Керра эффекти

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</button> <ul id="toc-Kerr_qonuni-sublist" class="vector-toc-list"> <li id="toc-Miqdorlar_nazariyasi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Miqdorlar_nazariyasi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Миқдорлар назарияси</span> </div> </a> <ul id="toc-Miqdorlar_nazariyasi-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ayrim_moddalar_uchun_Kerr_doimiysi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ayrim_moddalar_uchun_Kerr_doimiysi"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Айрим моддалар учун Керр доимийси</span> </div> </a> <ul id="toc-Ayrim_moddalar_uchun_Kerr_doimiysi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nazariya" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Nazariya"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Назария</span> </div> </a> <button aria-controls="toc-Nazariya-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Назария subsection</span> </button> <ul id="toc-Nazariya-sublist" class="vector-toc-list"> <li id="toc-Kvadrat_elektro-optik_Kerr_effekti" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kvadrat_elektro-optik_Kerr_effekti"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Квадрат электро-оптик Керр эффекти</span> </div> </a> <ul id="toc-Kvadrat_elektro-optik_Kerr_effekti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Optik_Kerr_effekti" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Optik_Kerr_effekti"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Оптик Керр эффекти</span> </div> </a> <ul id="toc-Optik_Kerr_effekti-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Qoʻllanishi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Qoʻllanishi"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Қўлланиши</span> </div> </a> <button aria-controls="toc-Qoʻllanishi-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Қўлланиши subsection</span> </button> <ul id="toc-Qoʻllanishi-sublist" class="vector-toc-list"> <li id="toc-Elektro-optik_modulyatorlarda" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elektro-optik_modulyatorlarda"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Электро-оптик модуляторларда</span> </div> </a> <ul id="toc-Elektro-optik_modulyatorlarda-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lazerlarda_rejimni_qulflash" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lazerlarda_rejimni_qulflash"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Лазерларда режимни қулфлаш</span> </div> </a> <ul id="toc-Lazerlarda_rejimni_qulflash-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Yana_qarang" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Yana_qarang"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Яна қаранг</span> </div> </a> <ul id="toc-Yana_qarang-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Manbalar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Manbalar"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Манбалар</span> </div> </a> <ul id="toc-Manbalar-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Adabiyotlar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Adabiyotlar"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Адабиётлар</span> </div> </a> <ul id="toc-Adabiyotlar-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Havolalar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Havolalar"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Ҳаволалар</span> </div> </a> <ul id="toc-Havolalar-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="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" lang="uz-Cyrl" dir="ltr"> <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="Toggle the table of contents" > <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" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </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" lang="uz-Cyrl" dir="ltr"><span class="mw-page-title-main">Керра эффекти</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" lang="uz-Cyrl" dir="ltr"> <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="Go to an article in another language. Available in 29 languages" > <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-29" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">29 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B8%D8%A7%D9%87%D8%B1%D8%A9_%D9%83%D9%8A%D8%B1" title="ظاهرة كير – арабча" lang="ar" hreflang="ar" data-title="ظاهرة كير" data-language-autonym="العربية" data-language-local-name="арабча" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Efeutu_Kerr" title="Efeutu Kerr – астурийча" lang="ast" hreflang="ast" data-title="Efeutu Kerr" data-language-autonym="Asturianu" data-language-local-name="астурийча" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D1%84%D0%B5%D0%BA%D1%82_%D0%9A%D0%B5%D1%80%D0%B0" title="Эфект Кера – беларусча" lang="be" hreflang="be" data-title="Эфект Кера" data-language-autonym="Беларуская" data-language-local-name="беларусча" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Efecte_Kerr" title="Efecte Kerr – каталонча" lang="ca" hreflang="ca" data-title="Efecte Kerr" data-language-autonym="Català" data-language-local-name="каталонча" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kerr-effekt" title="Kerr-effekt – датча" lang="da" hreflang="da" data-title="Kerr-effekt" data-language-autonym="Dansk" data-language-local-name="датча" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kerr-Effekt" title="Kerr-Effekt – немисча" lang="de" hreflang="de" data-title="Kerr-Effekt" data-language-autonym="Deutsch" data-language-local-name="немисча" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Kerr_effect" title="Kerr effect – инглизча" lang="en" hreflang="en" data-title="Kerr effect" data-language-autonym="English" data-language-local-name="инглизча" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Efecto_Kerr" title="Efecto Kerr – испанча" lang="es" hreflang="es" data-title="Efecto Kerr" data-language-autonym="Español" data-language-local-name="испанча" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kerr_efektua" title="Kerr efektua – баскча" lang="eu" hreflang="eu" data-title="Kerr