個參數可以直接測量獲得。<a href="#cite_note-GoldsteinGoldstein2011-5">[5]</a>:xiv-xv 那時，電磁學理論雜亂無章，<a href="/wiki/%E8%A9%B9%E5%A7%86%E6%96%AF%C2%B7%E9%A6%AC%E5%85%8B%E5%A3%AB%E5%A8%81" class="mw-redirect" title="詹姆斯·馬克士威">詹姆斯·馬克士威</a>將這些理論加以整合，於1865年提出<a href="/wiki/%E9%A6%AC%E5%85%8B%E5%A3%AB%E5%A8%81%E6%96%B9%E7%A8%8B%E7%B5%84" title="馬克士威方程組">馬克士威方程組</a>。從這方程組，他推導出<a href="/wiki/%E9%9B%BB%E7%A3%81%E6%B3%A2%E6%96%B9%E7%A8%8B%E5%BC%8F" title="電磁波方程式">電磁波方程式</a>，推論出光波是一種<a href="/wiki/%E9%9B%BB%E7%A3%81%E6%B3%A2" class="mw-redirect" title="電磁波">電磁波</a>，可以用馬克士威方程組作精確描述。菲涅耳的波動理論是建立於一些貌似合理的假定，由於能夠正確描述光波的一些物理行為，例如，傳播、衍射、偏振等等，符合實驗得到的結果，所以才被學術界接受。從馬克士威方程組可以嚴格地推導出菲涅耳的波動理論，給予這理論堅實穩固的基礎。<a href="#cite_note-GoldsteinGoldstein2011-5">[5]</a>:2 <div class="mw-heading mw-heading2"><h2 id="理論概述">理論概述</h2>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=2" title="编辑章节：理論概述">编辑</a>]</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Vertical_polarization.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Vertical_polarization.svg/200px-Vertical_polarization.svg.png" decoding="async" width="200" height="155" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Vertical_polarization.svg/300px-Vertical_polarization.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Vertical_polarization.svg/400px-Vertical_polarization.svg.png 2x" data-file-width="940" data-file-height="730" /></a><figcaption>從<a href="/wiki/%E7%99%BD%E7%86%BE%E7%87%88" title="白熾燈">白熾燈</a>（1）發射出的非偏振光（2）入射於傳輸軸為垂直方向的<a href="/wiki/%E8%B5%B7%E5%81%8F%E5%99%A8" class="mw-redirect" title="起偏器">起偏器</a>（3），透射出來的是垂直平面偏振光（4）。</figcaption></figure> 大多數光源屬於非偏振光源，例如，太陽、白熾燈等等，因為它們所發射出的光波是由一組不同空間特徵、<a href="/wiki/%E9%A0%BB%E7%8E%87_(%E7%89%A9%E7%90%86%E5%AD%B8)" title="頻率 (物理學)">頻率</a>（<a href="/wiki/%E6%B3%A2%E9%95%B7" class="mw-redirect" title="波長">波長</a>）、<a href="/wiki/%E7%9B%B8%E4%BD%8D" title="相位">相位</a>、偏振的光波隨機混合所組成。為了了解光波的偏振性質，最簡單的方法就是先只思考<a href="/wiki/%E5%96%AE%E8%89%B2%E5%85%89" title="單色光">單色</a><a href="/wiki/%E5%B9%B3%E9%9D%A2%E6%B3%A2" title="平面波">平面波</a>，這種波是具有特定傳播方向、頻率、相位、振盪方向的<a href="/wiki/%E6%AD%A3%E5%BC%A6%E6%B3%A2" class="mw-redirect" title="正弦波">正弦波</a>。從研究平面波光學系統的性質與行為，可以對於一般案例給出預測，這是因為任何特定空間結構的光波都可以分解為一組不同頻率、不同振幅的平面波，稱為其<a href="/w/index.php?title=%E8%A7%92%E8%AD%9C&action=edit&redlink=1" class="new" title="角譜（页面不存在）">角譜</a>（英语：<a href="https://en.wikipedia.org/wiki/Angular_spectrum_method" class="extiw" title="en:Angular spectrum method">Angular spectrum method</a>）（angular spectrum）。<a href="#cite_note-Goodman2005-6">[6]</a>:55ff <div class="mw-heading mw-heading3"><h3 id="橫電磁波">橫電磁波</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=3" title="编辑章节：橫電磁波">编辑</a>]</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Onde_electromagn%C3%A9tique.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Onde_electromagn%C3%A9tique.png/200px-Onde_electromagn%C3%A9tique.png" decoding="async" width="200" height="132" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Onde_electromagn%C3%A9tique.png/300px-Onde_electromagn%C3%A9tique.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Onde_electromagn%C3%A9tique.png/400px-Onde_electromagn%C3%A9tique.png 2x" data-file-width="1621" data-file-height="1073" /></a><figcaption>傳播於自由空間的電磁波是橫波，電場方向與磁場方向彼此相互垂直，又都垂直於傳播方向。</figcaption></figure> 光波是一種電磁波。在自由空間裏，電磁波是橫波，其電場與磁場的方向都垂直於電磁波的傳播方向，並且相互垂直。<a href="#cite_note-7">[註 1]</a>設想一個頻率為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}">的電磁平面波朝著+z-軸方向傳播，電磁波的電場<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} (z,t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} (z,t)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20475434ab96ad3e5abadd4ba904912b55649fec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.528ex; height:2.843ex;" alt="{\displaystyle \mathbf {E} (z,t)}">、磁場<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} (z,t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} (z,t)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/faa3d38ce2a474d14fc9503601801dcd736b898e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.672ex; height:2.843ex;" alt="{\displaystyle \mathbf {B} (z,t)}">必定平行於xy-平面，以方程表示為<a href="#cite_note-Jackson1999-8">[7]</a>:295-299<a href="#cite_note-Goodman2005-6">[6]</a>:64-65 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} (z,t)=\mathbf {E} _{0}e^{i(kz-2\pi ft)}=({\hat {x}}E_{0x}+{\hat {y}}E_{0y})e^{i(kz-2\pi ft)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mi>z</mi> <mo>−</mo> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mi>z</mi> <mo>−</mo> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} (z,t)=\mathbf {E} _{0}e^{i(kz-2\pi ft)}=({\hat {x}}E_{0x}+{\hat {y}}E_{0y})e^{i(kz-2\pi ft)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/081715ecdbbbae02b8701a812d9cbcc2adffb798" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:48.771ex; height:3.509ex;" alt="{\displaystyle \mathbf {E} (z,t)=\mathbf {E} _{0}e^{i(kz-2\pi ft)}=({\hat {x}}E_{0x}+{\hat {y}}E_{0y})e^{i(kz-2\pi ft)}}">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} (z,t)=\mathbf {B} _{0}e^{i(kz-2\pi ft)}=({\hat {x}}B_{0x}+{\hat {y}}B_{0y})e^{i(kz-2\pi ft)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mi>z</mi> <mo>−</mo> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mi>z</mi> <mo>−</mo> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} (z,t)=\mathbf {B} _{0}e^{i(kz-2\pi ft)}=({\hat {x}}B_{0x}+{\hat {y}}B_{0y})e^{i(kz-2\pi ft)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18d9cb856ecd1533e2d73e9373d124d39ebdd0bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:49.157ex; height:3.509ex;" alt="{\displaystyle \mathbf {B} (z,t)=\mathbf {B} _{0}e^{i(kz-2\pi ft)}=({\hat {x}}B_{0x}+{\hat {y}}B_{0y})e^{i(kz-2\pi ft)}}">；</dd></dl> 其中，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75ee4610a644d1b4e038ff152ef47f067925f722" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.811ex; height:2.509ex;" alt="{\displaystyle \mathbf {E} _{0}}">與<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b3fadd132fae64ad10e1d704431b474a09b905f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.955ex; height:2.509ex;" alt="{\displaystyle \mathbf {B} _{0}}">分別是複常數向量，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}">是波數。 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75ee4610a644d1b4e038ff152ef47f067925f722" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.811ex; height:2.509ex;" alt="{\displaystyle \mathbf {E} _{0}}">的x-分量、y-分量分別描述電磁波的電場朝著x方向、y方向的振輻；類似地，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b3fadd132fae64ad10e1d704431b474a09b905f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.955ex; height:2.509ex;" alt="{\displaystyle \mathbf {B} _{0}}">的x-分量、y-分量分別描述電磁波的磁場朝著x方向、y方向的振輻。對於這朝著+z-軸方向傳播的橫電磁波，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75ee4610a644d1b4e038ff152ef47f067925f722" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.811ex; height:2.509ex;" alt="{\displaystyle \mathbf {E} _{0}}">與<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b3fadd132fae64ad10e1d704431b474a09b905f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.955ex; height:2.509ex;" alt="{\displaystyle \mathbf {B} _{0}}">的z-分量都等於0。<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b3fadd132fae64ad10e1d704431b474a09b905f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.955ex; height:2.509ex;" alt="{\displaystyle \mathbf {B} _{0}}">與<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75ee4610a644d1b4e038ff152ef47f067925f722" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.811ex; height:2.509ex;" alt="{\displaystyle \mathbf {E} _{0}}">之間的關係為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} _{0}={\sqrt {\mu _{0}\epsilon _{0}}}{\hat {z}}\times \mathbf {E} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </msqrt> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} _{0}={\sqrt {\mu _{0}\epsilon _{0}}}{\hat {z}}\times \mathbf {E} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9bde40b022c4598df674c77ba228551a044ebbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:19.392ex; height:3.009ex;" alt="{\displaystyle \mathbf {B} _{0}={\sqrt {\mu _{0}\epsilon _{0}}}{\hat {z}}\times \mathbf {E} _{0}}">；</dd></dl> 其中，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2cae6289b0fe626d1f9472a3416ac73e87bc5a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.998ex; height:2.009ex;" alt="{\displaystyle \epsilon _{0}}">為<a href="/wiki/%E9%9B%BB%E5%B8%B8%E6%95%B8" class="mw-redirect" title="電常數">電常數</a>，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe2fd9b8decb38a3cd158e7b6c0c6e2d987fefcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.456ex; height:2.176ex;" alt="{\displaystyle \mu _{0}}">為<a href="/wiki/%E7%A3%81%E5%B8%B8%E6%95%B8" class="mw-redirect" title="磁常數">磁常數</a>。 所以，從電磁波的電場可以計算出磁場。 類似地，在簡單介質裏，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b3fadd132fae64ad10e1d704431b474a09b905f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.955ex; height:2.509ex;" alt="{\displaystyle \mathbf {B} _{0}}">與<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75ee4610a644d1b4e038ff152ef47f067925f722" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.811ex; height:2.509ex;" alt="{\displaystyle \mathbf {E} _{0}}">之間的關係為<a href="#cite_note-9">[註 2]</a> <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} _{0}={\sqrt {\mu \epsilon }}{\hat {z}}\times \mathbf {E} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>μ</mi> <mi>ϵ</mi> </msqrt> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} _{0}={\sqrt {\mu \epsilon }}{\hat {z}}\times \mathbf {E} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5296db1a868c3ddc2f770c4c4f9457c50211c3f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:17.283ex; height:3.009ex;" alt="{\displaystyle \mathbf {B} _{0}={\sqrt {\mu \epsilon }}{\hat {z}}\times \mathbf {E} _{0}}">；</dd></dl> 其中，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϵ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3837cad72483d97bcdde49c85d3b7b859fb3fd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.944ex; height:1.676ex;" alt="{\displaystyle \epsilon }">為<a href="/wiki/%E7%94%B5%E5%AE%B9%E7%8E%87" title="电容率">電容率</a>，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }">為<a href="/wiki/%E7%A3%81%E5%AF%BC%E7%8E%87" title="磁导率">磁導率</a>。 所以，儘管電磁波傳播於簡單介質，仍舊可以從電磁波的電場計算出磁場。 由於<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75ee4610a644d1b4e038ff152ef47f067925f722" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.811ex; height:2.509ex;" alt="{\displaystyle \mathbf {E} _{0}}">是常數向量，不會隨著時間的流易而改變方向，所以，這電磁波具有偏振性質，偏振方向是<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75ee4610a644d1b4e038ff152ef47f067925f722" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.811ex; height:2.509ex;" alt="{\displaystyle \mathbf {E} _{0}}">的方向，偏振平面是<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75ee4610a644d1b4e038ff152ef47f067925f722" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.811ex; height:2.509ex;" alt="{\displaystyle \mathbf {E} _{0}}">與z-軸共同組成的平面。由<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} _{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75ee4610a644d1b4e038ff152ef47f067925f722" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.811ex; height:2.509ex;" alt="{\displaystyle \mathbf {E} _{0}}">的x-分量、y-分量所組成的向量稱為<a href="/wiki/%E7%93%8A%E6%96%AF%E5%90%91%E9%87%8F" class="mw-redirect" title="瓊斯向量">瓊斯向量</a>，可以用來描述偏振。除了給定偏振以外，瓊斯向量還給定了整體電磁波的大小與相位。<a href="#cite_note-Hecht2002-1">[1]</a>:376-377特別而言，電磁波的<a href="/wiki/%E8%BC%BB%E7%85%A7%E5%BA%A6" title="輻照度">輻照度</a><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}">以方程表示為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=(|E_{0x}|^{2}+|E_{0y}|^{2})/2\eta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mi>η</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=(|E_{0x}|^{2}+|E_{0y}|^{2})/2\eta }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e588ae1c9e49cc1f4d7ef51715c900ca13da0bd1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.406ex; height:3.509ex;" alt="{\displaystyle I=(|E_{0x}|^{2}+|E_{0y}|^{2})/2\eta }">；</dd></dl> 其中，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eta ={\sqrt {\mu /\epsilon }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>η</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>ϵ</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta ={\sqrt {\mu /\epsilon }}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61ea9dcf775f74cf9660d477351dada32201c684" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.1ex; height:4.843ex;" alt="{\displaystyle \eta ={\sqrt {\mu /\epsilon }}}">是這簡單介質的<a href="/w/index.php?title=%E7%89%B9%E6%80%A7%E9%98%BB%E6%8A%97&action=edit&redlink=1" class="new" title="特性阻抗（页面不存在）">特性阻抗</a>（英语：<a href="https://en.wikipedia.org/wiki/Characteristic_impedance" class="extiw" title="en:Characteristic impedance">Characteristic impedance</a>）（characteristic impedance） 偏振與兩個分量的比率有關，在解析偏振問題時，可以約化為只思考<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |E_{0x}|^{2}+|E_{0y}|^{2}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |E_{0x}|^{2}+|E_{0y}|^{2}=1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af8d41660c7322e3c261f2eb4852456c30eff76c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.093ex; height:3.509ex;" alt="{\displaystyle |E_{0x}|^{2}+|E_{0y}|^{2}=1}">的電磁波，將電磁波<a href="/wiki/%E6%AD%B8%E4%B8%80%E5%8C%96" class="mw-redirect" title="歸一化">歸一化</a>；偏振與兩個分量的相對向位有關，因此可以設定<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0x}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22e4da03dfed795de425f79181304cad8fabdf17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.71ex; height:2.509ex;" alt="{\displaystyle E_{0x}}">的相位為零，換句話說，約化為只思考<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0x}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22e4da03dfed795de425f79181304cad8fabdf17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.71ex; height:2.509ex;" alt="{\displaystyle E_{0x}}">是實數，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0y}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/033fedf2a625661d78bc47664a4d649c82fcb95a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.587ex; height:2.843ex;" alt="{\displaystyle E_{0y}}">是複數的偏振問題，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0x}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22e4da03dfed795de425f79181304cad8fabdf17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.71ex; height:2.509ex;" alt="{\displaystyle E_{0x}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0y}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/033fedf2a625661d78bc47664a4d649c82fcb95a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.587ex; height:2.843ex;" alt="{\displaystyle E_{0y}}">分別表示為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0x}={\sqrt {\frac {1+Q}{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>Q</mi> </mrow> <mn>2</mn> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0x}={\sqrt {\frac {1+Q}{2}}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dd4a0dd5f4fa3bfb45feebee48233909032cbea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.809ex; height:6.176ex;" alt="{\displaystyle E_{0x}={\sqrt {\frac {1+Q}{2}}}}">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0y}={\sqrt {\frac {1-Q}{2}}}\,e^{i\phi }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mi>Q</mi> </mrow> <mn>2</mn> </mfrac> </msqrt> </mrow> <mspace width="thinmathspace" /> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>ϕ</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0y}={\sqrt {\frac {1-Q}{2}}}\,e^{i\phi }}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ab174667da4ff179ddc9d1d79173c61ace3dbd5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:18.936ex; height:6.176ex;" alt="{\displaystyle E_{0y}={\sqrt {\frac {1-Q}{2}}}\,e^{i\phi }}">；</dd></dl> 其中，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }">是偏振態的兩個參數，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -1\leq Q\leq 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mn>1</mn> <mo>≤</mo> <mi>Q</mi> <mo>≤</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -1\leq Q\leq 1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a10cb91f169c66411fa2ca2522e4a2b8e83f4aa7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.168ex; height:2.509ex;" alt="{\displaystyle -1\leq Q\leq 1}">。 