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class="vector-toc-list"> </ul> </li> <li id="toc-Organic_materials" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Organic_materials"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Organic materials</span> </div> </a> <ul id="toc-Organic_materials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Plasmonic_and_magnetic_materials" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Plasmonic_and_magnetic_materials"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Plasmonic and magnetic materials</span> </div> </a> <ul id="toc-Plasmonic_and_magnetic_materials-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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" 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class="mw-page-title-main">Faraday effect</span></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="Go to an article in another language. Available in 34 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-34" 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">34 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%AA%D8%A3%D8%AB%D9%8A%D8%B1_%D9%81%D8%A7%D8%B1%D8%A7%D8%AF%D8%A7%D9%8A" title="تأثير فاراداي – Arabic" lang="ar" hreflang="ar" data-title="تأثير فاراداي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Faradey_effekti" title="Faradey effekti – Azerbaijani" lang="az" hreflang="az" data-title="Faradey effekti" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</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%A4%D0%B0%D1%80%D0%B0%D0%B4%D1%8D%D1%8F" title="Эфект Фарадэя – Belarusian" lang="be" hreflang="be" data-title="Эфект Фарадэя" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D1%84%D0%B5%D0%BA%D1%82_%D0%BD%D0%B0_%D0%A4%D0%B0%D1%80%D0%B0%D0%B4%D0%B5%D0%B9" title="Ефект на Фарадей – Bulgarian" lang="bg" hreflang="bg" data-title="Ефект на Фарадей" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Efecte_Faraday" title="Efecte Faraday – Catalan" lang="ca" hreflang="ca" data-title="Efecte Faraday" data-language-autonym="Català" data-language-local-name="Catalan" 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/Faradayeffekten" title="Faradayeffekten – Danish" lang="da" hreflang="da" data-title="Faradayeffekten" data-language-autonym="Dansk" data-language-local-name="Danish" 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/Faraday-Effekt" title="Faraday-Effekt – German" lang="de" hreflang="de" data-title="Faraday-Effekt" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Faraday_efekt" title="Faraday efekt – Estonian" lang="et" hreflang="et" data-title="Faraday efekt" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Efecto_Faraday" title="Efecto Faraday – Spanish" lang="es" hreflang="es" data-title="Efecto Faraday" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Efiko_de_Faraday" title="Efiko de Faraday – Esperanto" lang="eo" hreflang="eo" data-title="Efiko de Faraday" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</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_%D9%81%D8%A7%D8%B1%D8%A7%D8%AF%DB%8C" title="اثر فارادی – Persian" lang="fa" hreflang="fa" data-title="اثر فارادی" data-language-autonym="فارسی" data-language-local-name="Persian" 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_Faraday" title="Effet Faraday – French" lang="fr" hreflang="fr" data-title="Effet Faraday" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Iarmhairt_Faraday" title="Iarmhairt Faraday – Irish" lang="ga" hreflang="ga" data-title="Iarmhairt Faraday" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8C%A8%EB%9F%AC%EB%8D%B0%EC%9D%B4_%ED%9A%A8%EA%B3%BC" title="패러데이 효과 – Korean" lang="ko" hreflang="ko" data-title="패러데이 효과" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%96%D5%A1%D6%80%D5%A1%D5%A4%D5%A5%D5%B5%D5%AB_%D5%A5%D6%80%D6%87%D5%B8%D6%82%D5%B5%D5%A9" title="Ֆարադեյի երևույթ – Armenian" lang="hy" hreflang="hy" data-title="Ֆարադեյի երևույթ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" 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_Faraday" title="Effetto Faraday – Italian" lang="it" hreflang="it" data-title="Effetto Faraday" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A4%D7%A7%D7%98_%D7%A4%D7%90%D7%A8%D7%90%D7%93%D7%99%D7%99" title="אפקט פאראדיי – Hebrew" lang="he" hreflang="he" data-title="אפקט פאראדיי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A4%D0%B0%D1%80%D0%B0%D0%B4%D0%B5%D0%B9_%D2%9B%D2%B1%D0%B1%D1%8B%D0%BB%D1%8B%D1%81%D1%8B" title="Фарадей құбылысы – Kazakh" lang="kk" hreflang="kk" data-title="Фарадей құбылысы" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Faradeja_efekts" title="Faradeja efekts – Latvian" lang="lv" hreflang="lv" data-title="Faradeja efekts" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Faraday-effect" title="Faraday-effect – Dutch" lang="nl" hreflang="nl" data-title="Faraday-effect" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%95%E3%82%A1%E3%83%A9%E3%83%87%E3%83%BC%E5%8A%B9%E6%9E%9C" title="ファラデー効果 – Japanese" lang="ja" hreflang="ja" data-title="ファラデー効果" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Faradayeffekt" title="Faradayeffekt – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Faradayeffekt" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Faradey_effekti" title="Faradey effekti – Uzbek" lang="uz" hreflang="uz" data-title="Faradey effekti" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Zjawisko_Faradaya" title="Zjawisko Faradaya – Polish" lang="pl" hreflang="pl" data-title="Zjawisko Faradaya" data-language-autonym="Polski" data-language-local-name="Polish" 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_Faraday" title="Efeito Faraday – Portuguese" lang="pt" hreflang="pt" data-title="Efeito Faraday" data-language-autonym="Português" data-language-local-name="Portuguese" 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_Faraday" title="Efectul Faraday – Romanian" lang="ro" hreflang="ro" data-title="Efectul Faraday" data-language-autonym="Română" data-language-local-name="Romanian" 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%A4%D0%B0%D1%80%D0%B0%D0%B4%D0%B5%D1%8F" title="Эффект Фарадея – Russian" lang="ru" hreflang="ru" data-title="Эффект Фарадея" data-language-autonym="Русский" data-language-local-name="Russian" 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/Faradayev_pojav" title="Faradayev pojav – Slovenian" lang="sl" hreflang="sl" data-title="Faradayev pojav" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" 