efektua" data-language-autonym="Euskara" data-language-local-name="баскча" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%AB%D8%B1_%DA%A9%D8%B1" title="اثر کر – форсий" lang="fa" hreflang="fa" data-title="اثر کر" data-language-autonym="فارسی" data-language-local-name="форсий" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Effet_Kerr" title="Effet Kerr – французча" lang="fr" hreflang="fr" data-title="Effet Kerr" data-language-autonym="Français" data-language-local-name="французча" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%94%D5%A5%D6%80%D5%AB_%D5%A5%D6%80%D6%87%D5%B8%D6%82%D5%B5%D5%A9" title="Քերի երևույթ – арманча" lang="hy" hreflang="hy" data-title="Քերի երևույթ" data-language-autonym="Հայերեն" data-language-local-name="арманча" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Effetto_Kerr" title="Effetto Kerr – италянча" lang="it" hreflang="it" data-title="Effetto Kerr" data-language-autonym="Italiano" data-language-local-name="италянча" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%AB%E3%83%BC%E5%8A%B9%E6%9E%9C" title="カー効果 – японча" lang="ja" hreflang="ja" data-title="カー効果" data-language-autonym="日本語" data-language-local-name="японча" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%95%E0%B3%86%E0%B2%B0%E0%B3%8D_%E0%B2%AA%E0%B2%B0%E0%B2%BF%E0%B2%A3%E0%B2%BE%E0%B2%AE" title="ಕೆರ್ ಪರಿಣಾಮ – каннада" lang="kn" hreflang="kn" data-title="ಕೆರ್ ಪರಿಣಾಮ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="каннада" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%BB%A4_%ED%9A%A8%EA%B3%BC" title="커 효과 – корейсча" lang="ko" hreflang="ko" data-title="커 효과" data-language-autonym="한국어" data-language-local-name="корейсча" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kerreffect" title="Kerreffect – голландча" lang="nl" hreflang="nl" data-title="Kerreffect" data-language-autonym="Nederlands" data-language-local-name="голландча" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kerreffekt" title="Kerreffekt – норвегча нюнорск" lang="nn" hreflang="nn" data-title="Kerreffekt" data-language-autonym="Norsk nynorsk" data-language-local-name="норвегча нюнорск" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Zjawiska_Kerra" title="Zjawiska Kerra – полякча" lang="pl" hreflang="pl" data-title="Zjawiska Kerra" data-language-autonym="Polski" data-language-local-name="полякча" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Efeito_Kerr" title="Efeito Kerr – португалча" lang="pt" hreflang="pt" data-title="Efeito Kerr" data-language-autonym="Português" data-language-local-name="португалча" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Efectul_Kerr" title="Efectul Kerr – руминча" lang="ro" hreflang="ro" data-title="Efectul Kerr" data-language-autonym="Română" data-language-local-name="руминча" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D1%84%D1%84%D0%B5%D0%BA%D1%82_%D0%9A%D0%B5%D1%80%D1%80%D0%B0" title="Эффект Керра – русча" lang="ru" hreflang="ru" data-title="Эффект Керра" data-language-autonym="Русский" data-language-local-name="русча" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kerrov_pojav" title="Kerrov pojav – словенча" lang="sl" hreflang="sl" data-title="Kerrov pojav" data-language-autonym="Slovenščina" data-language-local-name="словенча" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%B5%D1%80%D0%BE%D0%B2_%D0%B5%D1%84%D0%B5%D0%BA%D0%B0%D1%82" title="Керов ефекат – сербча" lang="sr" hreflang="sr" data-title="Керов ефекат" data-language-autonym="Српски / srpski" data-language-local-name="сербча" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kerreffekt" title="Kerreffekt – шведча" lang="sv" hreflang="sv" data-title="Kerreffekt" data-language-autonym="Svenska" data-language-local-name="шведча" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D1%84%D0%B5%D0%BA%D1%82_%D0%9A%D0%B5%D1%80%D1%80%D0%B0" title="Ефект Керра – украинча" lang="uk" hreflang="uk" data-title="Ефект Керра" data-language-autonym="Українська" data-language-local-name="украинча" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Hi%E1%BB%87u_%E1%BB%A9ng_Kerr" title="Hiệu ứng Kerr – ветнамча" lang="vi" hreflang="vi" data-title="Hiệu ứng Kerr" data-language-autonym="Tiếng Việt" data-language-local-name="ветнамча" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%85%8B%E5%B0%94%E6%95%88%E5%BA%94" title="克尔效应 – Wu" lang="wuu" hreflang="wuu" data-title="克尔效应" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%85%8B%E7%88%BE%E6%95%88%E5%BA%94" title="克爾效应 – хитойча" lang="zh" hreflang="zh" data-title="克爾效应" data-language-autonym="中文" data-language-local-name="хитойча" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q883038#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet 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</div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Vikipediya</div> </div> <div id="contentSub" lang="uz-Cyrl" dir="ltr"><div id="mw-content-subtitle" lang="uz-Cyrl" dir="ltr"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="uz-Cyrl" dir="ltr"><p><b>Керр эффекти</b> ёки <b>квадратик электро-оптик эффект</b> — оптик материалининг синдириш кўрсаткичининг қийматини унга берилган <a href="/wiki/Elektr_maydon" title="Электр майдон">электр майдонининг</a> квадратига мутаносиб равишда ўзгариш ҳодисаси. Унинг Поcкелс эффектидан фарқи шундаки, синдириш кўрсаткичнинг ўзгариши электр майдонининг квадратига тўғри пропорционалдир ва чизиқли ўзгаришидадир. </p><p>1875 йилда шотланд физиги Жон Керр томонидан кашф этилган. Керр эффекти барча моддаларда кузатилади, лекн баъзи суюқликлар уни бошқа моддаларга нисбатан кўпроқ намоён қилади.. </p><p>Кучли майдонларда Керр қонунида кичик оғишлар кузатилади. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Elektro-optik_Kerr_effekti">Электро-оптик Керр эффекти</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=1" title="Edit section: Электро-оптик Керр эффекти" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=1" title="Edit section's source code: Электро-оптик Керр эффекти"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Sifatli_tavsif">Сифатли тавсиф</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=2" title="Edit section: Сифатли тавсиф" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=2" title="Edit section's source code: Сифатли тавсиф"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fayl:Kerr_effect-ru.