按照常規，當提到偏振時，假若沒有特別設定，通常指的是電場的偏振。磁場的偏振通常與電場類似，唯一不同之處是90°空間角度差。 <div class="mw-heading mw-heading3"><h3 id="偏振態">偏振態</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=4" title="编辑章节：偏振態">编辑</a>]</div> <style data-mw-deduplicate="TemplateStyles:r70089473/mw-parser-output/.tmulti">.mw-parser-output .tmulti .thumbinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}</style><div class="thumb tmulti tright"><div class="thumbinner" style="width:312px;max-width:312px"><div class="trow"><div class="tsingle" style="width:102px;max-width:102px"><div class="thumbimage"><a href="/wiki/File:Polarisation_(Linear)_With.Phase.Indicators.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Polarisation_%28Linear%29_With.Phase.Indicators.svg/100px-Polarisation_%28Linear%29_With.Phase.Indicators.svg.png" decoding="async" width="100" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Polarisation_%28Linear%29_With.Phase.Indicators.svg/150px-Polarisation_%28Linear%29_With.Phase.Indicators.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Polarisation_%28Linear%29_With.Phase.Indicators.svg/200px-Polarisation_%28Linear%29_With.Phase.Indicators.svg.png 2x" data-file-width="250" data-file-height="625" /></a></div><div class="thumbcaption"><center>線偏振</center></div></div><div class="tsingle" style="width:102px;max-width:102px"><div class="thumbimage"><a href="/wiki/File:Polarisation_(Circular).svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Polarisation_%28Circular%29.svg/100px-Polarisation_%28Circular%29.svg.png" decoding="async" width="100" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Polarisation_%28Circular%29.svg/150px-Polarisation_%28Circular%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Polarisation_%28Circular%29.svg/200px-Polarisation_%28Circular%29.svg.png 2x" data-file-width="250" data-file-height="625" /></a></div><div class="thumbcaption"><center>圓偏振</center></div></div><div class="tsingle" style="width:102px;max-width:102px"><div class="thumbimage"><a href="/wiki/File:Polarisation_(Elliptical).svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Polarisation_%28Elliptical%29.svg/100px-Polarisation_%28Elliptical%29.svg.png" decoding="async" width="100" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Polarisation_%28Elliptical%29.svg/150px-Polarisation_%28Elliptical%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Polarisation_%28Elliptical%29.svg/200px-Polarisation_%28Elliptical%29.svg.png 2x" data-file-width="250" data-file-height="625" /></a></div><div class="thumbcaption"><center>橢圓偏振</center></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">電場向量隨著時間（z-軸）流易而演變。電場向量以黑色粗線表示，它的x-分量、y-分量分別以紅色細線、藍色細線表示。在基部的圖樣是向量的矢端隨著時間流易對於xy-平面的投射。</div></div></div></div> 在<a href="/wiki/%E6%AD%A3%E5%BC%A6%E6%B3%A2" class="mw-redirect" title="正弦波">正弦波</a>的每一個周期，電場向量和磁場向量都會描繪出一個橢圓形（注意到線偏振與圓偏振是橢圓偏振的特別案例）。這橢圓的形狀與<a href="/wiki/%E5%AE%9A%E5%90%91" class="mw-disambig" title="定向">定向</a>定義了電磁波的偏振態。右圖展示出幾種不同種類的偏振。假設電場的x-分量、y-分量完全同相，則隨著時間流易，電場向量的矢端對於xy-平面的投射，會描繪出一條直線段，這案例因此稱為「線偏振」，又稱為「平面偏振」。假設電場的x-分量、y-分量擁有同樣的振輻，但是失相90°，則隨著時間流易，電場向量的矢端對於xy-平面的投射，會描繪出一條圓圈，這案例因此稱為「圓偏振」。根據光學領域常規，依相位差為-90°或+90°，圓偏振又分為右旋圓偏振（順時針旋轉）或左旋圓偏振（逆時針旋轉）。<a href="#cite_note-Hecht2002-1">[1]</a>:327-328假設除了失相以外，兩個分量的振輻不同，則隨著時間流易，電場向量的矢端對於xy-平面的投射，會描繪出一條橢圓，這案例因此稱為「橢圓偏振」。類似地，對應於不同的偏振態，電場的順時針旋轉或逆時針旋轉可以製成同樣的橢圓形狀。<a href="#cite_note-Chandrasekhar2013-10">[8]</a>:25-28 只要光波的傳播方向與z-軸同向，而xy-平面的定向可以任意選擇，就能夠正確地表現每一種偏振態。在解析問題時，通常會選擇合適的坐標軸，例如，光波的入射方向與x-軸同平面。另外，任意兩個相互正交的偏振態可以設定為基底函數；這樣，任意偏振態可以用基底函數來表示，例如，設定兩個相互正交的線偏振態為基底函數，則可很自然地處理表面反射、雙折射等問題。右旋圓偏振態與左旋圓偏振態也是很有用的選擇，可以用來研究光波傳播於<a href="/wiki/%E7%AB%8B%E4%BD%93%E5%BC%82%E6%9E%84" title="立体异构">立體異構</a>的問題。<a href="#cite_note-North1998-11">[9]</a>:49-50 <div class="mw-heading mw-heading3"><h3 id="非偏振光">非偏振光</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=5" title="编辑章节：非偏振光">编辑</a>]</div> <a href="/wiki/%E5%8F%AF%E8%A6%8B%E5%85%89" class="mw-redirect" title="可見光">可見光</a>的大多數常見光源，包括<a href="/wiki/%E9%BB%91%E9%AB%94%E8%BC%BB%E5%B0%84" class="mw-redirect" title="黑體輻射">黑體輻射</a>、<a href="/wiki/%E8%9E%A2%E5%85%89" class="mw-redirect" title="螢光">螢光</a>等，會發射出<a href="/wiki/%E7%9B%B8%E5%B9%B2%E6%80%A7" title="相干性">不相干</a>光波。在這些光源物質裏，處於<a href="/wiki/%E6%BF%80%E7%99%BC%E6%85%8B" class="mw-redirect" title="激發態">激發態</a>的<a href="/wiki/%E5%8E%9F%E5%AD%90" title="原子">原子</a>或<a href="/wiki/%E5%88%86%E5%AD%90" title="分子">分子</a>會獨立、毫無關聯地發射出這些<a href="/wiki/%E9%9A%A8%E6%A9%9F" class="mw-redirect" title="隨機">隨機</a>偏振的電磁輻射<a href="/wiki/%E6%B3%A2%E5%88%97" title="波列">波列</a>。每個波列持續大約10-8秒，所以，光波的偏振只能保持不變不超過10-8秒。這種光波稱為「非偏振光」。這術語所傳達出的意思並不精準，因為在任意時刻、任意位置，電場與磁場的方向都很明確，這術語所要傳達出的意思為，偏振隨時間流易而改變的速度非常快，它不是無法被測量到，就是與實驗結果無關。偏振光在通過<a href="/w/index.php?title=%E6%B6%88%E5%81%8F%E5%99%A8&action=edit&redlink=1" class="new" title="消偏器（页面不存在）">消偏器</a>（英语：<a href="https://en.wikipedia.org/wiki/Depolarizer_(optics)" class="extiw" title="en:Depolarizer (optics)">Depolarizer (optics)</a>）（depolarizer）之後，由於透射光的偏振隨時間流易而改變的速率非常快，實際而言，可以忽略透射光在任意時刻的偏振，因此將透射光歸類為「非偏振光」。 假若光波的一個偏振模的<a href="/wiki/%E5%8A%9F%E7%8E%87" title="功率">功率</a>與另一個偏振模的功率不一樣，則可稱此光波為「部分偏振光」。它可以統計描述為一個完全非偏振光與一個完全偏振光的<a href="/wiki/%E7%96%8A%E5%8A%A0%E5%8E%9F%E7%90%86" class="mw-redirect" title="疊加原理">疊加</a>。<a href="#cite_note-Hecht2002-1">[1]</a>:330<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF%E5%BA%A6&action=edit&redlink=1" class="new" title="偏振度（页面不存在）">偏振度</a>（英语：<a href="https://en.wikipedia.org/wiki/Degree_of_polarization" class="extiw" title="en:Degree of polarization">Degree of polarization</a>）（degree of polarization）是光波的偏振部分所佔有的百分比，可以用來描述光波的成分。部分偏振態最常用<a href="/w/index.php?title=%E6%96%AF%E6%89%98%E5%85%8B%E6%96%AF%E5%8F%83%E6%95%B8&action=edit&redlink=1" class="new" title="斯托克斯參數（页面不存在）">斯托克斯參數</a>（英语：<a href="https://en.wikipedia.org/wiki/Stokes_parameters" class="extiw" title="en:Stokes parameters">Stokes parameters</a>）（Stokes parameters）來設定。<a href="#cite_note-Hecht2002-1">[1]</a>:351,374-375 <div class="mw-heading mw-heading3"><h3 id="其它種類偏振">其它種類偏振</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=6" title="编辑章节：其它種類偏振">编辑</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Radial_and_Azimuthal_Polarisation_zh_hans.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Radial_and_Azimuthal_Polarisation_zh_hans.svg/150px-Radial_and_Azimuthal_Polarisation_zh_hans.svg.png" decoding="async" width="150" height="247" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Radial_and_Azimuthal_Polarisation_zh_hans.svg/225px-Radial_and_Azimuthal_Polarisation_zh_hans.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Radial_and_Azimuthal_Polarisation_zh_hans.svg/300px-Radial_and_Azimuthal_Polarisation_zh_hans.svg.png 2x" data-file-width="340" data-file-height="560" /></a><figcaption>上图是角向偏振，下图是径向偏振。</figcaption></figure> 除了橫波以外，很多種波動的振盪方向不局限為垂直於傳播方向。這些案例超過本條目範疇，本條目專注於橫波，可是，在有些案例裏，相干波的偏振不能簡單地用瓊斯向量或斯托克斯向量描述。 設想先前提到的傳播於均勻、各向同性、非衰減性介質的電磁平面波，假設改為傳播於<a href="/wiki/%E5%90%84%E5%90%91%E5%BC%82%E6%80%A7" title="各向异性">各向異性</a>介質，例如雙折射晶體，電場或磁場可能還會擁有<a href="/wiki/%E7%B8%B1%E5%A0%B4" class="mw-redirect" title="縱場">縱場</a>。對於這種案例，因為介質具有各向異性，它的<a href="/wiki/%E9%9B%BB%E6%A5%B5%E5%8C%96%E7%8E%87" title="電極化率">電極化率</a>或<a href="/wiki/%E7%A3%81%E5%AF%BC%E7%8E%87" title="磁导率">磁導率</a>必需用<a href="/wiki/%E5%BC%B5%E9%87%8F" title="張量">張量</a>來描述，電場的方向可能不同於<a href="/wiki/%E9%9B%BB%E4%BD%8D%E7%A7%BB" title="電位移">電位移</a>的方向，磁場強度的方向可能不同於磁場的方向。<a href="#cite_note-Griffiths1998-12">[10]</a>:179-184<a href="#cite_note-New2011-13">[11]</a>:51-52有些各向同性介質的<a href="/wiki/%E6%8A%98%E5%B0%84%E7%8E%87" title="折射率">折射率</a>是複數，折射率的很大一部分是虛數，例如，金屬。甚至在這些介質裏，非均勻波都可以傳播；嚴格而說，它的各個場並不完全是橫場。<a href="/wiki/%E8%A1%A8%E9%9D%A2%E6%B3%A2" class="mw-redirect" title="表面波">表面波</a>、傳播於<a href="/wiki/%E6%B3%A2%E5%B0%8E" class="mw-redirect" title="波導">波導</a>或<a href="/wiki/%E5%85%89%E7%BA%96" class="mw-redirect" title="光纖">光纖</a>的電磁波通常不是橫波，但是可以以<a href="/w/index.php?title=%E6%A9%AB%E6%A8%A1&action=edit&redlink=1" class="new" title="橫模（页面不存在）">橫模</a>（英语：<a href="https://en.wikipedia.org/wiki/Transverse_mode" class="extiw" title="en:Transverse mode">Transverse mode</a>）（transverse mode）的概念來描述。橫模又分為「橫電模」、「橫磁模」、「橫電磁模」、「混合模」四種。<a href="#cite_note-Griffiths1998-12">[10]</a>:405-408 在自由空間裏，縱場分量可以被生成於平面波近似不成立的焦區。舉一個極端例子，在<a href="/w/index.php?title=%E5%BE%91%E5%90%91%E5%81%8F%E6%8C%AF&action=edit&redlink=1" class="new" title="徑向偏振（页面不存在）">徑向偏振</a>（英语：<a href="https://en.wikipedia.org/wiki/Radial_polarization" class="extiw" title="en:Radial polarization">Radial polarization</a>）（radial polarization）光或<a href="/w/index.php?title=%E8%A7%92%E5%90%91%E5%81%8F%E6%8C%AF&action=edit&redlink=1" class="new" title="角向偏振（页面不存在）">角向偏振</a>（azimuthal polarization）光的焦點，電場與磁場完全是縱場，與傳播方向同向。<a href="#cite_note-14">[12]</a> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Pol.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Pol.jpg/250px-Pol.jpg" decoding="async" width="250" height="142" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Pol.jpg/375px-Pol.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/e/ed/Pol.jpg 2x" data-file-width="392" data-file-height="222" /></a><figcaption>引力波的十字型偏振h+與交叉型偏振h×對於排列成圓圈形狀的粒子所產生的振盪效應。</figcaption></figure> 像在<a href="/wiki/%E6%B5%81%E9%AB%94" class="mw-redirect" title="流體">流體</a>裏傳播的<a href="/wiki/%E8%81%B2%E6%B3%A2" class="mw-redirect" title="聲波">聲波</a>一類的縱波，振盪方向按照定義是沿著傳播方向，所以，偏振這論題通常不會被提出。從另一方面來說，在大塊固體傳播的聲波也可能是橫波，也可能是縱波，總共有三個偏振分量。對於這案例，橫偏振伴隨<a href="/wiki/%E5%89%AA%E6%87%89%E5%8A%9B" title="剪應力">剪應力</a>的方向，位移方向垂直於傳播方向；縱偏振描述固體的壓縮與振盪沿著傳播方向。在<a href="/wiki/%E5%9C%B0%E9%9C%87%E5%AD%B8" class="mw-redirect" title="地震學">地震學</a>裏，橫偏振與縱偏振之間的傳播差別是很重要的參數。<a href="#cite_note-SteinWysession2009-15">[13]</a>:56-57 傳遞<a href="/wiki/%E5%BC%95%E5%8A%9B" title="引力">引力</a>的<a href="/wiki/%E5%BC%95%E5%8A%9B%E5%AD%90" title="引力子">引力子</a>不帶質量，具有橫向偏振，<a href="#cite_note-Griffiths2008-16">[14]</a>:240-241因此引力波是橫波，引力波的振盪方向垂直於傳播方向，具有偏振性質。引力波可以呈兩種偏振態，十字型偏振h+與交叉型偏振h×。如右圖所示，假設一群粒子靜止排列成圓圈形狀，垂直於這圓圈傳播通過的引力波，其h+偏振會對這些粒子造成可觀察到的效應，在某一時刻，它會使得圓圈朝著上下方向拉伸，同時又會朝著左右方向壓縮；過一會兒，它又會將這變化逆轉回來。類似地，h×偏振會對這些粒子造成振盪效應。這兩種偏振態很相似，將其中一種偏振態旋轉45度，就可以得到另一種偏振態。<a href="#cite_note-Schutz2009-17">[15]</a>:210 <div class="mw-heading mw-heading2"><h2 id="數學表述">數學表述</h2>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=7" title="编辑章节：數學表述">编辑</a>]</div> <div class="mw-heading mw-heading3"><h3 id="偏振橢圓">偏振橢圓</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=8" title="编辑章节：偏振橢圓">编辑</a>]</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Polarisation_ellipse3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Polarisation_ellipse3.svg/200px-Polarisation_ellipse3.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Polarisation_ellipse3.svg/300px-Polarisation_ellipse3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/08/Polarisation_ellipse3.svg/400px-Polarisation_ellipse3.svg.png 2x" data-file-width="360" data-file-height="360" /></a><figcaption>偏振橢圓圖。</figcaption></figure> 「偏振橢圓」可以幫助想像與理解偏振問題。假設橫電磁波<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} (z,t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} (z,t)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20475434ab96ad3e5abadd4ba904912b55649fec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.528ex; height:2.843ex;" alt="{\displaystyle \mathbf {E} (z,t)}">的分量為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{x}=E_{0x}\cos(kz-\omega t+\varphi _{x})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>k</mi> <mi>z</mi> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{x}=E_{0x}\cos(kz-\omega t+\varphi _{x})}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b67d72165b7199fdc6570baab4e154d609f624d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.962ex; height:2.843ex;" alt="{\displaystyle E_{x}=E_{0x}\cos(kz-\omega t+\varphi _{x})}">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{y}=E_{0y}\cos(kz-\omega t+\varphi _{y})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>k</mi> <mi>z</mi> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{y}=E_{0y}\cos(kz-\omega t+\varphi _{y})}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b0c1c4e51d3c5c634ef9745660780157a64a4f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:27.592ex; height:3.009ex;" alt="{\displaystyle E_{y}=E_{0y}\cos(kz-\omega t+\varphi _{y})}">；</dd></dl> 其中，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0x}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22e4da03dfed795de425f79181304cad8fabdf17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.71ex; height:2.509ex;" alt="{\displaystyle E_{0x}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0y}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/033fedf2a625661d78bc47664a4d649c82fcb95a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.587ex; height:2.843ex;" alt="{\displaystyle E_{0y}}">分別為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{x}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/029e49fbec18ece71cdd1e68bc478444e2c99d30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.888ex; height:2.509ex;" alt="{\displaystyle E_{x}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{y}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff71d8c6b39b429ae113e95c77c0016bd4aa62ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.765ex; height:2.843ex;" alt="{\displaystyle E_{y}}">的最大實值。 如右圖所示，這個橫電磁波的偏振橢圓以方程表示為<a href="#cite_note-Collett2005-18">[16]</a>:7-9<a href="#cite_note-GoldsteinGoldstein2011-5">[5]</a>:29-30<a href="#cite_note-esa-19">[17]</a>:6-8 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {E_{x}}{E_{0x}}}\right)^{2}+\left({\frac {E_{y}}{E_{0y}}}\right)^{2}-2\left({\frac {E_{x}}{E_{0x}}}\right)\left({\frac {E_{y}}{E_{0y}}}\right)\cos \varphi =\sin ^{2}\varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mo>=</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {E_{x}}{E_{0x}}}\right)^{2}+\left({\frac {E_{y}}{E_{0y}}}\right)^{2}-2\left({\frac {E_{x}}{E_{0x}}}\right)\left({\frac {E_{y}}{E_{0y}}}\right)\cos \varphi =\sin ^{2}\varphi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a02c309798ea738f9153a283111b1065649aca5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:55.669ex; height:6.676ex;" alt="{\displaystyle \left({\frac {E_{x}}{E_{0x}}}\right)^{2}+\left({\frac {E_{y}}{E_{0y}}}\right)^{2}-2\left({\frac {E_{x}}{E_{0x}}}\right)\left({\frac {E_{y}}{E_{0y}}}\right)\cos \varphi =\sin ^{2}\varphi }">；</dd></dl> 其中，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi =\varphi _{x}-\varphi _{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> <mo>=</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi =\varphi _{x}-\varphi _{y}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e025fd3f8f62f12da413a8fb47441337d15f4986" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.721ex; height:2.676ex;" alt="{\displaystyle \varphi =\varphi _{x}-\varphi _{y}}">是相位差。 