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%A4%D0%B0%D1%80%D0%B0%D0%B4%D0%B5%D1%98%D0%B5%D0%B2_%D0%B5%D1%84%D0%B5%D0%BA%D0%B0%D1%82" title="Фарадејев ефекат – Serbian" lang="sr" hreflang="sr" data-title="Фарадејев ефекат" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" 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/Faradayeffekt" title="Faradayeffekt – Swedish" lang="sv" hreflang="sv" data-title="Faradayeffekt" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9B%E0%B8%A3%E0%B8%B2%E0%B8%81%E0%B8%8F%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%93%E0%B9%8C%E0%B8%9F%E0%B8%B2%E0%B8%A3%E0%B8%B2%E0%B9%80%E0%B8%94%E0%B8%A2%E0%B9%8C" title="ปรากฏการณ์ฟาราเดย์ – Thai" lang="th" hreflang="th" data-title="ปรากฏการณ์ฟาราเดย์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Faraday_etkisi" title="Faraday etkisi – Turkish" lang="tr" hreflang="tr" data-title="Faraday etkisi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</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%A4%D0%B0%D1%80%D0%B0%D0%B4%D0%B5%D1%8F" title="Ефект Фарадея – Ukrainian" lang="uk" hreflang="uk" data-title="Ефект Фарадея" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%B3%95%E6%8B%89%E7%AC%AC%E6%95%88%E5%BA%94" title="法拉第效应 – Chinese" lang="zh" hreflang="zh" data-title="法拉第效应" data-language-autonym="中文" data-language-local-name="Chinese" 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 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dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Physical magneto-optical phenomenon</div> <p>The <b>Faraday effect</b> or <b>Faraday rotation</b>, sometimes referred to as the <b>magneto-optic Faraday effect</b> (<b>MOFE</b>),<sup id="cite_ref-UrsMozooni2016_1-0" class="reference"><a href="#cite_note-UrsMozooni2016-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> is a <a href="/wiki/Physics" title="Physics">physical</a> <a href="/wiki/Magneto-optic" class="mw-redirect" title="Magneto-optic">magneto-optical</a> phenomenon. The Faraday effect causes a <a href="/wiki/Polarization_(waves)" title="Polarization (waves)">polarization</a> rotation which is proportional to the projection of the <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> along the direction of the <a href="/wiki/Light" title="Light">light</a> propagation. Formally, it is a special case of <a href="/w/index.php?title=Gyroelectromagnetism&action=edit&redlink=1" class="new" title="Gyroelectromagnetism (page does not exist)">gyroelectromagnetism</a> obtained when the <a href="/wiki/Dielectric_permittivity" class="mw-redirect" title="Dielectric permittivity">dielectric permittivity</a> <a href="/wiki/Tensor" title="Tensor">tensor</a> is diagonal.<sup id="cite_ref-Prati2003_2-0" class="reference"><a href="#cite_note-Prati2003-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> This effect occurs in most optically <a href="/wiki/Transparency_(optics)" class="mw-redirect" title="Transparency (optics)">transparent</a> <a href="/wiki/Dielectric" title="Dielectric">dielectric</a> materials (including liquids) under the influence of <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic fields</a>. </p><p>Discovered by <a href="/wiki/Michael_Faraday" title="Michael Faraday">Michael Faraday</a> in 1845, the Faraday effect was the first experimental evidence that light and electromagnetism are related. The theoretical basis of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> (which includes visible light) was completed by <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> in the 1860s. Maxwell's equations were rewritten in their current form in the 1870s by <a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Oliver Heaviside</a>. </p><p>The Faraday effect is caused by left and right <a href="/wiki/Circular_polarization" title="Circular polarization">circularly polarized</a> waves propagating at slightly different speeds, a property known as <a href="/wiki/Optical_rotation" title="Optical rotation">circular birefringence</a>. Since a linear polarization can be decomposed into the <a href="/wiki/Superposition_principle" title="Superposition principle">superposition</a> of two equal-amplitude circularly polarized components of opposite handedness and different phase, the effect of a relative <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase</a> shift, induced by the Faraday effect, is to rotate the orientation of a wave's linear polarization. </p><p>The Faraday effect has applications in measuring instruments. For instance, the Faraday effect has been used to measure optical rotatory power and for <a href="/wiki/Remote_sensing" title="Remote sensing">remote sensing</a> of magnetic fields (such as <a href="/wiki/Fiber_optic_current_sensor" class="mw-redirect" title="Fiber optic current sensor">fiber optic current sensors</a>). The Faraday effect is used in <a href="/wiki/Spintronics" title="Spintronics">spintronics</a> research to study the polarization of electron spins in semiconductors. <a href="/wiki/Faraday_rotator" title="Faraday rotator">Faraday rotators</a> can be used for amplitude modulation of light, and are the basis of <a href="/wiki/Optical_isolator" title="Optical isolator">optical isolators</a> and <a href="/wiki/Optical_circulators" class="mw-redirect" title="Optical circulators">optical circulators</a>; such components are required in optical telecommunications and other laser applications.<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> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Faraday_with_glass_bar_crop2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Faraday_with_glass_bar_crop2.jpg/170px-Faraday_with_glass_bar_crop2.jpg" decoding="async" width="170" height="170" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Faraday_with_glass_bar_crop2.jpg/255px-Faraday_with_glass_bar_crop2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Faraday_with_glass_bar_crop2.jpg/340px-Faraday_with_glass_bar_crop2.jpg 2x" data-file-width="1062" data-file-height="1065" /></a><figcaption><a href="/wiki/Michael_Faraday" title="Michael Faraday">Michael Faraday</a> holding a piece of glass of the type he used to demonstrate the effect of magnetism on polarization of light, c. 1857.