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Kerr_effect-ru.svg/300px-Kerr_effect-ru.svg.png" decoding="async" width="300" height="82" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Kerr_effect-ru.svg/450px-Kerr_effect-ru.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Kerr_effect-ru.svg/600px-Kerr_effect-ru.svg.png 2x" data-file-width="698" data-file-height="191" /></a><figcaption> Керр эффектини кузатиш ва ўлчаш учун созлаш схемаси. Керр катакчасидан текис қутбланган ёруғлик дастаси чиқгач, электр кучланиш таъсирида эллиптик қутбланган бўлади. Эллиптик қутбланган нур анализатор деб аталадиган иккинчи поларизатордан ўтганда унинг интенсивлиги ўзгаради ва интенсивликнинг ўзгариши фотодетектор <sup id="cite_ref-Физическая_энциклопедия_1-0" class="reference"><a href="#cite_note-Физическая_энциклопедия-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> томонидан қайд этилади.</figcaption></figure> <p>Ташқи доимий ёки ўзгарувчан электр майдони таъсирида модданинг қутбланишининг ўзгариши туфайли, муҳитда нурнинг <a href="/wiki/Yorug%E2%80%98likning_ikkilanib_sinishi" title="Ёруғликнинг иккиланиб синиши">қўшсиниши</a> кузатилиши мумкин. Бундай ҳолда, моддадан ўтадиган ёруғлик иккита нурга ажралади — моддада хар хил синдириш кўрсаткичларига эга бўлган оддий ва ғайриоддий нурларга. Шундай қилиб, ғайриоддий ва оддий нурлар учун фаза тезлиги ҳар хил бўлгани сабабли, текис қутбланган ёруғлик дастаси эллиптик қутбланган нурга айланади, ҳамда етарли йўл узунлиги туфайли қўш синдирувчи моддада нур айланма қутбланиш ўтади. </p><p><a href="/wiki/Yorug%E2%80%98likning_ikkilanib_sinishi" title="Ёруғликнинг иккиланиб синиши">Оддий</a> нур учун синдириш кўрсаткичини <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{o},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{o},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/343f95b9efb5d4a4f4543e1024daa53137473be2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.071ex; height:2.009ex;" alt="{\displaystyle n_{o},}"></span>ва <a href="/wiki/Yorug%E2%80%98likning_ikkilanib_sinishi" title="Ёруғликнинг иккиланиб синиши">ғайриоддий</a> учун <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e21303faca6e2167f4ecbf2a75aed982e817035" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.393ex; height:2.009ex;" alt="{\displaystyle n_{e}}"></span> бўлсин. Синиш кўрсаткичларининг фарқини ёйиб чиқсак <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{o}-n_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{o}-n_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e6d55747eb339a580ee847ff66e3cfda13b0711" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.658ex; height:2.343ex;" alt="{\displaystyle n_{o}-n_{e}}"></span>, уни ташқи электр майдонининг функцияси сифатида <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> даражаси <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> олиб қарасак, бундан келиб чиқадики, агар майдон таъсир этишидан олдин муҳит қутбланмаган ва <a href="/wiki/Izotropiya" title="Изотропия">изотроп</a> бўлса, у ҳолда <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{o}-n_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{o}-n_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e6d55747eb339a580ee847ff66e3cfda13b0711" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.658ex; height:2.343ex;" alt="{\displaystyle n_{o}-n_{e}}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span>нинг жуфт функцияси бўлиши керак (майдон йўналишини ўзгартирганда, эффект ўз ишорасини ўзгартирмаслиги керак). Бундан келиб чиқадикии, даражаси <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> да ёйганда, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e89b3e3b96f61772772279a8b7d6ee29e079521e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.848ex; height:2.676ex;" alt="{\displaystyle E^{2}}"></span> бошлаб фақат жуфт тартибли ҳадтар мавжуд бўлиши керак . Кучсиз майдонларда квадратикдан ташқари юқори тартибли ҳадларни эътибордан четда қолдириш мумкин, натижада: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{e}-n_{o}=kE^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mi>k</mi> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{e}-n_{o}=kE^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1306b992e243fcc630b25818a75fda41a1678452" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.462ex; height:3.009ex;" alt="{\displaystyle n_{e}-n_{o}=kE^{2},}"></span></dd></dl> <p>Бу ерга <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><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></span><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}"></span> баъзи коэффициэнтлардир. </p><p>Керр эффекти, асосан, <a href="/wiki/Atom" title="Атом">атом</a> ёки <a href="/wiki/Molekula" title="Молекула">молекулаларнинг</a> <a href="/wiki/Orbital" title="Орбитал">электрон орбиталларининг</a> деформацияси ёки уларнинг йўналишининг ўзгариши натижасида юзага келадиган муҳитнинг гиперполяризацияси билан боғлиқ. Оптик Керр эффекти жуда тез юз беради — пикосекундлардан бир неча наносекундларгача (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10^{-13}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>13</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{-13}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28325b7f413d5c3d3998872f6c6057ffda60a601" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.48ex; height:2.676ex;" alt="{\displaystyle 10^{-13}}"></span> — <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10^{-9}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>9</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{-9}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69ad2ba4cbe9e68b60b98de6b2875625abb3b446" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.658ex; height:2.676ex;" alt="{\displaystyle 10^{-9}}"></span> с), чунки <a href="/wiki/Qattiq_jism" title="Қаттиқ жисм">қаттиқ</a> жисмларда фақатгина атом электрон булутининг деформацияси содир бўлиши мумкин. </p> <div class="mw-heading mw-heading2"><h2 id="Kerr_qonuni">Керр