「橢圓幅」<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}">估算波動的功率密度，以方程定義為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\sqrt {E_{0x}^{2}+E_{0y}^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\sqrt {E_{0x}^{2}+E_{0y}^{2}}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c22edbd7eff0d00c1aeab23e9ef0b66da4602a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:17.302ex; height:4.843ex;" alt="{\displaystyle A={\sqrt {E_{0x}^{2}+E_{0y}^{2}}}}">。</dd></dl> 「定向角」<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }">定義為偏振橢圓的<a href="/wiki/%E5%8D%8A%E9%95%B7%E8%BB%B8" title="半長軸">半長軸</a>與x-軸之間的夾角： <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan(2\psi )={\frac {2E_{0x}E_{0y}\cos \varphi }{E_{0x}^{2}-E_{0y}^{2}}},\qquad 0\leq \psi \leq \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>ψ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> </mrow> <mrow> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="2em" /> <mn>0</mn> <mo>≤</mo> <mi>ψ</mi> <mo>≤</mo> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan(2\psi )={\frac {2E_{0x}E_{0y}\cos \varphi }{E_{0x}^{2}-E_{0y}^{2}}},\qquad 0\leq \psi \leq \pi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66f1c1a2b42c6c62e5e17eb7835375fcbd926c63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:41.527ex; height:6.843ex;" alt="{\displaystyle \tan(2\psi )={\frac {2E_{0x}E_{0y}\cos \varphi }{E_{0x}^{2}-E_{0y}^{2}}},\qquad 0\leq \psi \leq \pi }">。</dd></dl> 「橢圓角」<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.455ex; height:2.009ex;" alt="{\displaystyle \chi }">定義為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(2\chi )={\frac {2E_{0x}E_{0y}\sin \varphi }{E_{0x}^{2}+E_{0y}^{2}}},\qquad -\pi /4<\chi \leq \pi /4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>χ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> </mrow> <mrow> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="2em" /> <mo>−</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> <mo><</mo> <mi>χ</mi> <mo>≤</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(2\chi )={\frac {2E_{0x}E_{0y}\sin \varphi }{E_{0x}^{2}+E_{0y}^{2}}},\qquad -\pi /4<\chi \leq \pi /4}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fc7908f595edf3ba66f77516f6e0a37453a6618" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:47.279ex; height:6.843ex;" alt="{\displaystyle \sin(2\chi )={\frac {2E_{0x}E_{0y}\sin \varphi }{E_{0x}^{2}+E_{0y}^{2}}},\qquad -\pi /4<\chi \leq \pi /4}">。</dd></dl> 偏振橢圓是由橢圓幅、定向角、橢圓角設定。電磁波的偏振方向是由定向角、橢圓角設定。<a href="#cite_note-esa-19">[17]</a>:6-8 換另一種寫法，定義附屬角<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }">為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan \alpha =E_{0y}/E_{0x},\qquad 0\leq \alpha \leq \pi /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <mo>,</mo> <mspace width="2em" /> <mn>0</mn> <mo>≤</mo> <mi>α</mi> <mo>≤</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \alpha =E_{0y}/E_{0x},\qquad 0\leq \alpha \leq \pi /2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be6431084e14795900f6875216ea391228bf017d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:34.975ex; height:3.009ex;" alt="{\displaystyle \tan \alpha =E_{0y}/E_{0x},\qquad 0\leq \alpha \leq \pi /2}">，</dd></dl> 則定向角、橢圓角可以寫為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan(2\psi )=\tan(2\alpha )\cos \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>ψ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>α</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan(2\psi )=\tan(2\alpha )\cos \varphi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91d7d2db75b2f3917f96f864fe9234efccb64a75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.167ex; height:2.843ex;" alt="{\displaystyle \tan(2\psi )=\tan(2\alpha )\cos \varphi }">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(2\chi )=\sin(2\alpha )\sin \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>χ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>α</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(2\chi )=\sin(2\alpha )\sin \varphi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6eb9043a69eb77f76629ff42a0903d6d6d3bfe62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.846ex; height:2.843ex;" alt="{\displaystyle \sin(2\chi )=\sin(2\alpha )\sin \varphi }">。</dd></dl> 設定<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi (t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi (t)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d14b0b0146f7196ff6234dd7fc36608035da5b3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.679ex; height:2.843ex;" alt="{\displaystyle \xi (t)}">為電場向量與x-軸之間的夾角；隨著時間流易，電場向量的矢端會沿著橢圓旋轉，從+z-坐標位置朝原點看，假若呈逆時針旋轉，則<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi (t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi (t)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d14b0b0146f7196ff6234dd7fc36608035da5b3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.679ex; height:2.843ex;" alt="{\displaystyle \xi (t)}">正在單調遞增，電磁波是左旋橢圓偏振；假若呈順時針旋轉，則<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi (t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi (t)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d14b0b0146f7196ff6234dd7fc36608035da5b3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.679ex; height:2.843ex;" alt="{\displaystyle \xi (t)}">正在單調遞減，電磁波是右旋橢圓偏振。所以，從<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi (t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi (t)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d14b0b0146f7196ff6234dd7fc36608035da5b3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.679ex; height:2.843ex;" alt="{\displaystyle \xi (t)}">對於時間<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}">的導數，可以推斷出電磁波是哪一種偏振；假若導數大於零，則電磁波是左旋橢圓偏振；假若導數小於零，電磁波是右旋橢圓偏振。在任意固定位置<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e72d1d86e86355892b39b8eb32b964834e113bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.135ex; height:2.009ex;" alt="{\displaystyle z_{0}}">，判斷角<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi (t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi (t)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d14b0b0146f7196ff6234dd7fc36608035da5b3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.679ex; height:2.843ex;" alt="{\displaystyle \xi (t)}">以方程表示為<a href="#cite_note-esa-19">[17]</a>:6-8 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle tan\xi (t)={\frac {E_{y}(z_{0},t)}{E_{x}(z_{0},t)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>ξ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle tan\xi (t)={\frac {E_{y}(z_{0},t)}{E_{x}(z_{0},t)}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a422a54670d5fc9111ce1b53b044aab3f3312fd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:19.784ex; height:6.509ex;" alt="{\displaystyle tan\xi (t)={\frac {E_{y}(z_{0},t)}{E_{x}(z_{0},t)}}}">。</dd></dl> 導數與相位差<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }">之間的關係為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial \xi (t)}{\partial t}}\propto -\sin \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>∝</mo> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial \xi (t)}{\partial t}}\propto -\sin \varphi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b112637d174d5af34c6f06e6c001888b5bd0f4e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.89ex; height:5.843ex;" alt="{\displaystyle {\frac {\partial \xi (t)}{\partial t}}\propto -\sin \varphi }">。</dd></dl> 所以，假若相位差<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0<\varphi \leq \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo><</mo> <mi>φ</mi> <mo>≤</mo> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0<\varphi \leq \pi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d7d9c997aeb0b412ffeabbfa42be8e34724198b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.212ex; height:2.676ex;" alt="{\displaystyle 0<\varphi \leq \pi }">，則橢圓角<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0<\chi \leq \pi /4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo><</mo> <mi>χ</mi> <mo>≤</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0<\chi \leq \pi /4}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5cc957eaed5d241cb1467b5e871efed75fa138b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.471ex; height:2.843ex;" alt="{\displaystyle 0<\chi \leq \pi /4}">，電磁波是右旋橢圓偏振；假若相位差<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\pi \leq \varphi <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>π</mi> <mo>≤</mo> <mi>φ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\pi \leq \varphi <0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9d4dd77f5228e9e1a8263a8fe45d10e3d90ef83" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.02ex; height:2.676ex;" alt="{\displaystyle -\pi \leq \varphi <0}">，則橢圓角<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\pi /4\leq \chi <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> <mo>≤</mo> <mi>χ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\pi /4\leq \chi <0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e154906e1363faea3ddc394b69936bb3e39a2fde" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.28ex; height:2.843ex;" alt="{\displaystyle -\pi /4\leq \chi <0}">，電磁波是左旋橢圓偏振。 在十九世紀，偏振橢圓是唯一能幫助想像與理解偏振問題的方法。但是，這方法有個缺點，假若光束必須傳播通過很多偏振器材，描述偏振行為的方程會變得很煩雜，很難找到解答。一直等到1892年，<a href="/wiki/%E6%98%82%E5%88%A9%C2%B7%E5%BA%9E%E5%8A%A0%E8%8E%B1" class="mw-redirect" title="昂利·庞加莱">昂利·龐加萊</a>提出<a href="/w/index.php?title=%E9%BE%90%E5%8A%A0%E8%90%8A%E7%90%83&action=edit&redlink=1" class="new" title="龐加萊球（页面不存在）">龐加萊球</a>（Poincaré sphere）後，才有了更好的解析方法。<a href="#cite_note-Collett2003-20">[18]</a>:43 <div class="mw-heading mw-heading3"><h3 id="瓊斯向量與瓊斯矩陣">瓊斯向量與瓊斯矩陣</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=9" title="编辑章节：瓊斯向量與瓊斯矩陣">编辑</a>]</div> <style data-mw-deduplicate="TemplateStyles:r84833064">.mw-parser-output .hatnote{font-size:small}.mw-parser-output div.hatnote{padding-left:2em;margin-bottom:0.8em;margin-top:0.8em}.mw-parser-output .hatnote-notice-img::after{content:"\202f \202f \202f \202f "}.mw-parser-output .hatnote-notice-img-small::after{content:"\202f \202f "}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}body.skin-minerva .mw-parser-output .hatnote-notice-img,body.skin-minerva .mw-parser-output .hatnote-notice-img-small{display:none}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E7%93%8A%E6%96%AF%E9%81%8B%E7%AE%97" title="瓊斯運算">瓊斯運算</a></div> 瓊斯向量可以用來描述完全偏振光；它不能用來描述非偏振光與部分偏振光。假設橫電磁波<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} (z,t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} (z,t)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20475434ab96ad3e5abadd4ba904912b55649fec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.528ex; height:2.843ex;" alt="{\displaystyle \mathbf {E} (z,t)}">的分量為<a href="#cite_note-Collett2005-18">[16]</a>:57ff<a href="#cite_note-Hecht2002-1">[1]</a>:376-377 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{x}=E_{0x}e^{i(kz-\omega t+\varphi _{x})}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mi>z</mi> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{x}=E_{0x}e^{i(kz-\omega t+\varphi _{x})}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0355a661dc645c90cfa1a6f40b980e1e60474c64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.66ex; height:3.176ex;" alt="{\displaystyle E_{x}=E_{0x}e^{i(kz-\omega t+\varphi _{x})}}">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{y}=E_{0y}e^{i(kz-\omega t+\varphi _{y})}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mi>z</mi> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{y}=E_{0y}e^{i(kz-\omega t+\varphi _{y})}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39f6dbe03732d7fe5bbc518b432599de4c563d81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.314ex; height:3.509ex;" alt="{\displaystyle E_{y}=E_{0y}e^{i(kz-\omega t+\varphi _{y})}}">；</dd></dl> 其中，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0x}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22e4da03dfed795de425f79181304cad8fabdf17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.71ex; height:2.509ex;" alt="{\displaystyle E_{0x}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0y}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/033fedf2a625661d78bc47664a4d649c82fcb95a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.587ex; height:2.843ex;" alt="{\displaystyle E_{0y}}">分別為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{x}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/029e49fbec18ece71cdd1e68bc478444e2c99d30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.888ex; height:2.509ex;" alt="{\displaystyle E_{x}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{y}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff71d8c6b39b429ae113e95c77c0016bd4aa62ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.765ex; height:2.843ex;" alt="{\displaystyle E_{y}}">的最大實值。 這橫電磁波的瓊斯向量<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7686846b1a6b756cb514954000004ab5e7b2a5ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.381ex; height:2.176ex;" alt="{\displaystyle \mathbf {J} }">為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} ={\binom {E_{0x}e^{i\varphi _{x}}}{E_{0y}e^{i\varphi _{y}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> </msup> </mrow> <mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> </msup> </mrow> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} ={\binom {E_{0x}e^{i\varphi _{x}}}{E_{0y}e^{i\varphi _{y}}}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0be8092a9cd8621519385d1a4b1014c4b8a21ad6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:15.496ex; height:6.509ex;" alt="{\displaystyle \mathbf {J} ={\binom {E_{0x}e^{i\varphi _{x}}}{E_{0y}e^{i\varphi _{y}}}}}">。</dd></dl> 通常，瓊斯向量會被<a href="/wiki/%E6%AD%B8%E4%B8%80%E5%8C%96" class="mw-redirect" title="歸一化">歸一化</a>成為單位向量。通過歸一化後，幾個常用的瓊斯向量可以很容易地被辨認出來。例如，平行於x-軸的線偏振（水平偏振）、平行於y-軸的線偏振（垂直偏振），它們的瓊斯向量<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{h}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{h}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51dc7ff8b56c22c2ba8e63194229186cb0ffb91a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.56ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{h}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{v}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{v}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2463f73372df2d5de6937fcb94009339c7ac8a98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.41ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{v}}">分別為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{h}={\binom {1}{0}}\qquad \qquad \mathbf {J} _{v}={\binom {0}{1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mn>1</mn> <mn>0</mn> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <mspace width="2em" /> <mspace width="2em" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mn>0</mn> <mn>1</mn> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{h}={\binom {1}{0}}\qquad \qquad \mathbf {J} _{v}={\binom {0}{1}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2e1a9824e6ffdb28e9cce145f2c27e5ec52cfac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:29.625ex; height:6.176ex;" alt="{\displaystyle \mathbf {J} _{h}={\binom {1}{0}}\qquad \qquad \mathbf {J} _{v}={\binom {0}{1}}}">。