</figcaption></figure> <p>By 1845, it was known through the work of <a href="/wiki/Augustin-Jean_Fresnel" title="Augustin-Jean Fresnel">Augustin-Jean Fresnel</a>, <a href="/wiki/%C3%89tienne-Louis_Malus" title="Étienne-Louis Malus">Étienne-Louis Malus</a>, and others that different materials are able to modify the direction of polarization of light when appropriately oriented,<sup id="cite_ref-horvath-thesis_4-0" class="reference"><a href="#cite_note-horvath-thesis-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> making polarized light a very powerful tool to investigate the properties of transparent materials. Faraday firmly believed that light was an electromagnetic phenomenon, and as such should be affected by electromagnetic forces. He spent considerable effort looking for evidence of electric forces affecting the polarization of light through what are now known as <a href="/wiki/Electro-optic_effect" class="mw-redirect" title="Electro-optic effect">electro-optic effects</a>, starting with decomposing electrolytes. However, his experimental methods were not sensitive enough, and the effect was only measured thirty years later by <a href="/wiki/John_Kerr_(physicist)" title="John Kerr (physicist)">John Kerr</a>.<sup id="cite_ref-crowther-1920_5-0" class="reference"><a href="#cite_note-crowther-1920-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Faraday then attempted to look for the effects of magnetic forces on light passing through various substances. After several unsuccessful trials, he happened to test a piece of "heavy" glass, containing equal proportions of silica, boracic acid and lead oxide, that he had made during his earlier work on glass manufacturing.<sup id="cite_ref-mansuripur_6-0" class="reference"><a href="#cite_note-mansuripur-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Faraday observed that when a beam of polarized light passed through the glass in the direction of an applied magnetic force, the polarization of light rotated by an angle that was proportional to the strength of the force. He used a <a href="/wiki/Nicol_prism" title="Nicol prism">Nicol prism</a> to measure the polarization. He was later able to reproduce the effect in several other solids, liquids, and gases by procuring stronger electromagnets.<sup id="cite_ref-crowther-1920_5-1" class="reference"><a href="#cite_note-crowther-1920-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>The discovery is well documented in Faraday's daily notebook.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> On 13 Sept. 1845, in paragraph #7504, under the rubric <i>Heavy Glass</i>, he wrote: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p><abbr style="text-decoration:none;border-bottom:1px dotted black;margin-bottom:1px;" title="quote text omitted">...</abbr> <b>BUT</b>, when the contrary magnetic poles were on the same side, <i>there was an effect produced on the polarized ray</i>, and thus magnetic force and light were proved to have relation to each other. <abbr style="text-decoration:none;border-bottom:1px dotted black;margin-bottom:1px;" title="quote text omitted">...</abbr></p><div class="templatequotecite">— <cite>Faraday, Paragraph #7504, Daily notebook</cite></div></blockquote> <p>He summarized the results of his experiments on 30 Sept. 1845, in paragraph #7718, famously writing: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p><abbr style="text-decoration:none;border-bottom:1px dotted black;margin-bottom:1px;" title="quote text omitted">...</abbr> Still, I have at last succeeded in illuminating a magnetic curve or line of force, and in magnetizing a ray of light. <abbr style="text-decoration:none;border-bottom:1px dotted black;margin-bottom:1px;" title="quote text omitted">...</abbr></p><div class="templatequotecite">— <cite>Faraday, Paragraph #7718, Daily notebook</cite></div></blockquote> <div class="mw-heading mw-heading2"><h2 id="Physical_interpretation">Physical interpretation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=2" title="Edit section: Physical interpretation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The linear polarized light that is seen to rotate in the Faraday effect can be seen as consisting of the superposition of a right- and a left- circularly polarized beam (this <a href="/wiki/Superposition_principle" title="Superposition principle">superposition principle</a> is fundamental in many branches of physics). We can look at the effects of each component (right- or left-polarized) separately, and see what effect this has on the result. </p><p>In <a href="/wiki/Circular_polarization" title="Circular polarization">circularly polarized light</a> the direction of the electric field rotates at the frequency of the light, either clockwise or counter-clockwise. In a material, this electric field causes a force on the charged particles that compose the material (because of their large charge to mass ratio, the electrons are most heavily affected). The motion thus effected will be circular, and circularly moving charges will create their own (magnetic) field in addition to the external magnetic field. There will thus be two different cases: the created field will be parallel to the external field for one (circular) polarization, and in the opposing direction for the other polarization direction – thus the net B field is enhanced in one direction and diminished in the opposite direction. This changes the dynamics of the interaction for each beam and one of the beams will be slowed more than the other, causing a phase difference between the left- and right-polarized beam. When the two beams are added after this phase shift, the result is again a linearly polarized beam, but with a rotation of the polarization vector. </p><p>The direction of polarization rotation depends on the properties of the material through which the light is shone. A full treatment would have to take into account the effect of the external and radiation-induced fields on the wave function of the electrons, and then calculate the effect of this change on the refractive index of the material for each polarization, to see whether the right- or left-circular polarization is slowed more. </p> <div class="mw-heading mw-heading2"><h2 id="Mathematical_formulation">Mathematical formulation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=3" title="Edit section: Mathematical formulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Formally, the magnetic <a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">permeability</a> is treated as a non-diagonal tensor as expressed by the equation:<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></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 {B} (\omega )={\begin{bmatrix}\mu _{1}&-i\mu _{2}&0\\i\mu _{2}&\mu _{1}&0\\0&0&\mu _{z}\\\end{bmatrix}}\mathbf {H} (\omega )}"> <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>ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <mo>−</mo> <mi>i</mi> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>i</mi> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} (\omega )={\begin{bmatrix}\mu _{1}&-i\mu _{2}&0\\i\mu _{2}&\mu _{1}&0\\0&0&\mu _{z}\\\end{bmatrix}}\mathbf {H} (\omega )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99fb74fc7a26f99401c015f3690d958694c8045c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:32.827ex; height:9.509ex;" alt="{\displaystyle \mathbf {B} (\omega )={\begin{bmatrix}\mu _{1}&-i\mu _{2}&0\\i\mu _{2}&\mu _{1}&0\\0&0&\mu _{z}\\\end{bmatrix}}\mathbf {H} (\omega )}"></span></dd></dl> <p>The relation between the <a href="/wiki/Angle_of_rotation" class="mw-redirect" title="Angle of rotation">angle of rotation</a> of the polarization and the magnetic field in a transparent material is: </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Faraday-effect.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Faraday-effect.svg/300px-Faraday-effect.svg.png" decoding="async" width="300" height="223" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Faraday-effect.svg/450px-Faraday-effect.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Faraday-effect.svg/600px-Faraday-effect.svg.png 2x" data-file-width="335" data-file-height="249" /></a><figcaption>Polarization rotation due to the Faraday effect</figcaption></figure> <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 \beta ={\mathcal {V}}Bd}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">V</mi> </mrow> </mrow> <mi>B</mi> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta ={\mathcal {V}}Bd}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b479397a797e907c10e211a9cb6b3647d29507b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.94ex; height:2.509ex;" alt="{\displaystyle \beta ={\mathcal {V}}Bd}"></span></dd></dl> <p>where </p> <dl><dd>β is the angle of rotation (in <a href="/wiki/Radian" title="Radian">radians</a>)</dd> <dd><i>B</i> is the magnetic flux density in the direction of propagation (in <a href="/wiki/Tesla_(unit)" title="Tesla (unit)">teslas</a>)</dd> <dd><i>d</i> is the length of the path (in meters) where the light and magnetic field interact</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 \scriptstyle {\mathcal {V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">V</mi> </mrow> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\mathcal {V}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec3af598ef332f11d37081355f5edf0ef9cd2b6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.081ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {\mathcal {V}}}"></span> is the <a href="/wiki/Verdet_constant" title="Verdet constant">Verdet constant</a> for the material. This empirical proportionality constant (in units of radians per tesla per meter) varies with wavelength and temperature<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> and is tabulated for various materials.</dd></dl> <p>A positive Verdet constant corresponds to L-rotation (anticlockwise) when the direction of propagation is parallel to the magnetic field and to R-rotation (clockwise) when the direction of propagation is anti-parallel. Thus, if a ray of light is passed through a material and reflected back through it, the rotation doubles. </p><p>Some materials, such as <a href="/wiki/Terbium_gallium_garnet" title="Terbium gallium garnet">terbium gallium garnet</a> (TGG) have extremely high Verdet constants (≈ <span class="nowrap"><span data-sort-value="2997866000000000000♠"></span>−134 rad/(T·m)</span> for 632 nm light).<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> By placing a rod of this material in a strong magnetic field, Faraday rotation angles of over 0.78 rad (45°) can be achieved. This allows the construction of <a href="/wiki/Faraday_rotator" title="Faraday rotator">Faraday rotators</a>, which are the principal component of <a href="/wiki/Faraday_isolator" class="mw-redirect" title="Faraday isolator">Faraday isolators</a>, devices which transmit light in only one direction. The Faraday effect can, however, be observed and measured in a Terbium-doped glass with Verdet constant as low as (≈ <span class="nowrap"><span data-sort-value="2998800000000000000♠"></span>−20 rad/(T·m)</span> for 632 nm light).<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Similar isolators are constructed for microwave systems by using <a href="/wiki/Ferrite_(magnet)" title="Ferrite (magnet)">ferrite</a> rods in a <a href="/wiki/Waveguide" title="Waveguide">waveguide</a> with a surrounding magnetic field. A thorough mathematical description can be found <a rel="nofollow" class="external text" href="http://farside.ph.utexas.edu/teaching/em/lectures/node101.html">here</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=4" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Interstellar_medium">Interstellar medium</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=5" title="Edit section: Interstellar medium"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The effect is imposed on light over the course of its propagation from its origin to the <a href="/wiki/Earth" title="Earth">Earth</a>, through the <a href="/wiki/Interstellar_medium" title="Interstellar medium">interstellar medium</a>. Here, the effect is caused by free <a href="/wiki/Electrons" class="mw-redirect" title="Electrons">electrons</a> and can be characterized as a difference in the <a href="/wiki/Refractive_index" title="Refractive index">refractive index</a> seen by the two circularly polarized propagation modes. Hence, in contrast to the Faraday effect in solids or liquids, interstellar Faraday rotation (β) has a simple dependence on the wavelength of light (λ), namely: </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 \beta =\mathrm {RM} \,\lambda ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">M</mi> </mrow> <mspace width="thinmathspace" /> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =\mathrm {RM} \,\lambda ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/344b31c6e566543847e28fd6fd266320dfe83a27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.069ex; height:3.009ex;" alt="{\displaystyle \beta =\mathrm {RM} \,\lambda ^{2}}"></span></dd></dl> <p>where the overall strength of the effect is characterized by RM, the <b>rotation measure</b>. This in turn depends on the axial component of the interstellar magnetic field <i>B<sub>||</sub></i>, and the number density of electrons <i>n<sub>e</sub></i>, both of which vary along the propagation path. In <a href="/wiki/Gaussian_units" title="Gaussian units">Gaussian cgs units</a> the rotation measure is given by: </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 \mathrm {RM} ={\frac {e^{3}}{2\pi m^{2}c^{4}}}\int _{0}^{d}n_{e}(s)B_{\parallel }(s)\;\mathrm {d} s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">M</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>π</mi> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msubsup> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {RM} ={\frac {e^{3}}{2\pi m^{2}c^{4}}}\int _{0}^{d}n_{e}(s)B_{\parallel }(s)\;\mathrm {d} s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4213016ebadcb011d30bee741e39a224941d8f60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:33.796ex; height:6.343ex;" alt="{\displaystyle \mathrm {RM} ={\frac {e^{3}}{2\pi m^{2}c^{4}}}\int _{0}^{d}n_{e}(s)B_{\parallel }(s)\;\mathrm {d} s}"></span></dd></dl> <p>or in <a href="/wiki/SI" class="mw-redirect" title="SI">SI</a> units: </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 \mathrm {RM} ={\frac {e^{3}}{8\pi ^{2}\varepsilon _{0}m^{2}c^{3}}}\int _{0}^{d}n_{e}(s)B_{||}(s)\;\mathrm {d} s\approx (2.62\times 10^{-13}\,\mathrm {T} ^{-1})\times \,\int _{0}^{d}n_{e}(s)B_{\parallel }(s)\;\mathrm {d} s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">M</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow> <mn>8</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msubsup> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>s</mi> <mo>≈</mo> <mo stretchy="false">(</mo> <mn>2.62</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>13</mn> </mrow> </msup> <mspace width="thinmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>×</mo> <mspace width="thinmathspace" /> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msubsup> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {RM} ={\frac {e^{3}}{8\pi ^{2}\varepsilon _{0}m^{2}c^{3}}}\int _{0}^{d}n_{e}(s)B_{||}(s)\;\mathrm {d} s\approx (2.62\times 10^{-13}\,\mathrm {T} ^{-1})\times \,\int _{0}^{d}n_{e}(s)B_{\parallel }(s)\;\mathrm {d} s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d388c5ae5ce227cd8dfe779c4e9ab8d8d5657afc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:80.052ex; height:6.509ex;" alt="{\displaystyle \mathrm {RM} ={\frac {e^{3}}{8\pi ^{2}\varepsilon _{0}m^{2}c^{3}}}\int _{0}^{d}n_{e}(s)B_{||}(s)\;\mathrm {d} s\approx (2.62\times 10^{-13}\,\mathrm {T} ^{-1})\times \,\int _{0}^{d}n_{e}(s)B_{\parallel }(s)\;\mathrm {d} s}"></span></dd></dl> <p>where </p> <dl><dd><i>n<sub>e</sub>(s)</i> is the density of electrons at each point <i>s</i> along the path</dd> <dd><i>B<sub>‖</sub>(s)</i> is the component of the interstellar magnetic field in the direction of propagation at each point <i>s</i> along the path</dd> <dd><i>e</i> is the <a href="/wiki/Electric_charge" title="Electric charge">charge</a> of an electron;</dd> <dd><i>c</i> is the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light in vacuum</a>;</dd> <dd><i>m</i> is the <a href="/wiki/Mass" title="Mass">mass</a> of an electron;</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 \scriptstyle \epsilon _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \epsilon _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cae66efee5220d3dff43eb5314929681024450a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.499ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \epsilon _{0}}"></span> is the <a href="/wiki/Vacuum_permittivity" title="Vacuum permittivity">vacuum permittivity</a>;</dd></dl> <p>The integral is taken over the entire path from the source to the observer. </p><p>Faraday rotation is an important tool in <a href="/wiki/Astronomy" title="Astronomy">astronomy</a> for the measurement of magnetic fields, which can be estimated from rotation measures given a knowledge of the electron number density.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> In the case of <a href="/wiki/Radio_pulsar" class="mw-redirect" title="Radio pulsar">radio pulsars</a>, the <a href="/wiki/Dispersion_(optics)" title="Dispersion (optics)">dispersion</a> caused by these electrons results in a time delay between pulses received at different wavelengths, which can be measured in terms of the electron column density, or <a href="/wiki/Dispersion_measure" class="mw-redirect" title="Dispersion measure">dispersion measure</a>. A measurement of both the dispersion measure and the rotation measure therefore yields the weighted mean of the magnetic field along the line of sight. The same information can be obtained from objects other than pulsars, if the dispersion measure can be estimated based on reasonable guesses about the propagation path length and typical electron densities. In particular, Faraday rotation measurements of polarized radio signals from extragalactic radio sources occulted by the solar corona can be used to estimate both the electron density distribution and the direction and strength of the magnetic field in the coronal plasma.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ionosphere">Ionosphere</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=6" title="Edit section: Ionosphere"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Radio_wave" title="Radio wave">Radio waves</a> passing through the Earth's <a href="/wiki/Ionosphere" title="Ionosphere">ionosphere</a> are likewise subject to the Faraday effect. The ionosphere consists of a <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">plasma</a> containing free electrons which contribute to Faraday rotation according to the above equation, whereas the positive ions are relatively massive and have little influence. In conjunction with the Earth's magnetic field, rotation of the polarization of radio waves thus occurs. Since the density of electrons in the ionosphere varies greatly on a daily basis, as well as over the <a href="/wiki/Sunspot_cycle" class="mw-redirect" title="Sunspot cycle">sunspot cycle</a>, the magnitude of the effect varies. However the effect is always proportional to the square of the wavelength, so even at the UHF television frequency of 500 MHz (λ = 60 cm), there can be more than a complete rotation of the axis of polarization.