қонуни</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=3" title="Edit section: Керр қонуни" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=3" title="Edit section's source code: Керр қонуни"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Керр қонуни — оддий ва ғайриоддий нурларининг синиш кўрсаткичлари орасидаги фарқ ўрнатилган электр майдонининг квадратига пропорционалдир: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{e}-n_{o}=b\lambda _{0}E^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mi>b</mi> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{e}-n_{o}=b\lambda _{0}E^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3033005b01d1d461a896ff1a0771679f9a25d780" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.658ex; height:3.009ex;" alt="{\displaystyle n_{e}-n_{o}=b\lambda _{0}E^{2},}"></span></dd> <dd>Бу ерда <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfa5ad1eb6cdaf3d8dfd77991ee9ce7bdf169184" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.409ex; height:2.509ex;" alt="{\displaystyle \lambda _{0}}"></span> ёруғликнинг вакуумдаги <a href="/wiki/To%CA%BBlqin_uzunligi" title="Тўлқин узунлиги">тўлқин узунлиги</a> ;</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> — Керр доимийси бўлиб, у модданинг табиатига, тўлқин узунлигига боғлиқ</dd></dl> <p>Керр доимийси модданинг табиатига, тўлқин узунлигига ва ҳароратга боғлиқ. </p><p>Баъзан Керр доимийсини қуйидаги кўринишда ҳам бўлади <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K=b\lambda _{0}/n,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo>=</mo> <mi>b</mi> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K=b\lambda _{0}/n,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63836b35df246a6a2791b25ca8a096f9aec0afcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.775ex; height:2.843ex;" alt="{\displaystyle K=b\lambda _{0}/n,}"></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> электр майдон таъсирисиз синдириш кўрсаткичи <sup id="cite_ref-Физическая_энциклопедия_1-1" class="reference"><a href="#cite_note-Физическая_энциклопедия-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> . </p><p>Кўп моддалар учун коэффициэнт <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94436473a90bd55191a79c59474cb5456dcbec00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.258ex; height:2.176ex;" alt="{\displaystyle b>0}"></span>, яъни улар оптик жиҳатдан ижобий бир эксенли кристалларга ўхшашлигини кўрсатади. </p> <div class="mw-heading mw-heading3"><h3 id="Miqdorlar_nazariyasi">Миқдорлар назарияси</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=4" title="Edit section: Миқдорлар назарияси" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=4" title="Edit section's source code: Миқдорлар назарияси"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/1910" title="1910">1910</a> йилда Лангевин томонидан газлар учун миқдорий назария яратилган. </p><p>Берилган моддада Керр эффектини характерловчи параметр, бу учинчи тартибли сезувчанликдир, чунки Керр эффекти электр майдон кучининг учинчи даражасига пропорционалдир (юқоридаги тенгламада қўшимча электр майдони- <a href="/wiki/Elektromagnit_nurlanish" title="Электромагнит нурланиш">ёруғлик тўлқинининг</a> электр майдонидир). </p> <div class="mw-heading mw-heading2"><h2 id="Ayrim_moddalar_uchun_Kerr_doimiysi">Айрим моддалар учун Керр доимийси</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=5" title="Edit section: Айрим моддалар учун Керр доимийси" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=5" title="Edit section's source code: Айрим моддалар учун Керр доимийси"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Тўлқин узунлиги 589 нмда баъзи моддалар учун Керр константалари <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> CГСЕ бирликларида жадвал <sup id="cite_ref-Физическая_энциклопедия_1-2" class="reference"><a href="#cite_note-Физическая_энциклопедия-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> да келтирилган. </p> <table class="wikitable"> <tbody><tr> <th>Модда </th> <th>Температура,<br /><br />°C </th> <th><i>В</i> </th> <th>Модда </th> <th>Температура,<br /><br />°C </th> <th><i>В</i> </th></tr> <tr> <td><a href="/wiki/Nitrobenzol" title="Нитробензол">нитробензол</a> </td> <td>20 </td> <td>2,2·10<sup>−5</sup> </td> <td><a href="/wiki/Xloroform" title="Хлороформ">хлороформ</a> </td> <td>20 </td> <td>−3,5·10<sup>−10</sup> </td></tr> <tr> <td>о-нитротолуон </td> <td>20 </td> <td>1,2-10<sup>−5</sup> </td> <td><a href="/wiki/Etil_spirti" title="Этил спирти">этанол</a> </td> <td>18 </td> <td>9,2·10<sup>−10</sup> </td></tr> <tr> <td><a href="/wiki/Xlorbenzol" title="Хлорбензол">хлорбензол</a> </td> <td>20 </td> <td>1,0·10<sup>−6</sup> </td> <td><a href="/wiki/Atseton" title="Ацетон">асетон</a> </td> <td>83 </td> <td>5,4·10<sup>−10</sup> </td></tr> <tr> <td>сув </td> <td>20 </td> <td>4,7·10<sup>−7</sup> </td> <td>углерод дисулфиди </td> <td>57 </td> <td>3,6·10<sup>−10</sup> </td></tr> <tr> <td>углерод дисулфиди </td> <td>20 </td> <td>3,2·10<sup>−8</sup> </td> <td><a href="/wiki/Etil_efir" title="Этил эфир">этанол</a> </td> <td>63 </td> <td>−0,66-10<sup>−10</sup> </td></tr> <tr> <td><a href="/wiki/Benzol" title="Бензол">бензол</a> </td> <td>20 </td> <td>6,0·10<sup>−9</sup> </td> <td>винил спирти </td> <td>20 </td> <td>−1,7·10<sup>−10</sup> </td></tr> </tbody></table> <div class="mw-heading mw-heading2"><h2 id="Nazariya">Назария</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=6" title="Edit section: Назария" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=6" title="Edit section's source code: Назария"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Kvadrat_elektro-optik_Kerr_effekti">Квадрат электро-оптик Керр эффекти</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=7" title="Edit section: Квадрат электро-оптик Керр эффекти" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=7" title="Edit section's source code: Квадрат электро-оптик Керр эффекти"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Чизиқли бўлмаган материал учун электр поларизация майдони <b>П</b> электр майдони <b>Э</b> га боғлиқдир : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {P} =\varepsilon _{0}\chi ^{(1)}:\mathbf {E} +\varepsilon _{0}\chi ^{(2)}:\mathbf {EE} +\varepsilon _{0}\chi ^{(3)}:\mathbf {EEE} +\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>=</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>+</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> <mi mathvariant="bold">E</mi> </mrow> <mo>+</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> <mi mathvariant="bold">E</mi> <mi mathvariant="bold">E</mi> </mrow> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {P} =\varepsilon _{0}\chi ^{(1)}:\mathbf {E} +\varepsilon _{0}\chi ^{(2)}:\mathbf {EE} +\varepsilon _{0}\chi ^{(3)}:\mathbf {EEE} +\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/654eb39fa6e5b8a270c618672ff9813def192dc5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:50.303ex; height:3.176ex;" alt="{\displaystyle \mathbf {P} =\varepsilon _{0}\chi ^{(1)}:\mathbf {E} +\varepsilon _{0}\chi ^{(2)}:\mathbf {EE} +\varepsilon _{0}\chi ^{(3)}:\mathbf {EEE} +\cdots }"></span></dd></dl> <p>Бу ерда ε <sub>0</sub> - диэлектрик ўтказувчанлик, χ <sup>(<i>н</i>)</sup> — муҳитнинг электр сезгирлигининг <i>н-</i> тартибдаги компоненти. „:“ белгиси матрицаларнинг скаляр кўпайтмасини ифодалайди. Бу муносабат аниқ ёзилиши мумкин; <i>П</i> векторининг <i>и-</i> компоненти қуйидагича ифодаланиши мумкин: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{i}=\varepsilon _{0}\sum _{j=1}^{3}\chi _{ij}^{(1)}E_{j}+\varepsilon _{0}\sum _{j=1}^{3}\sum _{k=1}^{3}\chi _{ijk}^{(2)}E_{j}E_{k}+\varepsilon _{0}\sum _{j=1}^{3}\sum _{k=1}^{3}\sum _{l=1}^{3}\chi _{ijkl}^{(3)}E_{j}E_{k}E_{l}+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </munderover> <msubsup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </munderover> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </munderover> <msubsup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </munderover> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </munderover> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </munderover> <msubsup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> <mi>k</mi> <mi>l</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{i}=\varepsilon _{0}\sum _{j=1}^{3}\chi _{ij}^{(1)}E_{j}+\varepsilon _{0}\sum _{j=1}^{3}\sum _{k=1}^{3}\chi _{ijk}^{(2)}E_{j}E_{k}+\varepsilon _{0}\sum _{j=1}^{3}\sum _{k=1}^{3}\sum _{l=1}^{3}\chi _{ijkl}^{(3)}E_{j}E_{k}E_{l}+\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/424323c707d684abe7a4b93093aa30c4cd0572f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:74.439ex; height:7.509ex;" alt="{\displaystyle P_{i}=\varepsilon _{0}\sum _{j=1}^{3}\chi _{ij}^{(1)}E_{j}+\varepsilon _{0}\sum _{j=1}^{3}\sum _{k=1}^{3}\chi _{ijk}^{(2)}E_{j}E_{k}+\varepsilon _{0}\sum _{j=1}^{3}\sum _{k=1}^{3}\sum _{l=1}^{3}\chi _{ijkl}^{(3)}E_{j}E_{k}E_{l}+\cdots }"></span></dd></dl> <p>Бу ерда <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i=1,2,3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i=1,2,3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a87b7e5d81c62b040a35078417fb9294b1ec7c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.456ex; height:2.509ex;" alt="{\displaystyle i=1,2,3}"></span> . Кўпи ҳолатда , <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{1}=P_{x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{1}=P_{x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94c56f99869a10525c1000aecc5dabc856849794" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.31ex; height:2.509ex;" alt="{\displaystyle P_{1}=P_{x}}"></span>, яъни қутубланиш майдонининг компонентаси х га параллел деб олинади<i>;</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{2}=E_{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{2}=E_{y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df77c630ada26bb9a6ab83fb529a08525f0ac7a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.632ex; height:2.843ex;" alt="{\displaystyle E_{2}=E_{y}}"></span> ва ҳоказо. </p><p>Чизиқли муҳит учун ушбу тенгламанинг фақат биринчи ҳади муҳим аҳамиятга эгадир, ва қутбланиш муҳитдаги электр майдони билан чизиқли равишда ўзгариб боради. </p><p>Керр эффектини кўрсатувчи материаллар учун, эътибордан четда қолдириб бўлмайдиган учинчи ҳад χ<sup>(3)</sup> муҳим ҳисса қўшади, одатда Керр муҳитининг инверсияси туфайли жуфт тартибли ҳадлар тушиб қолади. Частотаси ω бўлган ёруғлик тўлқинининг ташқи электр майдони <b>Э</b><sub>0</sub> билан бирга ҳосил қилган умумий электр майдонини Э кўриб чиқайлик: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} =\mathbf {E} _{0}+\mathbf {E} _{\omega }\cos(\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>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} =\mathbf {E} _{0}+\mathbf {E} _{\omega }\cos(\omega t),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7f93fcf5e1c769141d0e6e7da2b37eb55b11bcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.759ex; height:2.843ex;" alt="{\displaystyle \mathbf {E} =\mathbf {E} _{0}+\mathbf {E} _{\omega }\cos(\omega t),}"></span></dd></dl> <p>бу ерда <b>Э</b> <sub>ō</sub> — тўлқиннинг вектор амплитудаси. </p><p>Бу икки тенгламани бирлаштириб, <b>П</b> нинг мураккаб ифодасини ҳосил қилсак бўлади. Доимий Керр эффекти учун чизиқли ҳадлар, ҳамда <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi ^{(3)}|\mathbf {E} _{0}|^{2}\mathbf {E} _{\omega }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi ^{(3)}|\mathbf {E} _{0}|^{2}\mathbf {E} _{\omega }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec63e9a83446d185e608ca4a7425f09d375c6390" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.96ex; height:3.343ex;" alt="{\displaystyle \chi ^{(3)}|\mathbf {E} _{0}|^{2}\mathbf {E} _{\omega }}"></span> ҳадлардан ташқари ҳаммасини эътибордан қолдиришимиз мумкин : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {P} \simeq \varepsilon _{0}\left(\chi ^{(1)}+3\chi ^{(3)}|\mathbf {E} _{0}|^{2}\right)\mathbf {E} _{\omega }\cos(\omega t),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>≃</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo>+</mo> <mn>3</mn> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {P} \simeq \varepsilon _{0}\left(\chi ^{(1)}+3\chi ^{(3)}|\mathbf {E} _{0}|^{2}\right)\mathbf {E} _{\omega }\cos(\omega