</dd></dl> 左旋圓偏振、右旋圓偏振的瓊斯向量<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{L}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77a9016022dc1b2ccc1370df4a1bdacdcccebede" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.732ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{L}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{R}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0246f5fb04a5464d3ec7f2866d5efe3b250556bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.86ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{R}}">分別為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{L}={\frac {1}{\sqrt {2}}}{\binom {1}{-i}}\qquad \qquad \mathbf {J} _{R}={\frac {1}{\sqrt {2}}}{\binom {1}{+i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mn>1</mn> <mrow> <mo>−</mo> <mi>i</mi> </mrow> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <mspace width="2em" /> <mspace width="2em" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mn>1</mn> <mrow> <mo>+</mo> <mi>i</mi> </mrow> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{L}={\frac {1}{\sqrt {2}}}{\binom {1}{-i}}\qquad \qquad \mathbf {J} _{R}={\frac {1}{\sqrt {2}}}{\binom {1}{+i}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d685055561a7dda45d7073147b30af760107eaa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:41.012ex; height:6.509ex;" alt="{\displaystyle \mathbf {J} _{L}={\frac {1}{\sqrt {2}}}{\binom {1}{-i}}\qquad \qquad \mathbf {J} _{R}={\frac {1}{\sqrt {2}}}{\binom {1}{+i}}}">。</dd></dl> 兩個偏振態<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} _{1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96dda96911121bf5e457b6c1921c52705ae0f156" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.811ex; height:2.509ex;" alt="{\displaystyle \mathbf {E} _{1}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} _{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9d714d2ed30aa25b0ee86391014ada89f5b105c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.811ex; height:2.509ex;" alt="{\displaystyle \mathbf {E} _{2}}">相互正交，若且唯若分別代表它們的兩個瓊斯向量<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d65391a5384e9f18b9b64abb03f6c7910db34280" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.435ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{1}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8be8932136abba5b331e127a7d9dc65c481ef2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.435ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{2}}">相互正交，以方程表示， <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{1}\cdot \mathbf {J} _{2}^{*}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{1}\cdot \mathbf {J} _{2}^{*}=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16d6058e1f56cc5ec3a242e386abfd94e0bb2d75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.81ex; height:2.843ex;" alt="{\displaystyle \mathbf {J} _{1}\cdot \mathbf {J} _{2}^{*}=0}">。</dd></dl> 因此，水平偏振態與垂直偏振態相互正交，因為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{h}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{h}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51dc7ff8b56c22c2ba8e63194229186cb0ffb91a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.56ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{h}}">與<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{v}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{v}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2463f73372df2d5de6937fcb94009339c7ac8a98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.41ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{v}}">相互正交： <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{h}\cdot \mathbf {J} _{v}^{*}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> <mo>⋅</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{h}\cdot \mathbf {J} _{v}^{*}=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f93ccaddcd5668f8ae6a14f814fa7582bd3003b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.935ex; height:2.843ex;" alt="{\displaystyle \mathbf {J} _{h}\cdot \mathbf {J} _{v}^{*}=0}">；</dd></dl> 左旋圓偏振態與右旋圓偏振態相互正交，因為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{L}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77a9016022dc1b2ccc1370df4a1bdacdcccebede" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.732ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{L}}">與<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{R}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0246f5fb04a5464d3ec7f2866d5efe3b250556bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.86ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{R}}">相互正交： <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{L}\cdot \mathbf {J} _{R}^{*}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>⋅</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{L}\cdot \mathbf {J} _{R}^{*}=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/205a962458878068b552b7c26372ec842ff4fbcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.533ex; height:2.843ex;" alt="{\displaystyle \mathbf {J} _{L}\cdot \mathbf {J} _{R}^{*}=0}">。</dd></dl> 這些相互正交的瓊斯向量對形成一個<a href="/wiki/%E5%9F%BA%E5%BA%95" class="mw-redirect" title="基底">基底</a>，可以用來表示任意瓊斯向量。例如，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{L}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77a9016022dc1b2ccc1370df4a1bdacdcccebede" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.732ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{L}}">與<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{R}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0246f5fb04a5464d3ec7f2866d5efe3b250556bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.86ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{R}}">可以用來表示任意完全偏振態的瓊斯向量；在<a href="/wiki/%E5%8F%8C%E6%8A%98%E5%B0%84" title="双折射">雙折射</a>介質裏，左旋圓偏振態與右旋圓偏振態各自具有不同的物理行為，這可以分別用這兩個瓊斯向量來代表與作估算。 瓊斯矩陣是作用於瓊斯向量的算符。在實際實驗裏，瓊斯矩陣是由各種光學元件實現，例如，透鏡、分光器、鏡子等等。舉個簡單例子，水平線性偏振片、垂直線性偏振片的瓊斯矩陣分別為<a href="#cite_note-Hecht2002-1">[1]</a>:377-379 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {M} _{h}={\begin{pmatrix}1&0\\0&0\end{pmatrix}}\qquad \qquad \mathbb {M} _{v}={\begin{pmatrix}0&0\\0&1\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mspace width="2em" /> <mspace width="2em" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {M} _{h}={\begin{pmatrix}1&0\\0&0\end{pmatrix}}\qquad \qquad \mathbb {M} _{v}={\begin{pmatrix}0&0\\0&1\end{pmatrix}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23a366ef65238ad081a9e62b06bb953b56676cbb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:39.724ex; height:6.176ex;" alt="{\displaystyle \mathbb {M} _{h}={\begin{pmatrix}1&0\\0&0\end{pmatrix}}\qquad \qquad \mathbb {M} _{v}={\begin{pmatrix}0&0\\0&1\end{pmatrix}}}">。</dd></dl> 給定入射光為左旋圓偏振光<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{L}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77a9016022dc1b2ccc1370df4a1bdacdcccebede" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.732ex; height:2.509ex;" alt="{\displaystyle \mathbf {J} _{L}}">，光學元件為水平線性偏振片<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {M} _{h}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {M} _{h}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf446d5d6df8b5e7688609ba21cd2bfa4a2837b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.373ex; height:2.509ex;" alt="{\displaystyle \mathbb {M} _{h}}">，那麼，透射光為水平偏振光，其瓊斯向量為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} =\mathbb {M} _{h}\mathbf {J} _{L}={\begin{pmatrix}1&0\\0&0\end{pmatrix}}{\frac {1}{\sqrt {2}}}{\binom {1}{-i}}={\frac {1}{\sqrt {2}}}{\binom {1}{0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mn>1</mn> <mrow> <mo>−</mo> <mi>i</mi> </mrow> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mn>1</mn> <mn>0</mn> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} =\mathbb {M} _{h}\mathbf {J} _{L}={\begin{pmatrix}1&0\\0&0\end{pmatrix}}{\frac {1}{\sqrt {2}}}{\binom {1}{-i}}={\frac {1}{\sqrt {2}}}{\binom {1}{0}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a6144d7d8695a756d9e45aa09a13d593bb27115" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:44.086ex; height:6.509ex;" alt="{\displaystyle \mathbf {J} =\mathbb {M} _{h}\mathbf {J} _{L}={\begin{pmatrix}1&0\\0&0\end{pmatrix}}{\frac {1}{\sqrt {2}}}{\binom {1}{-i}}={\frac {1}{\sqrt {2}}}{\binom {1}{0}}}">。</dd></dl> <div class="mw-heading mw-heading3"><h3 id="斯托克斯參數與穆勒矩陣">斯托克斯參數與穆勒矩陣</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=10" title="编辑章节：斯托克斯參數與穆勒矩陣">编辑</a>]</div> 非偏振光與部分偏振光不能用瓊斯向量來描述，必需使用<a href="/w/index.php?title=%E6%96%AF%E6%89%98%E5%85%8B%E6%96%AF%E5%8F%83%E6%95%B8&action=edit&redlink=1" class="new" title="斯托克斯參數（页面不存在）">斯托克斯參數</a>（英语：<a href="https://en.wikipedia.org/wiki/Stokes_parameters" class="extiw" title="en:Stokes parameters">Stokes_parameters</a>）才能正確描述。斯托克斯參數<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe0ac45a38c4437bd2689a14ec434cd499e7e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.479ex; height:2.509ex;" alt="{\displaystyle S_{0}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bf84e7fd4fb8259a9b37f956afdf83ee2a020f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.479ex; height:2.509ex;" alt="{\displaystyle S_{1}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1143e284d5f25cef778ab482edf6617a523ddd9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.479ex; height:2.509ex;" alt="{\displaystyle S_{2}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70e15f3e200aaa247f69c43110cc5a09ecc91b89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.479ex; height:2.509ex;" alt="{\displaystyle S_{3}}">是可以用儀器測量到的物理量，假設<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/893d08e90ea73781dc133414d661529d0651ca80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{0}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03f18d041b2df30adef07164dbf285878893dedc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{1}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e3506ae39df854f347365bae6f326ef4f565be5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{2}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/becba5d3350c4dd244f3cda48eb13439f21ed350" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{3}}">分別是光束的總體、水平偏振部分、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +45^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <msup> <mn>45</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +45^{\circ }}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cade0bbd039b9abb87a81bdd141ca38237611f05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.187ex; height:2.509ex;" alt="{\displaystyle +45^{\circ }}">偏振部分、右旋圓偏振部分的輻照度，斯托克斯參數<a href="/wiki/%E6%93%8D%E4%BD%9C%E5%AE%9A%E4%B9%89" title="操作定义">操作定義</a>為<a href="#cite_note-Collett2005-18">[16]</a>:12-14 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{0}=I_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{0}=I_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/143158b2244a001429256246a3555d3537b0b6e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.655ex; height:2.509ex;" alt="{\displaystyle S_{0}=I_{0}}">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{1}=I_{1}-I_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{1}=I_{1}-I_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de6e6479a8cccb1bb0c972d8cae556f578a9f94c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.573ex; height:2.509ex;" alt="{\displaystyle S_{1}=I_{1}-I_{0}}">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{2}=I_{2}-I_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{2}=I_{2}-I_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6edb727971210568aab1fb1320f4017fdb1bbfa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.573ex; height:2.509ex;" alt="{\displaystyle S_{2}=I_{2}-I_{0}}">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{3}=I_{3}-I_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{3}=I_{3}-I_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1457edc625505537d76a9026853835658c6a331" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.573ex; height:2.509ex;" alt="{\displaystyle S_{3}=I_{3}-I_{0}}">。</dd></dl> 只要測量光束的<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/893d08e90ea73781dc133414d661529d0651ca80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{0}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03f18d041b2df30adef07164dbf285878893dedc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{1}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e3506ae39df854f347365bae6f326ef4f565be5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{2}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/becba5d3350c4dd244f3cda48eb13439f21ed350" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{3}}">，就可簡單估算出斯托克斯參數。 <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Poincar%C3%A9_sphere.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Poincar%C3%A9_sphere.svg/200px-Poincar%C3%A9_sphere.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Poincar%C3%A9_sphere.svg/300px-Poincar%C3%A9_sphere.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Poincar%C3%A9_sphere.svg/400px-Poincar%C3%A9_sphere.svg.png 2x" data-file-width="360" data-file-height="360" /></a><figcaption>龐加萊球圖。<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{p}=I_{0}{\mathcal {P}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{p}=I_{0}{\mathcal {P}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29c18d620ebca17e0be51212c0a5b3b5adf02476" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.962ex; height:2.843ex;" alt="{\displaystyle I_{p}=I_{0}{\mathcal {P}}}">。</figcaption></figure> 為了便利運算，將斯托克斯參數組成一個向量，稱為「斯托克斯向量」。