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> A consequence is that although most radio transmitting antennas are either vertically or horizontally polarized, the polarization of a medium or short wave signal after <a href="/wiki/Skywave" title="Skywave">reflection by the ionosphere</a> is rather unpredictable. However the Faraday effect due to free electrons diminishes rapidly at higher frequencies (shorter wavelengths) so that at <a href="/wiki/Microwave" title="Microwave">microwave</a> frequencies, used by <a href="/wiki/Satellite_communications" class="mw-redirect" title="Satellite communications">satellite communications</a>, the transmitted polarization is maintained between the satellite and the ground. </p> <div class="mw-heading mw-heading3"><h3 id="Semiconductors">Semiconductors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=7" title="Edit section: Semiconductors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:GaAs-Faraday_rotation_spectrum.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/GaAs-Faraday_rotation_spectrum.png/280px-GaAs-Faraday_rotation_spectrum.png" decoding="async" width="280" height="197" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/GaAs-Faraday_rotation_spectrum.png/420px-GaAs-Faraday_rotation_spectrum.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/GaAs-Faraday_rotation_spectrum.png/560px-GaAs-Faraday_rotation_spectrum.png 2x" data-file-width="4062" data-file-height="2858" /></a><figcaption>GaAs-Faraday rotation spectrum</figcaption></figure> <p>Due to spin-orbit coupling, undoped GaAs single crystal exhibits much larger Faraday rotation than glass (SiO<sub>2</sub>). Considering the atomic arrangement is different along the (100) and (110) plane, one might think the Faraday rotation is polarization dependent. However, experimental work revealed an immeasurable anisotropy in the wavelength range from 880–1,600 nm. Based on the large Faraday rotation, one might be able to use GaAs to calibrate the B field of the terahertz electromagnetic wave which requires very fast response time. Around the band gap, the Faraday effect shows resonance behavior.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>More generally, (ferromagnetic) semiconductors return both <a href="/w/index.php?title=Electro-gyration&action=edit&redlink=1" class="new" title="Electro-gyration (page does not exist)">electro-gyration</a> and a Faraday response in the high frequency domain. The combination of the two is described by <a href="/w/index.php?title=Gyroelectromagnetic_media&action=edit&redlink=1" class="new" title="Gyroelectromagnetic media (page does not exist)">gyroelectromagnetic media</a>,<sup id="cite_ref-Prati2003_2-1" class="reference"><a href="#cite_note-Prati2003-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> for which gyroelectricity and gyromagnetism (Faraday effect) may occur at the same time. </p> <div class="mw-heading mw-heading3"><h3 id="Organic_materials">Organic materials</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=8" title="Edit section: Organic materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In organic materials, Faraday rotation is typically small, with a <a href="/wiki/Verdet_constant" title="Verdet constant">Verdet constant</a> in the visible wavelength region on the order of a few hundred degrees per Tesla per meter, decreasing proportional to <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 ^{-2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda ^{-2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f4054ef3203101f810209044d5c3008a80f4759" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.688ex; height:2.676ex;" alt="{\displaystyle \lambda ^{-2}}"></span> in this region.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> While the Verdet constant of organic materials does increase around electronic transitions in the molecule, the associated light absorption makes most organic materials bad candidates for applications. There are however also isolated reports of large Faraday rotation in organic liquid crystals without associated absorption.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Plasmonic_and_magnetic_materials">Plasmonic and magnetic materials</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=9" title="Edit section: Plasmonic and magnetic materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Optical_cavity_created_by_plasmonic_materials.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Optical_cavity_created_by_plasmonic_materials.png/300px-Optical_cavity_created_by_plasmonic_materials.png" decoding="async" width="300" height="78" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Optical_cavity_created_by_plasmonic_materials.png/450px-Optical_cavity_created_by_plasmonic_materials.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Optical_cavity_created_by_plasmonic_materials.png/600px-Optical_cavity_created_by_plasmonic_materials.png 2x" data-file-width="1123" data-file-height="292" /></a><figcaption></figcaption></figure> <p>In 2009 <sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> γ-Fe<sub>2</sub>O<sub>3</sub>-Au core-shell nanostructures were synthesized to integrate magnetic (γ-Fe<sub>2</sub>O<sub>3</sub>) and plasmonic (Au) properties into one composite. Faraday rotation with and without the plasmonic materials was tested and rotation enhancement under 530 nm light irradiation was observed. Researchers claim that the magnitude of the magneto-optical enhancement is governed primarily by the spectral overlap of the magneto-optical transition and the plasmon resonance. </p><p>The reported composite magnetic/plasmonic nanostructure can be visualized to be a magnetic particle embedded in a resonant optical cavity. Because of the large density of photon states in the cavity, the interaction between the electromagnetic field of the light and the electronic transitions of the magnetic material is enhanced, resulting in a larger difference between the velocities of the right- and left-hand circularized polarization, therefore enhancing Faraday rotation. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=10" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 22em;"> <ul><li><a href="/wiki/Kerr_effect" title="Kerr effect">Electro-optic Kerr effect</a></li> <li><a href="/wiki/Faraday_rotator" title="Faraday rotator">Faraday rotator</a></li> <li><a href="/wiki/Inverse_Faraday_effect" title="Inverse Faraday effect">Inverse Faraday effect</a></li> <li><a href="/wiki/Magnetic_circular_dichroism" title="Magnetic circular dichroism">Magnetic circular dichroism</a></li> <li><a href="/wiki/Magneto-optic_Kerr_effect" title="Magneto-optic Kerr effect">Magneto-optic Kerr effect</a></li> <li><a href="/wiki/Optical_rotation" title="Optical rotation">Optical rotation</a></li> <li><a href="/wiki/Polarization_spectroscopy" title="Polarization spectroscopy">Polarization spectroscopy</a></li> <li><a href="/wiki/QMR_effect" title="QMR effect">QMR effect</a> (quadratic rather than linear)</li> <li><a href="/wiki/Voigt_effect" title="Voigt effect">Voigt effect</a> (magnetic-linear birefringence)</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=11" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.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 mw-references-columns"><ol class="references"> <li id="cite_note-UrsMozooni2016-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-UrsMozooni2016_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFUrsMozooniMazalskiKustov2016" class="citation journal cs1">Urs, Necdet Onur; Mozooni, Babak; Mazalski, Piotr; Kustov, Mikhail; Hayes, Patrick; Deldar, Shayan; Quandt, Eckhard; McCord, Jeffrey (2016). <a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.4943760">"Advanced magneto-optical microscopy: Imaging from picoseconds to centimeters - imaging spin waves and temperature distributions (invited)"</a>. <i>AIP Advances</i>. <b>6</b> (5): 055605. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2016AIPA....6e5605U">2016AIPA....6e5605U</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.4943760">10.1063/1.4943760</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10044%2F1%2F34544">10044/1/34544</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2158-3226">2158-3226</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=AIP+Advances&rft.atitle=Advanced+magneto-optical+microscopy%3A+Imaging+from+picoseconds+to+centimeters+-+imaging+spin+waves+and+temperature+distributions+%28invited%29&rft.volume=6&rft.issue=5&rft.pages=055605&rft.date=2016&rft_id=info%3Ahdl%2F10044%2F1%2F34544&rft.issn=2158-3226&rft_id=info%3Adoi%2F10.1063%2F1.4943760&rft_id=info%3Abibcode%2F2016AIPA....6e5605U&rft.aulast=Urs&rft.aufirst=Necdet+Onur&rft.au=Mozooni%2C+Babak&rft.au=Mazalski%2C+Piotr&rft.au=Kustov%2C+Mikhail&rft.au=Hayes%2C+Patrick&rft.au=Deldar%2C+Shayan&rft.au=Quandt%2C+Eckhard&rft.au=McCord%2C+Jeffrey&rft_id=https%3A%2F%2Fdoi.org%2F10.1063%252F1.4943760&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFaraday+effect" class="Z3988"></span></span> </li> <li id="cite_note-Prati2003-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Prati2003_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Prati2003_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPrati2003" class="citation journal cs1">Prati, E. (2003). "Propagation in gyroelectromagnetic guiding systems". <i><a href="/wiki/Journal_of_Electromagnetic_Waves_and_Applications" title="Journal of Electromagnetic Waves and Applications">Journal of Electromagnetic Waves and Applications</a></i>. <b>17</b> (8): <span class="nowrap">1177–</span>1196. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003JEWA...17.1177P">2003JEWA...17.1177P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1163%2F156939303322519810">10.1163/156939303322519810</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121509049">121509049</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Electromagnetic+Waves+and+Applications&rft.atitle=Propagation+in+gyroelectromagnetic+guiding+systems&rft.volume=17&rft.issue=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1177-%3C%2Fspan%3E1196&rft.date=2003&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121509049%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1163%2F156939303322519810&rft_id=info%3Abibcode%2F2003JEWA...17.1177P&rft.aulast=Prati&rft.aufirst=E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFaraday+effect" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">See <a rel="nofollow" class="external free" href="https://www.rp-photonics.com/regenerative_amplifiers.html">https://www.rp-photonics.com/regenerative_amplifiers.html</a></span> </li> <li id="cite_note-horvath-thesis-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-horvath-thesis_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHorváth2003" class="citation book cs1">Horváth, Gábor (2003). <a rel="nofollow" class="external text" href="https://arago.elte.hu/?q=node/11"><i>Polarization Patterns in Nature - Imaging Polarimetry with Atmospheric Optical and Biological Applications</i></a>. Budapest: Eötvös University<span class="reference-accessdate">. Retrieved <span class="nowrap">15 June</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Polarization+Patterns+in+Nature+-+Imaging+Polarimetry+with+Atmospheric+Optical+and+Biological+Applications&rft.place=Budapest&rft.pub=E%C3%B6tv%C3%B6s+University&rft.date=2003&rft.aulast=Horv%C3%A1th&rft.aufirst=G%C3%A1bor&rft_id=https%3A%2F%2Farago.elte.hu%2F%3Fq%3Dnode%2F11&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFaraday+effect" class="Z3988"></span></span> </li> <li id="cite_note-crowther-1920-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-crowther-1920_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-crowther-1920_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCrowther1920" class="citation book cs1">Crowther, James Arnold (1920). <a rel="nofollow" class="external text" href="https://archive.org/details/lifediscoverieso00crowrich"><i>The life and discoveries of Michael Faraday</i></a>. Society for promoting Christian knowledge. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/lifediscoverieso00crowrich/page/n59">54</a>–57<span class="reference-accessdate">. Retrieved <span class="nowrap">15 June</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+life+and+discoveries+of+Michael+Faraday&rft.pages=54-57&rft.pub=Society+for+promoting+Christian+knowledge&rft.date=1920&rft.aulast=Crowther&rft.aufirst=James+Arnold&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Flifediscoverieso00crowrich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFaraday+effect" class="Z3988"></span></span> </li> <li id="cite_note-mansuripur-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-mansuripur_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMansuripur" class="citation journal cs1">Mansuripur, Masud. <a rel="nofollow" class="external text" href="http://www.mmresearch.com/articles/article3/">"The Faraday Effect"</a>. <i>Optics and Photonics News</i> (10): <span class="nowrap">32–</span>36<span class="reference-accessdate">. Retrieved <span class="nowrap">15 June</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Optics+and+Photonics+News&rft.atitle=The+Faraday+Effect&rft.issue=10&rft.pages=%3Cspan+class%3D%22nowrap%22%3E32-%3C%2Fspan%3E36&rft.aulast=Mansuripur&rft.aufirst=Masud&rft_id=http%3A%2F%2Fwww.mmresearch.com%2Farticles%2Farticle3%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFaraday+effect" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFaraday1933" class="citation book cs1 cs1-prop-long-vol"><a href="/wiki/Michael_Faraday" title="Michael Faraday">Faraday, Michael</a> (1933). <a rel="nofollow" class="external text" href="https://archive.org/details/faradaysdiarybei00fara_2"><i>Faraday's Diary</i></a>. Vol. IV, Nov. 12, 1839 - June 26, 1847 (Thomas Martin ed.). London: George Bell and Sons, Ltd. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7503-0570-9" title="Special:BookSources/978-0-7503-0570-9"><bdi>978-0-7503-0570-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Faraday%27s+Diary&rft.place=London&rft.edition=Thomas+Martin&rft.pub=George+Bell+and+Sons%2C+Ltd.&rft.date=1933&rft.isbn=978-0-7503-0570-9&rft.aulast=Faraday&rft.aufirst=Michael&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffaradaysdiarybei00fara_2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFaraday+effect" class="Z3988"></span> The diary is indexed by Faraday's original running paragraph numbers, not by page. For this discovery see #7504, 13 Sept. 1845 to #7718, 30 Sept. 1845.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKales1953" class="citation journal cs1">Kales, M. L. (1953). 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"Surface Plasmon Resonance Enhanced Magneto-optics(SuPREMO): Faraday Rotation Enhancement in Gold-Coated Iron Oxide Nanocrystals". <i>Nano Letters</i>. <b>9</b> (4): <span class="nowrap">1644–</span>1650. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009NanoL...9.1644J">2009NanoL...9.1644J</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fnl900007k">10.1021/nl900007k</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/19351194">19351194</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nano+Letters&rft.atitle=Surface+Plasmon+Resonance+Enhanced+Magneto-optics%28SuPREMO%29%3A+Faraday+Rotation+Enhancement+in+Gold-Coated+Iron+Oxide+Nanocrystals&rft.volume=9&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1644-%3C%2Fspan%3E1650&rft.date=2009&rft_id=info%3Apmid%2F19351194&rft_id=info%3Adoi%2F10.1021%2Fnl900007k&rft_id=info%3Abibcode%2F2009NanoL...9.1644J&rft.aulast=Cohen&rft.aufirst=Adam&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFaraday+effect" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Faraday_effect&action=edit&section=12" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://scienceworld.wolfram.com/physics/FaradayRotation.html">Faraday Rotation</a> <i>(at Eric W. Weisstein's World of Physics)</i></li> <li><a rel="nofollow" class="external text" href="https://home.earthlink.net/~jimlux/hv/eo.htm">Electro-optical measurements (Kerr, Pockels, and Faraday)</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060510050745/http://home.earthlink.net/~jimlux/hv/eo.htm">Archived</a> 2006-05-10 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://ned.ipac.caltech.edu/level5/Sept04/Govoni/Govoni3_5.html">Faraday Rotation Effect</a> in (radio)astronomy</li> <li>A simple <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=XhU-nNiAgtI"><span class="plainlinks">demonstration of the effect</span></a> on <a href="/wiki/YouTube_video_(identifier)" class="mw-redirect" title="YouTube video (identifier)">YouTube</a></li></ul> <div class="navbox-styles"><style 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style="width:1%">Physics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law of induction</a></li> <li><a class="mw-selflink selflink">Faraday effect</a></li> <li><a href="/wiki/Faraday_cage" title="Faraday cage">Faraday cage</a></li> <li><a href="/wiki/Faraday_constant" title="Faraday constant">Faraday constant</a></li> <li><a href="/wiki/Farad" title="Farad">Farad</a></li> <li><a href="/wiki/Faraday_cup" title="Faraday cup">Faraday cup</a></li> <li><a href="/wiki/Faraday%27s_laws_of_electrolysis" title="Faraday's laws of electrolysis">Faraday's laws of electrolysis</a></li> <li><a href="/wiki/Faraday_paradox" title="Faraday paradox">Faraday paradox</a></li> <li><a href="/wiki/Faraday_rotator" title="Faraday rotator">Faraday rotator</a></li> <li><a href="/wiki/Faraday-efficiency_effect" title="Faraday-efficiency effect">Faraday-efficiency effect</a></li> <li><a href="/wiki/Faraday_wave" title="Faraday wave">Faraday wave</a></li> <li><a href="/wiki/Faraday%27s_ice_pail_experiment" title="Faraday's ice pail experiment">Faraday's ice pail experiment</a></li> <li><a href="/wiki/Faraday_efficiency" title="Faraday efficiency">Faraday efficiency</a></li> <li><a href="/wiki/Electrochemistry" title="Electrochemistry">Electrochemistry</a></li> <li><a href="/wiki/Homopolar_generator#The_Faraday_disc" title="Homopolar generator">Faraday disc</a></li> <li><a href="/wiki/Line_of_force" title="Line of force">Line of force</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lectures</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Royal_Institution_Christmas_Lectures" title="Royal Institution Christmas Lectures">Royal Institution Christmas Lectures</a></li> <li><i><a 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href="/wiki/Royal_Society_of_London_Michael_Faraday_Prize" title="Royal Society of London Michael Faraday Prize">Royal Society of London Michael Faraday Prize</a></li> <li><a href="/wiki/Institute_of_Physics_Michael_Faraday_Medal_and_Prize" title="Institute of Physics Michael Faraday Medal and Prize">Institute of Physics Michael Faraday Medal and Prize</a></li> <li><a href="/wiki/Faraday_Medal_(electrochemistry)" title="Faraday Medal (electrochemistry)">Faraday Medal (electrochemistry)</a></li> <li><a href="/wiki/Faraday_Lectureship_Prize" title="Faraday Lectureship Prize">Faraday Lectureship Prize</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" 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