t),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5da1b990a4eeffde44ca0e506fbed2ce47b7ae31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:38.603ex; height:4.843ex;" alt="{\displaystyle \mathbf {P} \simeq \varepsilon _{0}\left(\chi ^{(1)}+3\chi ^{(3)}|\mathbf {E} _{0}|^{2}\right)\mathbf {E} _{\omega }\cos(\omega t),}"></span></dd></dl> <p>бу қутбланиш ва тўлқиннинг электр майдонининг чизиқли бўлмаган сезувчанликнинг қўшимча ҳади ўртасидаги чизиқли муносабатни, ташқи майдон амплитудасининг квадратига пропорсионаллигини ҳисобга олишга ўхшайд. </p><p>Изотроп муҳитлар (масалан, суюқликлар) учун, сезувчанликнинг бундай индуксияланган ўзгариши, синиш кўрсаткичининг электр майдон йўналиши бўйича ўзгаришига олиб келади: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta n=\lambda _{0}K|\mathbf {E} _{0}|^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>n</mi> <mo>=</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta n=\lambda _{0}K|\mathbf {E} _{0}|^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbacef4bd4331e539a1df3dc9fbfa9c836c73d6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.711ex; height:3.343ex;" alt="{\displaystyle \Delta n=\lambda _{0}K|\mathbf {E} _{0}|^{2},}"></span></dd></dl> <p>бу ерда λ 0 — вакуумдаги тўлқин узунлиги ва К — муҳит учун Керр доимийси .Муҳидга қўлланилганган элекрт майдон таъсирида, шу майдон йўналишига параллел бўлган йўналишда муҳитда нурнинг икки марта синиши юзага келади. Шундай қилиб, кўндаланг майдонга эга бўлган Керр катакчаси ўзгарувчан тўлқин пластинаси сифатида, ундан ўтадиган тўлқиннинг поларизация текислигини айлантира олади. Поларизаторлар билан биргаликда у тўсиқ ёки модулятор сифатида ишлатилиши мумкин. </p><p>К қиймати муҳитга боғлиқ бўлиб, у сув учун тахминан 9,4 × 10 −14 м В −2 ва нитробензол учун эса 4,4 × 10 −12 м В −2 ни ташкил қилади. </p><p>Кристаллар учун муҳитнинг сезгирлиги одатда тензор шаклини бўлгани сабаб, Керр эффекти бу тенсознинг модификациясини келтириб чиқаради. </p> <div class="mw-heading mw-heading3"><h3 id="Optik_Kerr_effekti">Оптик Керр эффекти</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=8" title="Edit section: Оптик Керр эффекти" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=8" title="Edit section's source code: Оптик Керр эффекти"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Оптик ёки ўзгарувчан Керр эффектида, муҳитдаги кучли ёруғлик нуриннг ўзи ташқи майдон эҳтиёжисиз модуляция қилувчи электр майдонини яратиши мумкин. Бу ҳолда электр майдони қуйидагича ифодаланади: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} =\mathbf {E} _{\omega }\cos(\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>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} =\mathbf {E} _{\omega }\cos(\omega t),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28449bf85358359236812f79903a682248248b4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.107ex; height:2.843ex;" alt="{\displaystyle \mathbf {E} =\mathbf {E} _{\omega }\cos(\omega t),}"></span></dd></dl> <p>бу ерда <b>Э</b> <sub>ō</sub> — тўлқин амплитудаси. </p><p>Бу ифодани қутбланиш тенгламасига қўйиб ва фақат чизиқли ҳадлар, ҳамда χ<sup>(3)</sup> | <b>Э</b> <sub>ō</sub> | <sup>3</sup> ҳадларни ҳисобга оламиз: <sup id="cite_ref-New2011_2-0" class="reference"><a href="#cite_note-New2011-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <sup class="reference" style="white-space:nowrap;">:<span>81–82</span></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {P} \simeq \varepsilon _{0}\left(\chi ^{(1)}+{\frac {3}{4}}\chi ^{(3)}|\mathbf {E} _{\omega }|^{2}\right)\mathbf {E} _{\omega }\cos(\omega t).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>≃</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mrow> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {P} \simeq \varepsilon _{0}\left(\chi ^{(1)}+{\frac {3}{4}}\chi ^{(3)}|\mathbf {E} _{\omega }|^{2}\right)\mathbf {E} _{\omega }\cos(\omega t).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25b4ef0f5064d2408bc064a0383f412144b051b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:40.286ex; height:6.176ex;" alt="{\displaystyle \mathbf {P} \simeq \varepsilon _{0}\left(\chi ^{(1)}+{\frac {3}{4}}\chi ^{(3)}|\mathbf {E} _{\omega }|^{2}\right)\mathbf {E} _{\omega }\cos(\omega t).}"></span></dd></dl> <p>Аввалгидек, бу қўшимча чизиқли бўлмаган ҳадга эга бўлган, чизиқли сезгирликка ўхшайди: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi =\chi _{\mathrm {LIN} }+\chi _{\mathrm {NL} }=\chi ^{(1)}+{\frac {3\chi ^{(3)}}{4}}|\mathbf {E} _{\omega }|^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo>=</mo> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">I</mi> <mi mathvariant="normal">N</mi> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">L</mi> </mrow> </mrow> </msub> <mo>=</mo> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> <mn>4</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi =\chi _{\mathrm {LIN} }+\chi _{\mathrm {NL} }=\chi ^{(1)}+{\frac {3\chi ^{(3)}}{4}}|\mathbf {E} _{\omega }|^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c6c5422557c804caed42e303a8c8ddf38027fd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:37.403ex; height:5.843ex;" alt="{\displaystyle \chi =\chi _{\mathrm {LIN} }+\chi _{\mathrm {NL} }=\chi ^{(1)}+{\frac {3\chi ^{(3)}}{4}}|\mathbf {E} _{\omega }|^{2},}"></span></dd></dl> <p>ҳамда: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=(1+\chi )^{1/2}=\left(1+\chi _{\mathrm {LIN} }+\chi _{\mathrm {NL} }\right)^{1/2}\simeq n_{0}\left(1+{\frac {1}{2{n_{0}}^{2}}}\chi _{\mathrm {NL} }\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>χ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">I</mi> <mi mathvariant="normal">N</mi> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">L</mi> </mrow> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <mo>≃</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">L</mi> </mrow> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=(1+\chi )^{1/2}=\left(1+\chi _{\mathrm {LIN} }+\chi _{\mathrm {NL} }\right)^{1/2}\simeq n_{0}\left(1+{\frac {1}{2{n_{0}}^{2}}}\chi _{\mathrm {NL} }\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35d6aa44b225fdd4696d89356ccbc541fdafe304" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:60.203ex; height:6.176ex;" alt="{\displaystyle n=(1+\chi )^{1/2}=\left(1+\chi _{\mathrm {LIN} }+\chi _{\mathrm {NL} }\right)^{1/2}\simeq n_{0}\left(1+{\frac {1}{2{n_{0}}^{2}}}\chi _{\mathrm {NL} }\right)}"></span></dd></dl> <p>бу ерда <i>н</i> <sub>0</sub> = (1 + ч <sub>ЛИН</sub>) <sup>1/2</sup> чизиқли синдириш кўрсаткичи. Тейлор формуласидан фойдаланиб, Х<sub>НЛ</sub> << <i>н</i> <sub>0</sub> <sup>2</sup> бўлгани учун, бу <i>синиши кўсаткичининг</i> (ИДРИ) интенсивликга боғлиқлигини беради: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=n_{0}+{\frac {3\chi ^{(3)}}{8n_{0}}}|\mathbf {E} _{\omega }|^{2}=n_{0}+n_{2}I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> <mrow> <mn>8</mn> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</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> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=n_{0}+{\frac {3\chi ^{(3)}}{8n_{0}}}|\mathbf {E} _{\omega }|^{2}=n_{0}+n_{2}I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e30b670ec1193ce28f94fc65f8348419bd105ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:32.938ex; height:6.176ex;" alt="{\displaystyle n=n_{0}+{\frac {3\chi ^{(3)}}{8n_{0}}}|\mathbf {E} _{\omega }|^{2}=n_{0}+n_{2}I}"></span></dd></dl> <p>бу ерда <i>н</i> <sub>2</sub> — чизиқли бўлмаган иккинчи тартибли синиш кўсаткичи, <i>И</i> — тўлқин интенсивлиги. Шундай қилиб, синиши кўсаткичининг ўзгариши, муҳитдан ўтувчи ёруғлик интенсивлигига пропорционалдир. </p><p>Кўпгина материаллар учун <i>н</i> <sub>2</sub> қиймати нисбатан кичик, одатий шишалар учун 10 <sup>−20</sup> м <sup>2</sup> Вт <sup>−1</sup> га тенг. Шундай қилиб, ўзгарувчан токли Керр эффекти орқали синиши кўрсаткичида сезиларли ўзгариш яратиш учун, 1 ГВт см <sup>-2</sup> (масалан, лазерлар томонидан ишлаб чиқарилган) ёруғлик интенсивлиги (нурланиш) керак бўлади. </p><p>Оптик Керр эффекти фазали ўз-ўзини модуляция қилишдир, яъни ёруғликнинг муҳитдан о;тганда, унинг фаза ва импулсининг частотали силжишини ўз-ўзидан индукциялантииш. Ушбу жараённи <a href="/wiki/Yorug%CA%BBlik_dispersiyasi" title="Ёруғлик дисперсияси">дисперсия</a> билан бирга оптик солитонлар яратиш учун ишлатилиши мумкин. </p><p>Фазовий жиҳатдан, муҳитдаги кучли ёруғлик нурлари, шу нур интенсивлигининг кўндаланг суратини тақлид қилувчи муҳитнинг синиши кўсаткичининг ўзгаришини ҳосил қилади. Мисол учун, Гаусс нури, линзадаги градиэнтли синиш кўрсаткичининг профилига ўхшаш, синиш кўрсаткичининг Гаусс профилни ҳосил қилади. Бу нурнинг фокусланишига олиб келади, бу <a href="/wiki/O%CA%BBz-o%CA%BBzini_yo%CA%BBnaltirish" title="Ўз-ўзини йўналтириш">ўз-ўзини фокуслаш</a> деб номланувчи ҳодиса. </p><p>Нур ўз-ўзидан фокусланганда, интенсивликнинг энг юқори кўрсаткичи ошиб боради, бу эса ўз-ўзидан фокусланишнинг кучайишига олиб келади. Нурнинг ўз-ўзини фокуслашига, интенсивлик жуда юқори бўлганда, муҳим бўлган <a href="/w/index.php?title=%D0%A4%D0%BE%D1%82%D0%BE%D1%8D%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D1%85%D0%B8%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B5_%D0%BF%D1%80%D0%BE%D1%86%D0%B5%D1%81%D1%81%D1%8B&action=edit&redlink=1" class="new" title="Фотоэлектрохимические процессы (саҳифа яратилмаган)">мултифотонли ионлашув</a> каби чизиқли бўлмаган аффектлар номаълум муддатга тўсқинлик қилади. Ўз-ўзидан фокусланган нуқтанинг интенсивлиги маълум бир қийматдан ошганда, муҳит кучли локал оптик майдон билан ионланади. Бу тарқаладиган ёруғлик нурини йўқотиб, синиш кўрсаткичинини пасайтиради. Кейин тарқалиш бир қатор такрорий фокуслаш ва дефокуслаш босқичлари сифатида содир бўлади <sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> . </p> <div class="mw-heading mw-heading2"><h2 id="Qoʻllanishi"><span id="Qo.CA.BBllanishi"></span>Қўлланиши</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=9" title="Edit section: Қўлланиши" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=9" title="Edit section's source code: Қўлланиши"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Elektro-optik_modulyatorlarda">Электро-оптик модуляторларда</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=10" title="Edit section: Электро-оптик модуляторларда" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=10" title="Edit section's source code: Электро-оптик модуляторларда"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Электро-оптик эффект, оптик толали технологиясида оптик сигналларнинг интенсивлигини электр модуляция қилиш учун ишлатилади. </p> <div class="mw-heading mw-heading3"><h3 id="Lazerlarda_rejimni_qulflash">Лазерларда режимни қулфлаш</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=11" title="Edit section: Лазерларда режимни қулфлаш" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=11" title="Edit section's source code: Лазерларда режимни қулфлаш"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Керр эффектига асосланган <a href="/wiki/Lazer" title="Лазер">лазерда</a> тезкор модлар синхронизациясини амалга ошириш имконияти мавжуд. Керр муҳитидаги нур <a href="/wiki/Umov_poynting_vektori" title="Умов пойнтинг вектори">интенсивлиги</a> кўндаланг (масалан, Гаусс) интенсивлик тақсимотига эга бўлсин. бундан келиб чиқадики, нурнинг марказидаги интенсивлиги формула бўйича <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}"></span> радиусли нур ўқидан <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> масофадан кўра каттароқ бўлади : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=n_{o}+n_{2}I,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>I</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=n_{o}+n_{2}I,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e153cb04310686995250eec6571ae6171e49d998" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.025ex; height:2.509ex;" alt="{\displaystyle n=n_{o}+n_{2}I,}"></span></dd></dl> <p>ва шунинг учун синдириш кўрсаткичида чизиқли бўлмаган <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/957caf97b0edee56d65cb0f5043e05125ba0ebe9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.443ex; height:2.343ex;" alt="{\displaystyle \delta n}"></span> ўзгариш мавжуд . <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (r/w)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>w</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (r/w)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38ca6a5a83f5da5074e81ae9a8bfba50b98a1b46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.739ex; height:3.176ex;" alt="{\displaystyle (r/w)^{2}}"></span> функсияни ёйиб чиққандаги биринчи яқинлашишда, фаза силжишини <img typeof="mw:Extension/math" data-mw="{&quot;name&quot;:&quot;math&quot;,&quot;attrs&quot;:{},&quot;body&quot;:{&quot;extsrc&quot;:&quot;r/w&quot;}}" about="#mwt23361041" class="mwe-math-element" id="10"> параметри орқали <a href="/wiki/Parabola_(chiziq)" title="Парабола (чизиқ)">параболик функсия</a> жиҳатидан тасвирланиши мумкин, бу Керр муҳитида <a href="/wiki/Linza" title="Линза">икки томонлама қавариқ линзанинг</a> таъсирига тенг. Нурнинг интенсивлиги қанчалик катта бўлса, у шунчалик кўп фокусланади ва натижада масофа ортиши билан камроқ йўқотишларни бошдан кечиради. Агар бу йўқотишлар лазер резонаторида тўғри тақсимланган бўлса, пассив модлар синхронизациясини олиш мумкин. </p> <div class="mw-heading mw-heading2"><h2 id="Yana_qarang">Яна қаранг</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=12" title="Edit section: Яна қаранг" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=12" title="Edit section's source code: Яна қаранг"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Керр катакчаси</li> <li>Поcкел эффекти</li> <li><a href="/wiki/Faradey_effekti" title="Фарадей эффекти">Фарадай эффекти</a></li> <li>Ўз фазали модуляция</li> <li>Чизиқсиз оптика</li></ul> <div class="mw-heading mw-heading2"><h2 id="Manbalar">Манбалар</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=13" title="Edit section: Манбалар" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=13" title="Edit section's source code: Манбалар"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r3605845">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Физическая_энциклопедия-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Физическая_энциклопедия_1-0">1,0</a></sup> <sup><a href="#cite_ref-Физическая_энциклопедия_1-1">1,1</a></sup> <sup><a href="#cite_ref-Физическая_энциклопедия_1-2">1,2</a></sup></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://femto.com.ua/articles/part_1/1597.html">Описаниэ эффекта Керра в физической энсиклопедии</a></span> </li> <li id="cite_note-New2011-2"><span class="mw-cite-backlink"><a href="#cite_ref-New2011_2-0">↑</a></span> <span class="reference-text"><span class="citation" id="CITEREFGeoffrey_New2011-04-07">Геоффрей Неw<i>. Интродуcтион то Нонлинеар Оптиcс</i>. <a href="/wiki/Cambridge_University_Press" class="mw-redirect" title="Cамбридге Университй Пресс">Cамбридге Университй Пресс</a>, 2011-04-07. 978-1-139-50076-0.</span><span class="Z3988" title="cтх_вер=З39.88-2004&рфт_вал_фмт=инфо%3Аофи%2Ффмт%3Акев%3Амтх%3Абоок&рфт.генре=боок&рфт.бтитле=Интродуcтион+то+Нонлинеар+Оптиcс&рфт.ауласт=Геоффрей+Неw&рфт.дате=2011-04-07&рфт.пуб=%5Б%5БCамбридге+Университй+Пресс%5Д%5Д"> </span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><span class="citation Journal">Дҳармадҳикари, А. К. (2008). "Висуализатион оф фоcусинг–рефоcусинг cйcлес дуринг филаментатион ин БаФ<sub>2</sub>". <i>Апплиэд Пҳйсиcс Б</i> <b>94</b> (2): 259. <a href="/wiki/Doi" class="mw-redirect" title="Дои">дои</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2Fs00340-008-3317-7">10.1007/s00340-008-3317-7</a>.</span><span class="Z3988" title="cтх_вер=З39.88-2004&рфт_вал_фмт=инфо%3Аофи%2Ффмт%3Акев%3Амтх%3Ажоурнал&рфт.генре=артиcле&рфт.атитле=Висуализатион+оф+фоcусинг%Э2%80%93рефоcусинг+cйcлес+дуринг+филаментатион+ин+БаФ%3Cсуб%3Э2%3C%2Фсуб%3Э&рфт.жтитле=Апплиэд+Пҳйсиcс+Б&рфт.ауласт=Дҳармадҳикари&рфт.ауфирст=А.+К.&рфт.ау=Дҳармадҳикари%2C%26%2332%3БА.+К.&рфт.дате=2008&рфт.волуме=94&рфт.иссуэ=2&рфт.пагес=259&рфт_ид=инфо:дои/10.1007%2Фс00340-008-3317-7&рфр_ид=инфо:сид/эн.wикипедиа.орг:Керра_эффекти"><span style="display: none;"> </span></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Adabiyotlar">Адабиётлар</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=14" title="Edit section: Адабиётлар" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=14" title="Edit section's source code: Адабиётлар"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Проҳоров А. М. Физик энсиклопедик луғат. Совет энсиклопедияси. 1983 — 280 -, 928- бетлар.</li> <li>Сивуҳин Д. В. Умумий физика курси. — М. — Т. ИВ. Оптика.</li> <li>Звелто О. Лазерлар принсипи. Лан,2008 — 404 -, 719- бетлар.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Havolalar">Ҳаволалар</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerra_effekti&veaction=edit&section=15" title="Edit section: Ҳаволалар" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kerra_effekti&action=edit&section=15" title="Edit section's source code: Ҳаволалар"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Керра эффекти-Катта совет энциклопедиясидан мақола. Й. Э. Светлов томонидан.</li> <li>Физик энциклопедияда Керр эффектининг тавсифи</li> <li>Лаборатория ишларида Керр таъсирининг назарий тавсифи</li> <li>Керр ишининг тавсифи, Керр эффекти ва бошқа эффектларнинг тавсифи</li> <li>Дастлабки телевизордаги Керр катакчалари (Керр катакчалари ҳақидаги дастлабки мақолаларни кўриш учун саҳифани пастга айлантиринг.)</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="" lang="uz-Cyrl" dir="ltr">Retrieved from "<a dir="ltr" href="https://uz.wikipedia.org/w/index.php?title=Kerra_effekti&oldid=5231111">https://uz.wikipedia.org/w/index.php?title=Kerra_effekti&oldid=5231111</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Maxsus:Categories" title="Maxsus:Categories">Category</a>: <ul><li><a href="/wiki/Turkum:Effektlar_haqidagi_maqolalar" title="Turkum:Effektlar haqidagi maqolalar">Эффектлар ҳақидаги мақолалар</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" lang="uz-Cyrl" dir="ltr"> <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 24 September 2024, at 04:10.</li> <li id="footer-info-copyright">Text is available under the <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-ShareAlike License</a>; additional terms may apply. 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