<a href="#cite_note-21">[註 3]</a>斯托克斯參數與輻照度、偏振度<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {P}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {P}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10d6ec962de5797ba4f161c40e66dca74ae95cc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.704ex; height:2.176ex;" alt="{\displaystyle {\mathcal {P}}}">、偏振橢圓參數之間的關係為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{0}=I_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{0}=I_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/143158b2244a001429256246a3555d3537b0b6e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.655ex; height:2.509ex;" alt="{\displaystyle S_{0}=I_{0}}">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{1}=I_{0}{\mathcal {P}}\cos 2\psi \cos 2\chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> <mi>cos</mi> <mo>⁡</mo> <mn>2</mn> <mi>ψ</mi> <mi>cos</mi> <mo>⁡</mo> <mn>2</mn> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{1}=I_{0}{\mathcal {P}}\cos 2\psi \cos 2\chi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f840877347c06e91f0e87b4fff043a99deee1a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.422ex; height:2.509ex;" alt="{\displaystyle S_{1}=I_{0}{\mathcal {P}}\cos 2\psi \cos 2\chi }">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{2}=I_{0}{\mathcal {P}}\sin 2\psi \cos 2\chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> <mi>sin</mi> <mo>⁡</mo> <mn>2</mn> <mi>ψ</mi> <mi>cos</mi> <mo>⁡</mo> <mn>2</mn> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{2}=I_{0}{\mathcal {P}}\sin 2\psi \cos 2\chi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e1dc080507cbcfb94ee9ca47b2fce0573a626d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.167ex; height:2.509ex;" alt="{\displaystyle S_{2}=I_{0}{\mathcal {P}}\sin 2\psi \cos 2\chi }">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{3}=I_{0}{\mathcal {P}}\sin 2\chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> <mi>sin</mi> <mo>⁡</mo> <mn>2</mn> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{3}=I_{0}{\mathcal {P}}\sin 2\chi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3da2f813d5a64e51d3e9b675c6b4646d8beb74ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.606ex; height:2.509ex;" alt="{\displaystyle S_{3}=I_{0}{\mathcal {P}}\sin 2\chi }">。</dd></dl> 對於偏振光，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {P}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {P}}=1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e80550bfffd88ae0e0a2a5bda42cf4cc2ebae73" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.965ex; height:2.176ex;" alt="{\displaystyle {\mathcal {P}}=1}">，所以， <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{0}\,^{2}=S_{1}\,^{2}+S_{2}\,^{2}+S_{3}\,^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{0}\,^{2}=S_{1}\,^{2}+S_{2}\,^{2}+S_{3}\,^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b59ab6e764aea17c187fc0cc47fb029a46249e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.461ex; height:3.009ex;" alt="{\displaystyle S_{0}\,^{2}=S_{1}\,^{2}+S_{2}\,^{2}+S_{3}\,^{2}}">。</dd></dl> 對於非偏振光，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {P}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {P}}=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/828072783263094bf641716a5c85069b6f4d37d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.965ex; height:2.176ex;" alt="{\displaystyle {\mathcal {P}}=0}">，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{0}=I_{1}=I_{2}=I_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{0}=I_{1}=I_{2}=I_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2536e84cfa8a9b3f889061e92d625eac7ddae754" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.605ex; height:2.509ex;" alt="{\displaystyle I_{0}=I_{1}=I_{2}=I_{3}}">，所以，斯托克斯向量為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {S} _{n}={\begin{pmatrix}S_{0}\\0\\0\\0\\\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {S} _{n}={\begin{pmatrix}S_{0}\\0\\0\\0\\\end{pmatrix}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a25990e2c9607f5923929db5a7ba5c8bd13dd81a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:13.1ex; height:12.509ex;" alt="{\displaystyle \mathbf {S} _{n}={\begin{pmatrix}S_{0}\\0\\0\\0\\\end{pmatrix}}}">。</dd></dl> 部分偏振光是偏振光與非偏振光的權重組合： <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {S} ={\begin{pmatrix}S_{0}\\S_{1}\\S_{2}\\S_{3}\\\end{pmatrix}}=(1-{\mathcal {P}}){\begin{pmatrix}S_{0}\\0\\0\\0\\\end{pmatrix}}+{\mathcal {P}}{\begin{pmatrix}S_{0}\\S_{1}'\\S_{2}'\\S_{3}'\\\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mo>′</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mo>′</mo> </msubsup> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {S} ={\begin{pmatrix}S_{0}\\S_{1}\\S_{2}\\S_{3}\\\end{pmatrix}}=(1-{\mathcal {P}}){\begin{pmatrix}S_{0}\\0\\0\\0\\\end{pmatrix}}+{\mathcal {P}}{\begin{pmatrix}S_{0}\\S_{1}'\\S_{2}'\\S_{3}'\\\end{pmatrix}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01261e63f72d9d43e65eb0828cabd5c25aa7140b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.851ex; margin-bottom: -0.32ex; width:41.634ex; height:13.509ex;" alt="{\displaystyle \mathbf {S} ={\begin{pmatrix}S_{0}\\S_{1}\\S_{2}\\S_{3}\\\end{pmatrix}}=(1-{\mathcal {P}}){\begin{pmatrix}S_{0}\\0\\0\\0\\\end{pmatrix}}+{\mathcal {P}}{\begin{pmatrix}S_{0}\\S_{1}'\\S_{2}'\\S_{3}'\\\end{pmatrix}}}">。</dd></dl> 部分偏振光的偏振度<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {P}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {P}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10d6ec962de5797ba4f161c40e66dca74ae95cc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.704ex; height:2.176ex;" alt="{\displaystyle {\mathcal {P}}}">為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {P}}={\sqrt {S_{1}\,^{2}+S_{2}\,^{2}+S_{3}\,^{2}}}/S_{0},\qquad 0\leq {\mathcal {P}}\leq 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mspace width="2em" /> <mn>0</mn> <mo>≤</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> <mo>≤</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {P}}={\sqrt {S_{1}\,^{2}+S_{2}\,^{2}+S_{3}\,^{2}}}/S_{0},\qquad 0\leq {\mathcal {P}}\leq 1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5120e103de0ad04941e5aa8ed71670d5d80698d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:44.114ex; height:4.843ex;" alt="{\displaystyle {\mathcal {P}}={\sqrt {S_{1}\,^{2}+S_{2}\,^{2}+S_{3}\,^{2}}}/S_{0},\qquad 0\leq {\mathcal {P}}\leq 1}">。</dd></dl> 通常，整個斯托克斯向量會被除以<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe0ac45a38c4437bd2689a14ec434cd499e7e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.479ex; height:2.509ex;" alt="{\displaystyle S_{0}}">，這意味著光束具有單位輻照度。例如，水平偏振光、垂直偏振光的斯托克斯向量分別為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {S} _{h}={\begin{pmatrix}1\\1\\0\\0\\\end{pmatrix}}\qquad \qquad \mathbf {S} _{v}={\begin{pmatrix}1\\-1\\0\\0\\\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mspace width="2em" /> <mspace width="2em" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {S} _{h}={\begin{pmatrix}1\\1\\0\\0\\\end{pmatrix}}\qquad \qquad \mathbf {S} _{v}={\begin{pmatrix}1\\-1\\0\\0\\\end{pmatrix}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3455db6eb426a4628f779d6aa993275fb5dbdbb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:34.436ex; height:12.509ex;" alt="{\displaystyle \mathbf {S} _{h}={\begin{pmatrix}1\\1\\0\\0\\\end{pmatrix}}\qquad \qquad \mathbf {S} _{v}={\begin{pmatrix}1\\-1\\0\\0\\\end{pmatrix}}}">。</dd></dl> 光學元件作用於光束的效應必須用<a href="/w/index.php?title=%E7%A9%86%E5%8B%92%E7%9F%A9%E9%99%A3&action=edit&redlink=1" class="new" title="穆勒矩陣（页面不存在）">穆勒矩陣</a>（英语：<a href="https://en.wikipedia.org/wiki/Mueller_matrix" class="extiw" title="en:Mueller matrix">Mueller matrix</a>）估算。一般而言，每一種實際光學元件都有其對應的穆勒矩陣，這是瓊斯矩陣的延伸至非偏振光與部分偏振光論題。穆勒矩陣是一個4×4實值矩陣。<a href="#cite_note-Collett2005-18">[16]</a>:17例如，水平線性偏振片、垂直線性偏振片的瓊斯矩陣分別為<a href="#cite_note-Hecht2002-1">[1]</a>:377-379 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {M} _{h}={\frac {1}{2}}{\begin{pmatrix}1&1&0&0\\1&1&0&0\\0&0&0&0\\0&0&0&0\\\end{pmatrix}}\qquad \qquad \mathbb {M} _{v}={\frac {1}{2}}{\begin{pmatrix}1&-1&0&0\\-1&1&0&0\\0&0&0&0\\0&0&0&0\\\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mspace width="2em" /> <mspace width="2em" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {M} _{h}={\frac {1}{2}}{\begin{pmatrix}1&1&0&0\\1&1&0&0\\0&0&0&0\\0&0&0&0\\\end{pmatrix}}\qquad \qquad \mathbb {M} _{v}={\frac {1}{2}}{\begin{pmatrix}1&-1&0&0\\-1&1&0&0\\0&0&0&0\\0&0&0&0\\\end{pmatrix}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7800cd7d31701c62cfd0f2a1951e79852c2c5c97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:62.569ex; height:12.509ex;" alt="{\displaystyle \mathbb {M} _{h}={\frac {1}{2}}{\begin{pmatrix}1&1&0&0\\1&1&0&0\\0&0&0&0\\0&0&0&0\\\end{pmatrix}}\qquad \qquad \mathbb {M} _{v}={\frac {1}{2}}{\begin{pmatrix}1&-1&0&0\\-1&1&0&0\\0&0&0&0\\0&0&0&0\\\end{pmatrix}}}">。</dd></dl> 給定入射光的斯托克斯向量<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {S} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {S} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac8a515de34f0af7d15de46f73bf674950d444a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.485ex; height:2.176ex;" alt="{\displaystyle \mathbf {S} }">、光學元件的穆勒矩陣<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {M} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {M} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c466bc0f750f74236f81922b9bff54b6d50452a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.194ex; height:2.176ex;" alt="{\displaystyle \mathbb {M} }">，就可以算出透射光的斯托克斯向量<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {S} '}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {S} '}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/119b9dcefcb8b6404fca006ab919d1cffe0a8bdc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.17ex; height:2.509ex;" alt="{\displaystyle \mathbf {S} '}">： <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {S} '=\mathbb {M} \mathbf {S} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {S} '=\mathbb {M} \mathbf {S} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42c13c1c61e0a201d361ba704dc081aec3c230f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.947ex; height:2.509ex;" alt="{\displaystyle \mathbf {S} '=\mathbb {M} \mathbf {S} }">。</dd></dl> 例如，假設入射光為非偏振光<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {S} _{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {S} _{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43e77e8d41ddba671b9704afc960a0be4d09911b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.704ex; height:2.509ex;" alt="{\displaystyle \mathbf {S} _{n}}">，光學元件為水平線性偏振片<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {M} _{h}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {M} _{h}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf446d5d6df8b5e7688609ba21cd2bfa4a2837b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.373ex; height:2.509ex;" alt="{\displaystyle \mathbb {M} _{h}}">，那麼，透射光為水平偏振光，其斯托克斯向量為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {S} =\mathbb {M} _{h}\mathbf {S} _{n}={\frac {1}{2}}{\begin{pmatrix}1&1&0&0\\1&1&0&0\\0&0&0&0\\0&0&0&0\\\end{pmatrix}}{\begin{pmatrix}1\\0\\0\\0\\\end{pmatrix}}={\frac {1}{2}}{\begin{pmatrix}1\\1\\0\\0\\\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {S} =\mathbb {M} _{h}\mathbf {S} _{n}={\frac {1}{2}}{\begin{pmatrix}1&1&0&0\\1&1&0&0\\0&0&0&0\\0&0&0&0\\\end{pmatrix}}{\begin{pmatrix}1\\0\\0\\0\\\end{pmatrix}}={\frac {1}{2}}{\begin{pmatrix}1\\1\\0\\0\\\end{pmatrix}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f282967b6dadb6daa5316cc6eae01f9804ef356a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:49.252ex; height:12.509ex;" alt="{\displaystyle \mathbf {S} =\mathbb {M} _{h}\mathbf {S} _{n}={\frac {1}{2}}{\begin{pmatrix}1&1&0&0\\1&1&0&0\\0&0&0&0\\0&0&0&0\\\end{pmatrix}}{\begin{pmatrix}1\\0\\0\\0\\\end{pmatrix}}={\frac {1}{2}}{\begin{pmatrix}1\\1\\0\\0\\\end{pmatrix}}}">。</dd></dl> 更進階的矩陣方法涉及到<a href="/w/index.php?title=%E7%9B%B8%E5%B9%B2%E7%9F%A9%E9%99%A3&action=edit&redlink=1" class="new" title="相干矩陣（页面不存在）">相干矩陣</a>（coherency matrix）的表述。<a href="#cite_note-O'Neill2004-22">[19]</a>:137-142 <div class="mw-heading mw-heading2"><h2 id="偏振測量技術">偏振測量技術</h2>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=11" title="编辑章节：偏振測量技術">编辑</a>]</div> <div class="mw-heading mw-heading3"><h3 id="測量應力">測量應力</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=12" title="编辑章节：測量應力">编辑</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Transmission_planar_Polariscope_zh_hans.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Transmission_planar_Polariscope_zh_hans.svg/250px-Transmission_planar_Polariscope_zh_hans.svg.png" decoding="async" width="250" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Transmission_planar_Polariscope_zh_hans.svg/375px-Transmission_planar_Polariscope_zh_hans.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Transmission_planar_Polariscope_zh_hans.svg/500px-Transmission_planar_Polariscope_zh_hans.svg.png 2x" data-file-width="1000" data-file-height="600" /></a><figcaption>平面偏光仪工作示意图。</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Polarized_Stress_Glasses.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Polarized_Stress_Glasses.jpg/250px-Polarized_Stress_Glasses.jpg" decoding="async" width="250" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Polarized_Stress_Glasses.jpg/375px-Polarized_Stress_Glasses.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Polarized_Stress_Glasses.jpg/500px-Polarized_Stress_Glasses.jpg 2x" data-file-width="2430" data-file-height="1203" /></a><figcaption>使用偏光儀，可以觀察到塑膠玻璃感受到的應力。</figcaption></figure> 假若兩塊不同類型的<a href="/wiki/%E5%81%8F%E6%8C%AF%E7%89%87" title="偏振片">偏振片</a>分別製成的兩種偏振光相互正交，則稱它們為「正交偏振片」。例如，水平偏振片與垂直偏振片分別製成的水平偏振光與垂直偏振光相互正交，它們是兩塊正交偏振片。類似地，左旋圓偏振片與右旋圓偏振片也是兩塊正交偏振片。這實驗設置簡單地組成<a href="/w/index.php?title=%E5%81%8F%E5%85%89%E5%84%80&action=edit&redlink=1" class="new" title="偏光儀（页面不存在）">偏光儀</a>（polariscope），又稱「偏振光鏡」；光束最先入射的偏振片為起偏器，然後再入射的偏振片為<a href="/wiki/%E6%AA%A2%E5%81%8F%E5%99%A8" title="檢偏器">檢偏器</a>；水平偏振片與垂直偏振片共同組成「平面偏光儀」；左旋圓偏振片與右旋圓偏振片共同組成「圓偏光儀」。如右圖所示，假設照射光束於由水平偏振片製成的起偏器，因為透射過的水平偏振光會被由垂直偏振片製成的檢偏器吸收，不能透射過垂直偏振片；所以，光束無法通過兩塊正交偏振片共同組成的偏光儀，透射的<a href="/wiki/%E5%B9%85%E7%85%A7%E5%BA%A6" class="mw-redirect" title="幅照度">幅照度</a>為零。但是假設將雙折射物質置入偏光儀內，即兩塊正交偏振片之間，光束在通過雙折射物質的過程中，偏振會被旋轉，因此可以從偏光儀觀察到透射光的色彩圖樣，並且測量到其<a href="/wiki/%E5%B9%85%E7%85%A7%E5%BA%A6" class="mw-redirect" title="幅照度">幅照度</a>。<a href="#cite_note-Driggers2003-3">[3]</a>:2142 各向同性固體不會顯示出<a href="/wiki/%E5%8F%8C%E6%8A%98%E5%B0%84" title="双折射">雙折射</a>現象。但是，假設施加機械<a href="/wiki/%E6%87%89%E5%8A%9B" title="應力">應力</a>，則會發生雙折射現象。製造塑膠成品的<a href="/wiki/%E6%B3%A8%E5%B0%84%E6%88%90%E5%9E%8B" class="mw-redirect" title="注射成型">注射成型</a>過程可能會將所施加的機械應力冷凍在塑膠成品裏。偏光儀可以用來分析雙折射物質所感受到的應力與<a href="/wiki/%E5%BA%94%E5%8F%98_(%E7%89%A9%E7%90%86%E5%AD%A6)" title="应变 (物理学)">應變</a>。將雙折射物質置入偏光儀內，從測量到在任意位置的透射幅照度，可以估算在雙折射物質對應位置所感受到的應力與<a href="/wiki/%E5%BA%94%E5%8F%98_(%E7%89%A9%E7%90%86%E5%AD%A6)" title="应变 (物理学)">應變</a>。<a href="/w/index.php?title=%E5%85%89%E5%BD%88%E6%80%A7%E6%B3%95&action=edit&redlink=1" class="new" title="光彈性法（页面不存在）">光彈性法</a>（photoelasticity）應用這偏振理論來分析固體所感受到的機械應力。這是一種極具功能的實驗方法，在結構工程學與機械工程學有廣泛的用途。<a href="#cite_note-23">[20]</a>:167-170 <div class="mw-heading mw-heading3"><h3 id="橢圓偏振測量術">橢圓偏振測量術</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=13" title="编辑章节：橢圓偏振測量術">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84833064"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E6%A9%A2%E5%9C%93%E5%81%8F%E6%8C%AF%E6%8A%80%E8%A1%93" title="橢圓偏振技術">橢圓偏振測量術</a></div> 橢圓偏振測量術是一種用途極廣的技術，可用來測量均勻表面的光學性質；簡略描述其程序，就是在均勻表面做鏡面反射後，測量光波的偏振態的改變；通常這函數的參數為入射角與波長。由於橢圓偏振測量術倚賴反射機制，樣品不需要具有透明性質，探測儀器也不需要從樣品背部測量透射光的輻照度，這技術還可以應用於<a href="/wiki/%E5%90%B8%E5%85%89%E5%BA%A6" title="吸光度">吸光度</a>極高的物質，並且不具有破壞性，只需要很少量的樣品就可以做測量。 橢圓偏振測量術也可以用來測量薄膜的複<a href="/wiki/%E6%8A%98%E5%B0%84%E7%8E%87" title="折射率">折射率</a>與厚度。應用橢圓偏振技術，照射光束於薄膜樣品，然後分析反射光的偏振改變，即可估算複數<a href="/wiki/%E6%8A%98%E5%B0%84%E7%8E%87" title="折射率">折射率</a>或<a href="/wiki/%E4%BB%8B%E7%94%B5%E5%B8%B8%E6%95%B0" class="mw-redirect" title="介电常数">介電函數</a><a href="/wiki/%E5%BC%B5%E9%87%8F" title="張量">張量</a>，以此獲得基本的物理參數，這包括表面<a href="/w/index.php?title=%E7%B2%97%E7%B3%99%E5%BA%A6&action=edit&redlink=1" class="new" title="粗糙度（页面不存在）">粗糙度</a>（roughness）、晶體質量、化學成分或<a href="/wiki/%E5%AF%BC%E7%94%B5%E6%80%A7" class="mw-redirect" title="导电性">導電性</a>。它常被用來鑑定單層或多層堆疊的薄膜厚度，可量測厚度由數<a href="/wiki/%C3%85" title="Å">Å</a>到幾<a href="/wiki/%E5%BE%AE%E7%B1%B3" title="微米">微米</a>，甚至小至一個單原子層，並且準確性極高。<a href="#cite_note-GoldsteinGoldstein2011-5">[5]</a>:585ff<a href="#cite_note-Mansuripur2009-24">[21]</a>:632 <div class="mw-heading mw-heading3"><h3 id="地質學">地質學</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=14" title="编辑章节：地質學">编辑</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:LvMS-Lvm.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/LvMS-Lvm.jpg/220px-LvMS-Lvm.jpg" decoding="async" width="220" height="289" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/LvMS-Lvm.jpg/330px-LvMS-Lvm.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/LvMS-Lvm.jpg/440px-LvMS-Lvm.jpg 2x" data-file-width="1770" data-file-height="2328" /></a><figcaption><a href="/wiki/%E7%81%AB%E5%B1%B1" title="火山">火山</a> <a href="/wiki/%E6%B2%99" title="沙">沙粒</a>的顯微照片；上圖使用的是平面偏振光，下圖是<a href="#測量應力">偏光儀</a>。在中間靠左位置的尺寸塊寬度為0.25 mm。</figcaption></figure> 很多晶體礦石具有線性<a href="/wiki/%E5%8F%8C%E6%8A%98%E5%B0%84" title="双折射">雙折射</a>性質，這促成了偏振現象的初始發現。在<a href="/wiki/%E7%A4%A6%E7%89%A9%E5%AD%B8" class="mw-redirect" title="礦物學">礦物學</a>裏，<a href="/wiki/%E9%A1%AF%E5%BE%AE%E9%8F%A1" title="顯微鏡">偏振顯微鏡</a>時常會應用這雙折射性質來辨識礦石。更詳盡說明，請參閱<a href="/w/index.php?title=%E5%85%89%E5%AD%B8%E7%A4%A6%E7%89%A9%E5%AD%B8&action=edit&redlink=1" class="new" title="光學礦物學（页面不存在）">光學礦物學</a>（optical mineralogy）。<a href="#cite_note-Wayne2013-25">[22]</a>:163-164 <div class="mw-heading mw-heading3"><h3 id="地震學">地震學</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=15" title="编辑章节：地震學">编辑</a>]</div> 在<a href="/wiki/%E5%9C%B0%E9%9C%87%E5%AD%B8" class="mw-redirect" title="地震學">地震學</a>裏，<a href="/wiki/%E5%9C%B0%E9%9C%87%E6%B3%A2" title="地震波">地震波</a>主要分為兩種，一種是<a href="/wiki/%E9%9D%A2%E6%B3%A2" title="面波">面波</a>，一種是<a href="/wiki/%E5%9C%B0%E9%9C%87%E6%B3%A2" title="地震波">體波</a>。面波傳播於地球表面，體波傳播於地球內部。體波又分成<a href="/wiki/%E7%B8%B1%E6%B3%A2" class="mw-redirect" title="縱波">縱波</a>和<a href="/wiki/%E6%A8%AA%E6%B3%A2" title="横波">橫波</a>兩種：<a href="#cite_note-Shearer2009-26">[23]</a>:48-50<a href="#cite_note-SteinWysession2009-15">[13]</a>:56-57 <ul><li>縱波在這裡被稱為<a href="/wiki/P%E6%B3%A2" title="P波">P波</a>，P代表主要（primary）或壓強（pressure），縱波是一種<a href="/wiki/%E7%B8%B1%E6%B3%A2" class="mw-redirect" title="縱波">壓縮波</a>，粒子振動方向平行於地震波的前進方向，在所有地震波中，它的前進速度最快，也最早抵達地表。P波能傳播於<a href="/wiki/%E5%9B%BA%E9%AB%94" class="mw-redirect" title="固體">固體</a>、<a href="/wiki/%E6%B6%B2%E9%AB%94" class="mw-redirect" title="液體">液體</a>或<a href="/wiki/%E6%B0%A3%E9%AB%94" class="mw-redirect" title="氣體">氣體</a>。</li> <li>橫波在這裡被稱為<a href="/wiki/S%E6%B3%A2" title="S波">S波</a>，S意指次要（secondary）或剪切力（shear），橫波是一種<a href="/w/index.php?title=%E5%89%AA%E5%88%87%E6%B3%A2&action=edit&redlink=1" class="new" title="剪切波（页面不存在）">剪切波</a>（shear wave），粒子振動方向垂直於地震波的前進方向，它的前進速度僅次於P波。S波只能在固體中傳播，由於地球<a href="/wiki/%E5%A4%96%E6%A0%B8" title="外核">外核</a>呈液態，S波無法穿過外核。</li></ul> 由於P波和S波的傳播速度不同，利用兩者之間的走時差，可作簡單的地震定位。 <div class="mw-heading mw-heading3"><h3 id="化學">化學</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=16" title="编辑章节：化學">编辑</a>]</div> 根据平面偏振光通過由<a href="/wiki/%E6%89%8B%E6%80%A7" title="手性">手性</a>物質時偏振平面旋轉的方向，可以將手性物質的<a href="/wiki/%E5%AF%B9%E6%98%A0%E5%BC%82%E6%9E%84%E4%BD%93" class="mw-redirect" title="对映异构体">對映異構體</a>分類為左旋、右旋兩種；朝著光源望去，左旋對映異構體會使得偏振平面朝著<a href="/wiki/%E9%80%86%E6%99%82%E9%87%9D%E6%96%B9%E5%90%91" title="逆時針方向">逆時針方向</a>旋轉，右旋對映異構體會使得偏振平面朝著<a href="/wiki/%E9%A0%86%E6%99%82%E9%87%9D%E6%96%B9%E5%90%91" title="順時針方向">順時針方向</a>旋轉。這種偏振平面被旋轉的現象，稱為「圓雙折射現象」，能夠造成這種現象的物質稱為<a href="/wiki/%E5%85%89%E5%AD%B8%E6%B4%BB%E6%80%A7" class="mw-redirect" title="光學活性">光學活性</a>物質。由於這兩種手性物質裏的每一個<a href="/wiki/%E5%8C%96%E5%AD%B8%E9%8D%B5" class="mw-redirect" title="化學鍵">化學鍵</a>的性質與能量都相同，兩種物質的<a href="/wiki/%E6%B2%B8%E9%BB%9E" class="mw-redirect" title="沸點">沸點</a>、<a href="/wiki/%E7%86%94%E9%BB%9E" class="mw-redirect" title="熔點">熔點</a>、<a href="/wiki/%E5%AF%86%E5%BA%A6" title="密度">密度</a>等等都一樣，應用圓雙折射現象，可以辨識手性物質的種類到底是左旋還是右旋。 假若在樣品溶液內，左旋與右旋對映異構體的數量相等（稱這種樣品為<a href="/wiki/%E5%A4%96%E6%B6%88%E6%97%8B%E6%B7%B7%E5%90%88%E7%89%A9" class="mw-redirect" title="外消旋混合物">外消旋混合物</a>），則它們各自產生的效應會相互抵銷，不會產生圓雙折射現象；假若只有一種對映異構體，或者其中某種對映異構體數量較多，則會出現圓雙折射現象（或<a href="/wiki/%E6%97%8B%E5%85%89%E6%80%A7" class="mw-redirect" title="旋光性">旋光性</a>，<a href="/wiki/%E5%85%89%E5%AD%B8%E6%B4%BB%E6%80%A7" class="mw-redirect" title="光學活性">光學活性</a>），從而顯示出不平衡程度的大小（或者物質的濃度，假若只有一種對映異構體存在）。<a href="/wiki/%E5%81%8F%E6%8C%AF%E8%A8%88" title="偏振計">偏振計</a>可以用來量度這種現象。偏振計裏面有一個起偏器與一個檢偏器。將起偏器製成的偏振光入射於光學活性液體，使偏振光被旋轉有限角度，調整檢偏器的旋轉角度，當透射過檢偏器的光強變得最大之時，檢偏器的旋轉角度可以用來估算光學活性液體所造成的旋轉角度。液體樣品的<a href="/w/index.php?title=%E6%97%8B%E5%85%89%E7%8E%87&action=edit&redlink=1" class="new" title="旋光率（页面不存在）">旋光率</a>（specific rotation）等於旋轉角度除以樣品長度。<a href="#cite_note-Hecht2002-1">[1]</a>:169-172 <div class="mw-heading mw-heading3"><h3 id="天文學">天文學</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=17" title="编辑章节：天文學">编辑</a>]</div> <a href="/w/index.php?title=%E6%81%86%E6%98%9F%E5%88%86%E5%85%89%E5%81%8F%E6%8C%AF%E8%AD%9C%E5%84%80&action=edit&redlink=1" class="new" title="恆星分光偏振譜儀（页面不存在）">恆星分光偏振譜儀</a>（stellar spectropolarimeter）可以用來測量恆星的<a href="/wiki/%E7%A3%81%E5%A0%B4" title="磁場">磁場</a>，這種儀器是<a href="/wiki/%E6%94%9D%E8%AD%9C%E5%84%80" title="攝譜儀">攝譜儀</a>和<a href="/wiki/%E5%81%8F%E6%8C%AF%E8%A8%88" title="偏振計">偏振計</a>的結合。第一個來研究恆星磁場的儀器命名為「NARVAL」，被安裝在<a href="/wiki/%E6%B3%95%E5%9C%8B" class="mw-redirect" title="法國">法國</a><a href="/wiki/%E6%AF%94%E5%88%A9%E7%89%9B%E6%96%AF%E5%B1%B1" class="mw-redirect" title="比利牛斯山">比利牛斯山</a>比格爾地區的<a href="/wiki/%E8%B2%9D%E7%88%BE%E7%B4%8D%C2%B7%E6%9D%8E%E5%A5%A7%E6%9C%9B%E9%81%A0%E9%8F%A1" title="貝爾納·李奧望遠鏡">貝爾納·李奧望遠鏡</a>上<a href="#cite_note-27">[24]</a>。 雖然關於<a href="/wiki/%E6%81%86%E6%98%9F" class="mw-redirect" title="恆星">恆星</a><a href="/wiki/%E7%86%B1%E8%BC%BB%E5%B0%84" title="熱輻射">熱輻射</a>的研究通常不會涉及到偏振，很多<a href="/wiki/%E7%9B%B8%E5%B9%B2%E6%80%A7" title="相干性">相干性</a>天文輻射源會發射出偏振輻射，例如<a href="/wiki/%E7%BE%A5%E5%9F%BA" class="mw-redirect" title="羥基">羥基</a><a href="/wiki/%E6%BF%80%E5%BE%AE%E6%B3%A2" title="激微波">微波激射</a>、<a href="/wiki/%E7%94%B2%E9%86%87" title="甲醇">甲醇</a>微波激射等等<a href="/wiki/%E5%A4%A9%E6%96%87%E7%89%A9%E7%90%86%E9%82%81%E5%B0%84" title="天文物理邁射">天文物理邁射</a>，另外，<a href="/wiki/%E5%AE%87%E5%AE%99%E5%A1%B5" class="mw-redirect" title="宇宙塵">星際塵埃</a>也會藉著<a href="/wiki/%E6%95%A3%E5%B0%84" title="散射">散射</a>機制將<a href="/wiki/%E6%98%9F%E5%85%89" title="星光">星光</a>偏振化。對於這些偏振輻射做偏振測量可以給出關於輻射源、輻射源附近<a href="/wiki/%E6%81%86%E6%98%9F%E5%BD%A2%E6%88%90" title="恆星形成">恆星形成</a>的區域關於磁場的信息。<a href="#cite_note-28">[25]</a>:119,124由於地球與太陽的磁場超強於<a href="/wiki/%E6%98%9F%E9%9A%9B%E7%89%A9%E8%B3%AA" class="mw-redirect" title="星際物質">星際磁場</a>，普通方法無法直接地測量到星際磁場；必需使用特別方法，例如，可以應用<a href="/wiki/%E6%B3%95%E6%8B%89%E7%AC%AC%E6%95%88%E5%BA%94" title="法拉第效应">法拉第效應</a>來測量星際<a href="/wiki/%E7%A3%81%E5%A0%B4" title="磁場">磁場</a>。從遙遠輻射源發射出的偏振<a href="/wiki/%E6%97%A0%E7%BA%BF%E7%94%B5" title="无线电">射電輻射</a>，其偏振平面因法拉第效應產生的旋轉角度與磁場成正比。使用這種方法測量到星際磁場大約為10-10-10-9<a href="/wiki/%E7%89%B9%E6%96%AF%E6%8B%89_(%E5%8D%95%E4%BD%8D)" title="特斯拉 (单位)">T</a>。<a href="#cite_note-KarttunenKröger2007-29">[26]</a>:336-337 <a href="/wiki/%E5%AE%87%E5%AE%99%E5%BE%AE%E6%B3%A2%E8%83%8C%E6%99%AF" title="宇宙微波背景">宇宙微波背景</a>的偏振可以用來研究<a href="/wiki/%E5%AE%87%E5%AE%99%E6%9A%B4%E8%84%B9" title="宇宙暴脹">宇宙暴脹</a>的各種物理行為，特別是宇宙暴脹產生的<a href="/wiki/%E5%BC%95%E5%8A%9B%E8%BE%90%E5%B0%84" class="mw-redirect" title="引力辐射">引力輻射</a>與<a href="/wiki/%E8%83%BD%E9%87%8F" title="能量">能量</a>尺寸(1015–1016 <a href="/wiki/GeV" class="mw-redirect" title="GeV">GeV</a>) 。<a href="#cite_note-boyle-30">[27]</a><a href="#cite_note-tegmark-31">[28]</a>這是<a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%8D%AB%E6%98%9F" title="普朗克卫星">普朗克衛星</a>的重要任務之一。<a href="#cite_note-bluebook_c1-32">[29]</a> 天文學者认为，天文輻射很可能促成了地球生物分子的手性。<a href="#cite_note-33">[30]</a> <div class="mw-heading mw-heading2"><h2 id="重要應用">重要應用</h2>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=18" title="编辑章节：重要應用">编辑</a>]</div> <div class="mw-heading mw-heading3"><h3 id="偏光太陽鏡">偏光太陽鏡</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=19" title="编辑章节：偏光太陽鏡">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84833064"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E5%81%8F%E5%85%89%E9%8F%A1" class="mw-redirect" title="偏光鏡">偏光镜</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Reflection_Polarizer2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Reflection_Polarizer2.jpg/300px-Reflection_Polarizer2.jpg" decoding="async" width="300" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Reflection_Polarizer2.jpg/450px-Reflection_Polarizer2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Reflection_Polarizer2.jpg/600px-Reflection_Polarizer2.jpg 2x" data-file-width="1024" data-file-height="384" /></a><figcaption>使用偏光镜之前（左）和之后（右）观察水面的视觉效果</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Mudflats-polariser.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Mudflats-polariser.jpg/300px-Mudflats-polariser.jpg" decoding="async" width="300" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Mudflats-polariser.jpg/450px-Mudflats-polariser.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Mudflats-polariser.jpg/600px-Mudflats-polariser.jpg 2x" data-file-width="6016" data-file-height="2000" /></a><figcaption>起偏器對於從淤泥灘的反射光所產生的效應：左圖顯示出，偏振軸與水平線平行的起偏器會透射這些反射光；右圖顯示出，旋轉這起偏器90°會阻擋幾乎全部<a href="/wiki/%E9%8F%A1%E9%9D%A2%E5%8F%8D%E5%B0%84" title="鏡面反射">鏡面反射光</a>，如同使用偏光太陽鏡<a href="#cite_note-Hecht2002-1">[1]</a>:348-350</figcaption></figure> 照射非偏振光於鏡面表面（光亮表面），通常得到的反射光會具有某種程度的偏振。1808年，法國物理學者<a href="/wiki/%E8%89%BE%E8%92%82%E5%AE%89-%E8%B7%AF%E6%98%93%C2%B7%E9%A9%AC%E5%90%95%E6%96%AF" title="艾蒂安-路易·马吕斯">艾蒂安-路易·馬呂斯</a>最先觀察到這現象。偏光太陽鏡利用這效應來降低水平表面反射出來的<a href="/wiki/%E7%9C%A9%E5%85%89" title="眩光">眩光</a>，特別是當太陽從前方斜照下來時，張眼往前方路面望去會看到的強勁<a href="/wiki/%E7%9C%A9%E5%85%89" title="眩光">眩光</a><a href="#cite_note-Hecht2002-1">[1]</a>:348-350。 许多现代的<a href="/wiki/%E4%BC%91%E9%97%B2%E6%8D%95%E9%B1%BC" title="休闲捕鱼">休闲捕鱼</a>爱好者在<a href="/wiki/%E5%9E%82%E9%92%93" class="mw-redirect" title="垂钓">垂钓</a>时会借助偏光镜的滤光作用来增加<a href="/wiki/%E5%B0%8D%E6%AF%94%E5%BA%A6" title="對比度">对比度</a>并帮助看穿水面寻找<a href="/wiki/%E6%B8%B8%E9%92%93%E9%B1%BC" title="游钓鱼">目标鱼</a>的位置，以便抛饵更有针对性——即俗称的“目视作钓”（sight fishing）。通常<a href="/wiki/%E6%A3%95%E8%89%B2" class="mw-redirect" title="棕色">棕色</a>/<a href="/wiki/%E9%93%9C%E7%BA%A2%E8%89%B2" class="mw-redirect" title="铜红色">铜红色</a>的偏光镜片比较适合在浅水区作钓，而额外带有<a href="/wiki/%E8%93%9D%E8%89%B2" class="mw-redirect" title="蓝色">蓝色</a>和<a href="/wiki/%E7%BB%BF%E8%89%B2" class="mw-redirect" title="绿色">绿色</a>反射<a href="/wiki/%E9%8D%8D%E8%86%9C" title="鍍膜">镀膜</a>的铜色镜片更适合海水环境。 <a href="/wiki/%E9%BB%84%E8%89%B2" title="黄色">黄色</a>的偏光镜片可以在尽可能少降低<a href="/wiki/%E4%BA%AE%E5%BA%A6" title="亮度">亮度</a>的情况下增加些许对比度，更适合低光环境下使用，许多<a href="/wiki/%E5%8F%B8%E6%9C%BA" class="mw-redirect" title="司机">司机</a>会在夜间驾驶时佩戴来减少对面<a href="/wiki/%E6%B1%BD%E8%BD%A6%E7%81%AF" title="汽车灯">汽车灯</a>造成的耀眼。 <div class="mw-heading mw-heading3"><h3 id="天空中的偏振光">天空中的偏振光</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=20" title="编辑章节：天空中的偏振光">编辑</a>]</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CircularPolarizer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/CircularPolarizer.jpg/300px-CircularPolarizer.jpg" decoding="async" width="300" height="114" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/CircularPolarizer.jpg/450px-CircularPolarizer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d8/CircularPolarizer.jpg/600px-CircularPolarizer.jpg 2x" data-file-width="2484" data-file-height="946" /></a><figcaption>右邊照片顯示出<a href="/wiki/%E8%B5%B7%E5%81%8F%E5%99%A8" class="mw-redirect" title="起偏器">偏振濾光片</a>對於天空景色產生的效應。</figcaption></figure> 傳播於地球大氣層的太陽光會因為被大氣分子<a href="/wiki/%E7%91%9E%E5%88%A9%E6%95%A3%E5%B0%84" title="瑞利散射">瑞利散射</a>而使得散射光產生偏振，從天空中的散射光可以觀察到這現象。散射光在清晰的天空中會顯得更明亮、更具色彩。在天空中，與太陽照射的光束呈直角方向的位置，最容易觀察到這偏振現象（偏振方向與太陽光方向、直角方向相垂直）。這種具有部分偏振的散射光，假若使用<a href="/wiki/%E8%B5%B7%E5%81%8F%E5%99%A8" class="mw-redirect" title="起偏器">起偏器</a>，可以使得照片裏的天空變得較黑，增加<a href="/wiki/%E5%B0%8D%E6%AF%94%E5%BA%A6" title="對比度">对比度</a>（contrast）；這樣，可以改良照片的品質。<a href="#cite_note-Hecht2002-1">[1]</a>:346-347<a href="#cite_note-Bekefi-34">[31]</a>:495-499 出現在天空中的偏振光常被用來導航定向。從九世紀至十一世紀間，<a href="/wiki/%E7%B6%AD%E4%BA%AC%E4%BA%BA" title="維京人">維京人</a>時常航行於北大西洋。那時期，歐洲人尚未知道怎樣使用<a href="/wiki/%E6%8C%87%E5%8D%97%E9%92%88" title="指南针">磁羅盤</a>，維京人主要是使用太陽與星星來導航定向，可是，在陰天，這方法無效。學者猜測他們可能知道怎樣使用一種稱為「太陽石」（sunstone）的簡單儀器，但這爭議性理論尚未被證實。1950年代，運輸飛機航行在<a href="/wiki/%E5%9C%B0%E7%A3%81%E5%9C%BA" title="地磁场">地磁極</a>附近時，由於無法使用磁羅盤，假若無法看到太陽或星星時（例如，在陰天或黃昏），時常會使用「天空羅盤」（sky compass）來導航。這儀器是一種很精緻的偏光儀，可以用來觀測天空中的偏振光。十九世紀後期， <a href="/w/index.php?title=%E6%9F%A5%E7%90%86%E6%96%AF%C2%B7%E6%83%A0%E6%96%AF%E9%80%9A&action=edit&redlink=1" class="new" title="查理斯·惠斯通（页面不存在）">查理斯·惠斯通</a>（Charles Wheatstone）發明了<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF%E9%90%98&action=edit&redlink=1" class="new" title="偏振鐘（页面不存在）">偏振鐘</a>（polar clock）。這也是一種偏光儀，可以用來計時。根據惠斯通，偏振鐘比<a href="/wiki/%E6%97%A5%E6%99%B7" title="日晷">日晷</a>的優點更多。<a href="#cite_note-Pye2001-35">[32]</a>:65-69 <div class="mw-heading mw-heading3"><h3 id="液晶顯示器">液晶顯示器</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=21" title="编辑章节：液晶顯示器">编辑</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:LiquidCrystalDisplay-field_off_and_on_with_label.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/LiquidCrystalDisplay-field_off_and_on_with_label.svg/250px-LiquidCrystalDisplay-field_off_and_on_with_label.svg.png" decoding="async" width="250" height="307" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/LiquidCrystalDisplay-field_off_and_on_with_label.svg/375px-LiquidCrystalDisplay-field_off_and_on_with_label.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/LiquidCrystalDisplay-field_off_and_on_with_label.svg/500px-LiquidCrystalDisplay-field_off_and_on_with_label.svg.png 2x" data-file-width="700" data-file-height="860" /></a><figcaption>上方：电路断开，液晶亮。 下方：回路接通，液晶不亮。</figcaption></figure> <a href="/wiki/%E6%B6%B2%E6%99%B6%E9%A1%AF%E7%A4%BA%E5%99%A8" class="mw-redirect" title="液晶顯示器">液晶顯示器</a>（LCD）科技倚賴<a href="/wiki/%E6%B6%B2%E6%99%B6" title="液晶">液晶</a>來旋轉偏振光的偏振平面。如右圖所示，在兩塊正交平面偏振片P1、P2之間置入透明電極層E1、E2和<a href="/wiki/%E6%89%AD%E6%9B%B2%E5%90%91%E5%88%97%E5%9E%8B%E6%B6%B2%E6%99%B6" class="mw-redirect" title="扭曲向列型液晶">扭曲向列型液晶</a>LC。照射非偏振光L於偏振片P1，透射光會呈平面偏振。<a href="#cite_note-Hecht2002-1">[1]</a>:370-373 <ul><li>上方圖：當E1、E2不通電時，液晶分子會呈螺旋狀排列，平面偏振光的偏振平面會被液晶LC逐漸扭曲，因此平面偏振光才能透射過正交的偏振片P2。假設安裝鏡子I，則透射過的平面偏振光會被反射回來（注意到顯示於鏡子的反射光箭頭），其偏振平面會再被液晶朝反方向扭曲，因此才能透射過正交的偏振片P1。從初始發光源位置朝著偏振片P1望去，會觀察到明亮的反射光。</li> <li>下方圖：當電極E1、E2通電時，液晶分子會順著電場方向排列，因此液晶不會扭曲平面偏振光的偏振平面，由於兩塊偏振片的偏振軸相互垂直，這時光線不能透射過偏振片P2。雖然安裝鏡子I，從原先發光源位置朝著平面偏振片P1望去，仍舊不會觀察到任何反射光。</li></ul> 應用這機制，液晶顯示器能夠顯示簡單的文字或圖案信息，它的主要優點是功耗較低，因此可以使用<a href="/wiki/%E5%85%89%E7%94%B5%E6%B1%A0" class="mw-redirect" title="光电池">光電池</a>來供電。 <div class="mw-heading mw-heading3"><h3 id="三維電影">三維電影</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=22" title="编辑章节：三維電影">编辑</a>]</div> <a href="/wiki/%E4%B8%89%E7%B6%AD%E9%9B%BB%E5%BD%B1" class="mw-redirect" title="三維電影">三維電影</a>所使用的<a href="/wiki/%E7%AB%8B%E9%AB%94%E7%9C%BC%E9%8F%A1" class="mw-redirect" title="立體眼鏡">立體顯示</a>技術將兩個不同影像分別傳輸至左眼、右眼。現今，這技術的首選方法是「偏振編碼」；使用兩台投影機將兩個不同影像都投射到投影屏，每一台投影機都安裝了偏振軸相互垂直的起偏器；或者使用單台能夠<a href="/wiki/%E6%97%B6%E5%88%86%E5%A4%8D%E7%94%A8" class="mw-redirect" title="时分复用">時分復用</a>偏振的投影機（內部安裝了快速過濾交替偏振的元件）。三維眼鏡的左邊鏡片與右邊鏡片分別具有對應的檢偏器，確使每一隻眼睛只會接收到對應的偏振影像。早先，採用平面偏振編碼，因為費用較便宜、分離效果很好。但是，圓偏振所形成的分離影像不會受到觀眾頭部傾斜的影響。現今，三維電影已廣泛採用圓偏振技術，例如<a href="/wiki/RealD_%E6%88%B2%E9%99%A2" title="RealD 戲院">RealD 戲院</a>系統。圓偏振技術需要使用特殊的投影屏，例如「銀屏」（silver screen），這種投影屏能夠維持投射影像的圓偏振，不會在反射時被非偏振化；普通的白色<a href="/wiki/%E6%BC%AB%E5%8F%8D%E5%B0%84" title="漫反射">漫反射</a>投影屏會造成投射影像在反射時被非偏振化，無法用來展示三維電影。<a href="#cite_note-36">[33]</a><a href="#cite_note-overview-37">[34]</a> <div class="mw-heading mw-heading3"><h3 id="動物視覺">動物視覺</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=23" title="编辑章节：動物視覺">编辑</a>]</div> 很多種動物可以感視到偏振光的光強與方向。通常牠們會用這能力來導航。很多種昆蟲也具有這種辨識偏振光的能力，包括<a href="/wiki/%E8%9C%9C%E8%9C%82" class="mw-redirect" title="蜜蜂">蜜蜂</a>在內，蜜蜂用來表達食物源方向的<a href="/wiki/%E8%9C%9C%E8%9C%82%E8%88%9E%E8%B9%88" title="蜜蜂舞蹈">舞蹈</a>就是用這信息來定向。<a href="#cite_note-Pye2001-35">[32]</a>:102-103生物學者經過仔細研究發覺，<a href="/wiki/%E7%AB%A0%E9%AD%9A" class="mw-redirect" title="章魚">章魚</a>、<a href="/wiki/%E9%AD%B7%E9%AD%9A" class="mw-redirect" title="魷魚">魷魚</a>、<a href="/wiki/%E7%83%8F%E8%B3%8A" class="mw-redirect" title="烏賊">烏賊</a>、<a href="/wiki/%E8%9D%A6%E8%9B%84" title="蝦蛄">蝦蛄</a>可以感視到偏振光。生物學者猜想，章魚、魷魚、烏賊使用這能力來探測會反射光的魚。有些魚會用反射光機制來掩飾自己。但是反射光的偏振與海水的散射偏振不同，因此魚的這種掩飾可以被破解。烏賊的快速變化、鮮艷顏色、具有偏振功能的表皮圖案，可以用來彼此傳達信息。<a href="#cite_note-Pye2001-35">[32]</a>:111-112某種蝦蛄能夠觀察偏振的所有六個正交分量（水平、垂直、對角、反對角、左旋圓、右旋圓），被認為具有最優化的偏振視覺。<a href="#cite_note-38">[35]</a>信鴿被認為能夠感視到天空的偏振光，這種能力可以幫助牠們遠距離歸巢。但是，嚴格做實驗檢驗證實這純屬謠傳。<a href="#cite_note-39">[36]</a> 假若不藉用任何濾光器，則人的肉眼對於偏振光的視覺非常微弱。偏振光會在視場中心附近造成很模糊的圖樣，稱為<a href="/wiki/%E6%B5%B7%E4%B8%81%E6%A0%BC%E5%88%B7" title="海丁格刷">海丁格刷</a>（Haidinger's brush）。這種圖樣非常難看到，但若經過一番練習，人可以用他的肉眼觀察到偏振光。<a href="#cite_note-Pye2001-35">[32]</a>:118 <div class="mw-heading mw-heading3"><h3 id="圓偏振的角動量">圓偏振的角動量</h3>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=24" title="编辑章节：圓偏振的角動量">编辑</a>]</div> 電磁輻射朝著傳播方向帶有線性<a href="/wiki/%E5%8B%95%E9%87%8F" class="mw-redirect" title="動量">動量</a>。另外，圓偏振光還帶有<a href="/wiki/%E8%A7%92%E5%8B%95%E9%87%8F" class="mw-redirect" title="角動量">角動量</a>。與動量相比，這角動量非常小，很難測得。可是，在一個很值得注意的實驗裏，應用這性質，達成了令人難以想像的高旋轉速度。 英國<a href="/wiki/%E5%9C%A3%E5%AE%89%E5%BE%B7%E9%B2%81%E6%96%AF%E5%A4%A7%E5%AD%A6" title="圣安德鲁斯大学">聖安德魯斯大學</a>實驗團隊使得一個直徑4微米的微觀尺度<a href="/wiki/%E7%A2%B3%E9%85%B8%E9%88%A3" title="碳酸鈣">碳酸鈣</a>圓球以每分鐘6億圈速度旋轉。應用<a href="/wiki/%E5%85%89%E9%91%B7" title="光鑷">光鑷</a>技術，這個圓球被圓偏振激光束懸浮起來。由於碳酸鈣圓球具有<a href="/wiki/%E5%8F%8C%E6%8A%98%E5%B0%84" title="双折射">雙折射</a>性質，透射光的<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF%E5%BA%A6&action=edit&redlink=1" class="new" title="偏振度（页面不存在）">偏振度</a>（degree of polarization）會被降低，因此失去一些角動量給圓球。被懸浮於幾乎真空，遭受到微乎其微的摩擦力，圓球的旋轉速度可以增加至每分鐘6億圈。這旋轉速度對應於<a href="/wiki/%E9%9B%A2%E5%BF%83%E5%8A%9B" title="離心力">離心加速度</a>大約為地球表面重力的10億倍，但是令人驚奇的是，圓球並沒有因此被擊碎。<a href="#cite_note-40">[37]</a><a href="#cite_note-41">[38]</a> <div class="mw-heading mw-heading2"><h2 id="參見">參見</h2>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=25" title="编辑章节：參見">编辑</a>]</div> <ul><li><a href="/w/index.php?title=%E6%B6%88%E5%81%8F%E5%99%A8&action=edit&redlink=1" class="new" title="消偏器（页面不存在）">消偏器</a>（英语：<a href="https://en.wikipedia.org/wiki/Depolarizer_(optics)" class="extiw" title="en:Depolarizer (optics)">Depolarizer (optics)</a>）</li> <li><a href="/w/index.php?title=%E5%BE%91%E5%90%91%E5%81%8F%E6%8C%AF&action=edit&redlink=1" class="new" title="徑向偏振（页面不存在）">徑向偏振</a>（英语：<a href="https://en.wikipedia.org/wiki/Radial_polarization" class="extiw" title="en:Radial polarization">Radial polarization</a>）</li> <li><a href="/wiki/%E5%81%8F%E6%8C%AF%E7%89%87" title="偏振片">偏振片</a></li> <li><a href="/wiki/%E5%85%8B%E7%88%BE%E6%95%88%E5%BA%94" title="克爾效应">克爾效应</a></li> <li><a href="/wiki/%E6%B3%A1%E5%85%8B%E8%80%B3%E6%96%AF%E6%95%88%E5%BA%94" title="泡克耳斯效应">泡克耳斯效应</a></li> <li><a href="/w/index.php?title=%E5%81%8F%E6%8C%AF%E5%85%89%E6%98%BE%E5%BE%AE%E9%95%9C&action=edit&redlink=1" class="new" title="偏振光显微镜（页面不存在）">偏振光显微镜</a>（英语：<a href="https://en.wikipedia.org/wiki/Polarized_light_microscopy" class="extiw" title="en:Polarized light microscopy">Polarized light microscopy</a>）</li> <li><a href="/wiki/%E9%A9%AC%E5%90%95%E6%96%AF%E5%AE%9A%E5%BE%8B" title="马吕斯定律">马吕斯定律</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="註釋">註釋</h2>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=26" title="编辑章节：註釋">编辑</a>]</div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-7"><a href="#cite_ref-7">^</a> 一般而言，在實際介質裏，由於介質的耗散性質或擁有自由電荷，電磁波不是橫波。<a href="#cite_note-Hecht2002-1">[1]</a>:46 </li> <li id="cite_note-9"><a href="#cite_ref-9">^</a> 在這裡，簡單介質指的是<a href="/wiki/%E8%87%AA%E7%94%B1%E7%A9%BA%E9%96%93" title="自由空間">自由空間</a>或<a href="/w/index.php?title=%E5%9D%87%E5%8B%BB&action=edit&redlink=1" class="new" title="均勻（页面不存在）">均勻</a>（homogeniety）、<a href="/wiki/%E5%90%84%E5%90%91%E5%90%8C%E6%80%A7" title="各向同性">各向同性</a>、<a href="/wiki/%E8%A1%B0%E5%87%8F" title="衰减">非衰減性</a>（non-attenuating）介質 </li> <li id="cite_note-21"><a href="#cite_ref-21">^</a> 回想在<a href="#瓊斯向量與瓊斯矩陣">瓊斯向量與瓊斯矩陣段落</a>的橫電磁波 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} (z,t)=\left(E_{0x}e^{i\varphi _{x}},\,E_{0y}e^{i\varphi _{y}}\right)e^{i(kz-\omega t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> </msup> <mo>,</mo> <mspace width="thinmathspace" /> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mi>z</mi> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} (z,t)=\left(E_{0x}e^{i\varphi _{x}},\,E_{0y}e^{i\varphi _{y}}\right)e^{i(kz-\omega t)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82c64b6b1b2eeaecba10add686f59f66cbcd3fdf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:36.215ex; height:3.509ex;" alt="{\displaystyle \mathbf {E} (z,t)=\left(E_{0x}e^{i\varphi _{x}},\,E_{0y}e^{i\varphi _{y}}\right)e^{i(kz-\omega t)}}">，</dd></dl> 這橫電磁波的斯托克斯向量為 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {S} ={\begin{pmatrix}S_{0}\\S_{1}\\S_{2}\\S_{3}\\\end{pmatrix}}={\begin{pmatrix}E_{0x}^{2}+E_{0y}^{2}\\E_{0x}^{2}-E_{0y}^{2}\\2E_{0x}E_{0y}\cos \varphi \\2E_{0x}E_{0y}\sin \varphi \\\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>x</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {S} ={\begin{pmatrix}S_{0}\\S_{1}\\S_{2}\\S_{3}\\\end{pmatrix}}={\begin{pmatrix}E_{0x}^{2}+E_{0y}^{2}\\E_{0x}^{2}-E_{0y}^{2}\\2E_{0x}E_{0y}\cos \varphi \\2E_{0x}E_{0y}\sin \varphi \\\end{pmatrix}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a2dd98cb892a7743e5400e8149a4f79d4ec8cc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.505ex; width:33.662ex; height:14.176ex;" alt="{\displaystyle \mathbf {S} ={\begin{pmatrix}S_{0}\\S_{1}\\S_{2}\\S_{3}\\\end{pmatrix}}={\begin{pmatrix}E_{0x}^{2}+E_{0y}^{2}\\E_{0x}^{2}-E_{0y}^{2}\\2E_{0x}E_{0y}\cos \varphi \\2E_{0x}E_{0y}\sin \varphi \\\end{pmatrix}}}">。</dd></dl> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="參考文獻">參考文獻</h2>[<a href="/w/index.php?title=%E5%81%8F%E6%8C%AF&action=edit&section=27" title="编辑章节：參考文獻">编辑</a>]</div> <div class="reflist references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-Hecht2002-1">^ <a href="#cite_ref-Hecht2002_1-0">1.00</a> <a href="#cite_ref-Hecht2002_1-1">1.01</a> <a href="#cite_ref-Hecht2002_1-2">1.02</a> <a href="#cite_ref-Hecht2002_1-3">1.03</a> <a href="#cite_ref-Hecht2002_1-4">1.04</a> <a href="#cite_ref-Hecht2002_1-5">1.05</a> <a href="#cite_ref-Hecht2002_1-6">1.06</a> <a href="#cite_ref-Hecht2002_1-7">1.07</a> <a href="#cite_ref-Hecht2002_1-8">1.08</a> <a href="#cite_ref-Hecht2002_1-9">1.09</a> <a href="#cite_ref-Hecht2002_1-10">1.10</a> <a href="#cite_ref-Hecht2002_1-11">1.11</a> <a href="#cite_ref-Hecht2002_1-12">1.12</a> <a href="#cite_ref-Hecht2002_1-13">1.13</a> <cite id="CITEREFHecht2002" class="citation">Hecht, Eugene, Optics 4th, United States of America: Addison Wesley, 2002, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-8053-8566-5" title="Special:网络书源/0-8053-8566-5">ISBN 0-8053-8566-5</a> （英语）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.aufirst=Eugene&rft.aulast=Hecht&rft.btitle=Optics&rft.date=2002&rft.edition=4th&rft.genre=book&rft.isbn=0-8053-8566-5&rft.place=United+States+of+America&rft.pub=Addison+Wesley&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Whittaker-2">^ <a href="#cite_ref-Whittaker_2-0">2.0</a> <a href="#cite_ref-Whittaker_2-1">2.1</a> <cite id="CITEREFWhittaker1951" class="citation">Whittaker, E. T., <a rel="nofollow" class="external text" href="http://www.archive.org/details/historyoftheorie00whitrich">A history of the theories of aether and electricity. Vol 1</a>, Nelson, London, 1951</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.aufirst=E.+T.&rft.aulast=Whittaker&rft.btitle=A+history+of+the+theories+of+aether+and+electricity.+Vol+1&rft.date=1951&rft.genre=book&rft.pub=Nelson%2C+London&rft_id=http%3A%2F%2Fwww.archive.org%2Fdetails%2Fhistoryoftheorie00whitrich&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Driggers2003-3">^ <a href="#cite_ref-Driggers2003_3-0">3.0</a> <a href="#cite_ref-Driggers2003_3-1">3.1</a> <cite class="citation book">Ronald G. Driggers. Encyclopedia of Optical Engineering. CRC Press. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-8247-4252-2" title="Special:网络书源/978-0-8247-4252-2">ISBN 978-0-8247-4252-2</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Ronald+G.+Driggers&rft.btitle=Encyclopedia+of+Optical+Engineering&rft.genre=book&rft.isbn=978-0-8247-4252-2&rft.pub=CRC+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-BuchwaldFox2013-4">^ <a href="#cite_ref-BuchwaldFox2013_4-0">4.0</a> <a href="#cite_ref-BuchwaldFox2013_4-1">4.1</a> <cite class="citation book">Jed Z. Buchwald; Robert Fox. <a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780199696253">The Oxford Handbook of the History of Physics</a>. Oxford University Press. October 2013. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-19-969625-3" title="Special:网络书源/978-0-19-969625-3">ISBN 978-0-19-969625-3</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Jed+Z.+Buchwald&rft.au=Robert+Fox&rft.btitle=The+Oxford+Handbook+of+the+History+of+Physics&rft.date=2013-10&rft.genre=book&rft.isbn=978-0-19-969625-3&rft.pub=Oxford+University+Press&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fisbn_9780199696253&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-GoldsteinGoldstein2011-5">^ <a href="#cite_ref-GoldsteinGoldstein2011_5-0">5.0</a> <a href="#cite_ref-GoldsteinGoldstein2011_5-1">5.1</a> <a href="#cite_ref-GoldsteinGoldstein2011_5-2">5.2</a> <a href="#cite_ref-GoldsteinGoldstein2011_5-3">5.3</a> <a href="#cite_ref-GoldsteinGoldstein2011_5-4">5.4</a> <cite class="citation book">Dennis Goldstein; Dennis H. Goldstein. Polarized Light, Revised and Expanded. CRC Press. 2011-01-03. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-203-91158-7" title="Special:网络书源/978-0-203-91158-7">ISBN 978-0-203-91158-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Dennis+Goldstein&rft.au=Dennis+H.+Goldstein&rft.btitle=Polarized+Light%2C+Revised+and+Expanded&rft.date=2011-01-03&rft.genre=book&rft.isbn=978-0-203-91158-7&rft.pub=CRC+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Goodman2005-6">^ <a href="#cite_ref-Goodman2005_6-0">6.0</a> <a href="#cite_ref-Goodman2005_6-1">6.1</a> <cite class="citation book">Joseph W. Goodman. <a rel="nofollow" class="external text" href="https://archive.org/details/introductiontofo0000good_u8t0">Introduction to Fourier Optics</a>. Roberts and Company Publishers. 2005. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-9747077-2-3" title="Special:网络书源/978-0-9747077-2-3">ISBN 978-0-9747077-2-3</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Joseph+W.+Goodman&rft.btitle=Introduction+to+Fourier+Optics&rft.date=2005&rft.genre=book&rft.isbn=978-0-9747077-2-3&rft.pub=Roberts+and+Company+Publishers&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontofo0000good_u8t0&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Jackson1999-8"><a href="#cite_ref-Jackson1999_8-0">^</a> <cite id="CITEREFJackson1999" class="citation">Jackson, John David, Classical Electrodynamic 3rd., USA: John Wiley & Sons, Inc.: pp. 1–2, 1999, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-471-30932-1" title="Special:网络书源/978-0-471-30932-1">ISBN 978-0-471-30932-1</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.aufirst=John+David&rft.aulast=Jackson&rft.btitle=Classical+Electrodynamic&rft.date=1999&rft.edition=3rd.&rft.genre=book&rft.isbn=978-0-471-30932-1&rft.pages=pp.+1-2&rft.place=USA&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  引文格式1维护：冗余文本 (<a href="/wiki/Category:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E7%BB%B4%E6%8A%A4%EF%BC%9A%E5%86%97%E4%BD%99%E6%96%87%E6%9C%AC" title="Category:引文格式1维护：冗余文本">link</a>) </li> <li id="cite_note-Chandrasekhar2013-10"><a href="#cite_ref-Chandrasekhar2013_10-0">^</a> <cite class="citation book">Subrahmanyan Chandrasekhar. Radiative Transfer. Dover Publications. 2013-04-15. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-486-31845-5" title="Special:网络书源/978-0-486-31845-5">ISBN 978-0-486-31845-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Subrahmanyan+Chandrasekhar&rft.btitle=Radiative+Transfer&rft.date=2013-04-15&rft.genre=book&rft.isbn=978-0-486-31845-5&rft.pub=Dover+Publications&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-North1998-11"><a href="#cite_ref-North1998_11-0">^</a> <cite class="citation book">Michael North. Principles and Applications of Stereochemistry. CRC Press. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-7487-3994-3" title="Special:网络书源/978-0-7487-3994-3">ISBN 978-0-7487-3994-3</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Michael+North&rft.btitle=Principles+and+Applications+of+Stereochemistry&rft.genre=book&rft.isbn=978-0-7487-3994-3&rft.pub=CRC+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Griffiths1998-12">^ <a href="#cite_ref-Griffiths1998_12-0">10.0</a> <a href="#cite_ref-Griffiths1998_12-1">10.1</a> <cite id="CITEREFGriffiths,_David_J.1998" class="citation">Griffiths, David J., Introduction to Electrodynamics (3rd ed.), Prentice Hall, 1998, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-13-805326-X" title="Special:网络书源/0-13-805326-X">ISBN 0-13-805326-X</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Griffiths%2C+David+J.&rft.btitle=Introduction+to+Electrodynamics+%283rd+ed.%29&rft.date=1998&rft.genre=book&rft.isbn=0-13-805326-X&rft.pub=Prentice+Hall&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-New2011-13"><a href="#cite_ref-New2011_13-0">^</a> <cite class="citation book">Geoffrey New. Introduction to Nonlinear Optics. Cambridge University Press. 2011-04-07. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-1-139-50076-0" title="Special:网络书源/978-1-139-50076-0">ISBN 978-1-139-50076-0</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Geoffrey+New&rft.btitle=Introduction+to+Nonlinear+Optics&rft.date=2011-04-07&rft.genre=book&rft.isbn=978-1-139-50076-0&rft.pub=Cambridge+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-14"><a href="#cite_ref-14">^</a> <cite class="citation journal">Dorn, R. and Quabis, S. and Leuchs, G. Sharper Focus for a Radially Polarized Light Beam. Physical Review Letters. dec 2003, 91 (23,): 233901–+. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003PhRvL..91w3901D">Bibcode:2003PhRvL..91w3901D</a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.91.233901">doi:10.1103/PhysRevLett.91.233901</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.atitle=Sharper+Focus+for+a+Radially+Polarized+Light+Beam&rft.au=Dorn%2C+R.+and+Quabis%2C+S.+and+Leuchs%2C+G.&rft.chron=dec+2003&rft.genre=article&rft.issue=23%2C&rft.jtitle=Physical+Review+Letters&rft.pages=233901-%2B&rft.volume=91&rft_id=info%3Abibcode%2F2003PhRvL..91w3901D&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.91.233901&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  请检查<code style="color:inherit; border:inherit; padding:inherit;">|date=</code>中的日期值 (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#bad_date" title="Help:引文格式1错误">帮助</a>) </li> <li id="cite_note-SteinWysession2009-15">^ <a href="#cite_ref-SteinWysession2009_15-0">13.0</a> <a href="#cite_ref-SteinWysession2009_15-1">13.1</a> <cite class="citation book">Seth Stein; Michael Wysession. An Introduction to Seismology, Earthquakes, and Earth Structure. John Wiley & Sons. 2009-04-01. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-1-4443-1131-0" title="Special:网络书源/978-1-4443-1131-0">ISBN 978-1-4443-1131-0</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Michael+Wysession&rft.au=Seth+Stein&rft.btitle=An+Introduction+to+Seismology%2C+Earthquakes%2C+and+Earth+Structure&rft.date=2009-04-01&rft.genre=book&rft.isbn=978-1-4443-1131-0&rft.pub=John+Wiley+%26+Sons&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Griffiths2008-16"><a href="#cite_ref-Griffiths2008_16-0">^</a> <cite id="CITEREFGriffiths,_David_J.2008" class="citation">Griffiths, David J., Introduction to Elementary Particles 2nd revised, WILEY-VCH, 2008, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-3-527-40601-2" title="Special:网络书源/978-3-527-40601-2">ISBN 978-3-527-40601-2</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Griffiths%2C+David+J.&rft.btitle=Introduction+to+Elementary+Particles&rft.date=2008&rft.edition=2nd+revised&rft.genre=book&rft.isbn=978-3-527-40601-2&rft.pub=WILEY-VCH&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Schutz2009-17"><a href="#cite_ref-Schutz2009_17-0">^</a> <cite class="citation book">Bernard Schutz. <a rel="nofollow" class="external text" href="https://archive.org/details/firstcourseingen00bern_0">A First Course in General Relativity</a>. Cambridge University Press. 2009-05-14. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-521-88705-2" title="Special:网络书源/978-0-521-88705-2">ISBN 978-0-521-88705-2</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Bernard+Schutz&rft.btitle=A+First+Course+in+General+Relativity&rft.date=2009-05-14&rft.genre=book&rft.isbn=978-0-521-88705-2&rft.pub=Cambridge+University+Press&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffirstcourseingen00bern_0&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Collett2005-18">^ <a href="#cite_ref-Collett2005_18-0">16.0</a> <a href="#cite_ref-Collett2005_18-1">16.1</a> <a href="#cite_ref-Collett2005_18-2">16.2</a> <a href="#cite_ref-Collett2005_18-3">16.3</a> <cite class="citation book">Edward Collett. <a rel="nofollow" class="external text" href="https://spie.org/x32276.xml">Field Guide to Polarization</a>. Society of Photo Optical. 2005 [2014-02-21]. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-8194-5868-1" title="Special:网络书源/978-0-8194-5868-1">ISBN 978-0-8194-5868-1</a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20150914015143/http://spie.org/x32276.xml">存档</a>于2015-09-14）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Edward+Collett&rft.btitle=Field+Guide+to+Polarization&rft.date=2005&rft.genre=book&rft.isbn=978-0-8194-5868-1&rft.pub=Society+of+Photo+Optical&rft_id=https%3A%2F%2Fspie.org%2Fx32276.xml&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-esa-19">^ <a href="#cite_ref-esa_19-0">17.0</a> <a href="#cite_ref-esa_19-1">17.1</a> <a href="#cite_ref-esa_19-2">17.2</a> <cite class="citation web"><a rel="nofollow" class="external text" href="https://earth.esa.int/documents/653194/656796/What_Is_Polarization.pdf">What is Polarisation</a> (PDF). Polarimetry Tutorial. European Space Agency. [2017-09-12]. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20140224202949/http://earth.eo.esa.int/polsarpro/Manuals/1_What_Is_Polarization.pdf">存档</a> (PDF)于2014-02-24）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.atitle=What+is+Polarisation&rft.genre=unknown&rft.jtitle=Polarimetry+Tutorial&rft_id=https%3A%2F%2Fearth.esa.int%2Fdocuments%2F653194%2F656796%2FWhat_Is_Polarization.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-Collett2003-20"><a href="#cite_ref-Collett2003_20-0">^</a> <cite class="citation book">Edward Collett. Polarized Light in Fiber Optics. SPIE Press. 2003. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-8194-5761-5" title="Special:网络书源/978-0-8194-5761-5">ISBN 978-0-8194-5761-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Edward+Collett&rft.btitle=Polarized+Light+in+Fiber+Optics&rft.date=2003&rft.genre=book&rft.isbn=978-0-8194-5761-5&rft.pub=SPIE+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-O'Neill2004-22"><a href="#cite_ref-O'Neill2004_22-0">^</a> <cite class="citation book">Edward L. O'Neill. Introduction to Statistical Optics. Courier Dover Publications. January 2004. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-486-43578-7" title="Special:网络书源/978-0-486-43578-7">ISBN 978-0-486-43578-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Edward+L.+O%27Neill&rft.btitle=Introduction+to+Statistical+Optics&rft.date=2004-01&rft.genre=book&rft.isbn=978-0-486-43578-7&rft.pub=Courier+Dover+Publications&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-23"><a href="#cite_ref-23">^</a> <cite class="citation book">Srinivasan, M. R. Physics for Engineers. New Age International. 1996-01-01. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-81-224-0892-8" title="Special:网络书源/978-81-224-0892-8">ISBN 978-81-224-0892-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.aufirst=M.+R.&rft.aulast=Srinivasan&rft.btitle=Physics+for+Engineers&rft.date=1996-01-01&rft.genre=book&rft.isbn=978-81-224-0892-8&rft.pub=New+Age+International&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Mansuripur2009-24"><a href="#cite_ref-Mansuripur2009_24-0">^</a> <cite class="citation book">Masud Mansuripur. Classical Optics and Its Applications. Cambridge University Press. 2009. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0521881692" title="Special:网络书源/978-0521881692">ISBN 978-0521881692</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Masud+Mansuripur&rft.btitle=Classical+Optics+and+Its+Applications&rft.date=2009&rft.genre=book&rft.isbn=978-0521881692&rft.pub=Cambridge+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Wayne2013-25"><a href="#cite_ref-Wayne2013_25-0">^</a> <cite class="citation book">Randy O. Wayne. Light and Video Microscopy. Academic Press. 2013-12-16. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-12-411536-1" title="Special:网络书源/978-0-12-411536-1">ISBN 978-0-12-411536-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Randy+O.+Wayne&rft.btitle=Light+and+Video+Microscopy&rft.date=2013-12-16&rft.genre=book&rft.isbn=978-0-12-411536-1&rft.pub=Academic+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Shearer2009-26"><a href="#cite_ref-Shearer2009_26-0">^</a> <cite class="citation book">Peter M. Shearer. <a rel="nofollow" class="external text" href="https://archive.org/details/introductiontose0000shea_q9q6">Introduction to Seismology</a>. Cambridge University Press. 2009. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-521-88210-1" title="Special:网络书源/978-0-521-88210-1">ISBN 978-0-521-88210-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.au=Peter+M.+Shearer&rft.btitle=Introduction+to+Seismology&rft.date=2009&rft.genre=book&rft.isbn=978-0-521-88210-1&rft.pub=Cambridge+University+Press&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontose0000shea_q9q6&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-27"><a href="#cite_ref-27">^</a> <cite class="citation news">Staff. <a rel="nofollow" class="external text" href="https://www.sciencedaily.com/releases/2007/02/070208131656.htm">NARVAL: First Observatory Dedicated To Stellar Magnetism</a>. Science Daily. 2007-02-22 [2007-06-21]. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20170911072136/https://www.sciencedaily.com/releases/2007/02/070208131656.htm">存档</a>于2017-09-11）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.atitle=NARVAL%3A+First+Observatory+Dedicated+To+Stellar+Magnetism&rft.au=Staff&rft.date=2007-02-22&rft.genre=article&rft_id=http%3A%2F%2Fwww.sciencedaily.com%2Freleases%2F2007%2F02%2F070208131656.htm&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-28"><a href="#cite_ref-28">^</a> <cite class="citation journal">Vlemmings, W. H. T. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210914080507/https://arxiv.org/pdf/0705.0885.pdf">A review of maser polarization and magnetic fields.</a> (PDF). Proceedings of the International Astronomical Union. Mar 2007, 3 (S242): 37–46 [2014-03-09]. （<a rel="nofollow" class="external text" href="http://arxiv.org/pdf/0705.0885.pdf">原始内容</a> (PDF)存档于2021-09-14）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%81%8F%E6%8C%AF&rft.atitle=A+review+of+maser+polarization+and+magnetic+fields.&rft.aufirst=W.+H.+T.&rft.aulast=Vlemmings&rft.date=2007-03&rft.genre=article&rft.issue=S242&rft.jtitle=Proceedings+of+the+International+Astronomical+Union&rft.pages=37-46&rft.volume=3&rft_id=http%3A%2F%2Farxiv.org%2Fpdf%2F0705.0885.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-KarttunenKröger2007-29"><a href="#cite_ref-KarttunenKröger2007_29-0">^</a> <cite class="citation book">Hannu Karttunen; Pekka Kröger; Heikki Oja. <a rel="nofollow" class="external text" href="https://archive.org/details/fundamentalastro0005unse">Fundamental Astronomy</a>. 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href="/wiki/%E5%87%A0%E4%BD%95%E5%85%89%E5%AD%A6" title="几何光学">几何光学</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%8F%8D%E5%B0%84_(%E7%89%A9%E7%90%86%E5%AD%A6)" title="反射 (物理学)">反射</a></li> <li><a href="/wiki/%E6%8A%98%E5%B0%84" title="折射">折射</a></li> <li><a href="/wiki/%E8%8F%B2%E6%B6%85%E8%80%B3%E6%96%B9%E7%A8%8B" title="菲涅耳方程">菲涅耳方程</a></li> <li><a href="/wiki/%E6%96%AF%E6%B6%85%E5%B0%94%E5%AE%9A%E5%BE%8B" title="斯涅尔定律">斯涅尔定律</a></li> <li><a href="/wiki/%E8%B2%BB%E9%A6%AC%E5%8E%9F%E7%90%86" title="費馬原理">費馬原理</a></li> <li><a href="/wiki/%E9%A9%AC%E5%90%95%E6%96%AF%E5%AE%9A%E7%90%86" title="马吕斯定理">马吕斯定理</a></li> <li><a href="/wiki/%E9%80%8F%E9%95%9C" title="透镜">透镜</a></li> <li><a href="/wiki/%E5%AF%A6%E5%83%8F" title="實像">實像</a></li> <li><a href="/wiki/%E8%99%9B%E5%83%8F" title="虛像">虛像</a></li> <li><a href="/wiki/%E5%83%8F%E5%B7%AE" title="像差">像差</a></li> <li><a href="/wiki/%E5%83%8F%E6%95%A3" title="像散">像散</a></li> <li><a href="/wiki/%E8%89%B2%E5%B7%AE" title="色差">色差</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%89%A9%E7%90%86%E5%85%89%E5%AD%A6" title="物理光学">物理光学</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%B9%B2%E6%B6%89_(%E7%89%A9%E7%90%86%E5%AD%A6)" title="干涉 (物理学)">干涉</a></li> <li><a href="/wiki/%E8%A1%8D%E5%B0%84" title="衍射">衍射</a></li> <li><a href="/wiki/%E6%95%A3%E5%B0%84" title="散射">散射</a></li> <li><a href="/wiki/%E9%9B%99%E7%B8%AB%E5%AF%A6%E9%A9%97" title="雙縫實驗">双缝干涉</a></li> <li><a href="/wiki/%E8%BF%88%E5%85%8B%E8%80%B3%E5%AD%99%E5%B9%B2%E6%B6%89%E4%BB%AA" title="迈克耳孙干涉仪">迈克耳孙干涉仪</a></li> <li><a href="/wiki/%E9%A6%AC%E8%B5%AB-%E6%9B%BE%E5%BE%B7%E7%88%BE%E5%B9%B2%E6%B6%89%E5%84%80" title="馬赫-曾德爾干涉儀">馬赫-曾德爾干涉儀</a></li> <li><a href="/wiki/%E6%B3%95%E5%B8%83%E9%87%8C-%E7%8F%80%E7%BD%97%E5%B9%B2%E6%B6%89%E4%BB%AA" title="法布里-珀罗干涉仪">法布里-珀罗干涉仪</a></li> <li><a href="/wiki/%E6%83%A0%E6%9B%B4%E6%96%AF-%E8%8F%B2%E6%B6%85%E8%80%B3%E5%8E%9F%E7%90%86" title="惠更斯-菲涅耳原理">惠更斯-菲涅耳原理</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%9F%BA%E7%88%BE%E9%9C%8D%E5%A4%AB%E8%A1%8D%E5%B0%84%E5%85%AC%E5%BC%8F" title="基爾霍夫衍射公式">菲涅耳-基尔霍夫衍射公式</a></li> <li><a href="/wiki/%E5%A4%AB%E7%90%85%E7%A6%BE%E8%B4%B9%E8%A1%8D%E5%B0%84" title="夫琅禾费衍射">夫琅禾费衍射</a></li> <li><a href="/wiki/%E8%8F%B2%E6%B6%85%E8%80%B3%E8%A1%8D%E5%B0%84" title="菲涅耳衍射">菲涅耳衍射</a></li> <li><a href="/wiki/%E5%85%89%E6%A0%85" title="光栅">光栅</a></li> <li><a href="/wiki/%E7%91%9E%E5%88%A9%E6%95%A3%E5%B0%84" title="瑞利散射">瑞利散射</a></li> <li><a href="/wiki/%E7%B1%B3%E6%B0%8F%E6%95%A3%E5%B0%84" title="米氏散射">米氏散射</a></li> <li><a href="/wiki/%E8%89%B2%E6%95%A3_(%E5%85%89%E5%AD%B8)" title="色散 (光學)">色散 (光學)</a></li> <li><a class="mw-selflink selflink">偏振</a></li> <li><a href="/w/index.php?title=%E5%82%85%E9%87%8C%E5%8F%B6%E5%85%89%E5%AD%A6&action=edit&redlink=1" class="new" title="傅里叶光学（页面不存在）">傅里叶光学</a>（英语：<a href="https://en.wikipedia.org/wiki/Fourier_optics" class="extiw" title="en:Fourier optics">Fourier optics</a>）</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">現代光学</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%BF%80%E5%85%89" title="激光">激光</a></li> <li><a href="/wiki/%E5%85%89%E8%B0%B1%E5%AD%A6" title="光谱学">光谱学</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%85%89%E5%AD%A6" title="量子光学">量子光学</a></li> <li><a href="/wiki/%E9%9D%9E%E7%BA%BF%E6%80%A7%E5%85%89%E5%AD%A6" title="非线性光学">非线性光学</a></li> <li><a href="/w/index.php?title=%E6%99%B6%E4%BD%93%E5%85%89%E5%AD%A6&action=edit&redlink=1" class="new" title="晶体光学（页面不存在）">晶体光学</a>（英语：<a href="https://en.wikipedia.org/wiki/Crystal_optics" class="extiw" title="en:Crystal optics">Crystal optics</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%85%89%E5%AD%A6%E5%B7%A5%E7%A8%8B" title="光学工程">光学工程</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%85%89%E5%AD%90%E5%AD%A6" title="光子学">光子学</a></li> <li><a href="/wiki/%E5%85%89%E5%B0%8E%E7%BA%96%E7%B6%AD" title="光導纖維">光導纖維</a></li> <li><a href="/wiki/%E5%85%89%E9%80%9A%E8%A8%8A" title="光通訊">光通訊</a></li> <li><a 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href="/wiki/%E4%BC%8A%E6%9C%AC%C2%B7%E6%B5%B7%E4%BB%80%E6%9C%A8" title="伊本·海什木">海什木</a></li> <li><a href="/wiki/%E5%85%8B%E9%87%8C%E6%96%AF%E8%92%82%E5%AE%89%C2%B7%E6%83%A0%E6%9B%B4%E6%96%AF" title="克里斯蒂安·惠更斯">惠更斯</a></li> <li><a href="/wiki/%E8%89%BE%E8%90%A8%E5%85%8B%C2%B7%E7%89%9B%E9%A1%BF" title="艾萨克·牛顿">牛顿</a></li> <li><a href="/wiki/%E7%AC%AC%E4%B8%89%E4%BB%A3%E7%91%9E%E5%88%A9%E7%94%B7%E7%88%B5%E7%B4%84%E7%BF%B0%C2%B7%E6%96%AF%E7%89%B9%E6%8B%89%E7%89%B9" title="第三代瑞利男爵約翰·斯特拉特">瑞利</a></li> <li><a href="/wiki/%E5%A8%81%E7%90%86%E5%8D%9A%C2%B7%E5%8F%B8%E4%B9%83%E8%80%B3" title="威理博·司乃耳">斯涅尔</a></li> <li><a href="/wiki/%E6%89%98%E9%A9%AC%E6%96%AF%C2%B7%E6%9D%A8" title="托马斯·杨">托马斯·杨</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84261037"><style 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偏振 - 维基百科，自由的百科全书