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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Kerr-Linse</span></h1>
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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><p>Die Bildung einer <b>Kerr-Linse</b> (nach <a href="John_Kerr_(Physiker)" title="John Kerr (Physiker)">John Kerr</a>) ist ein Effekt der <a href="Nichtlineare_Optik" title="Nichtlineare Optik">nichtlinearen Optik</a> und beruht auf dem <a href="Kerr-Effekt" title="Kerr-Effekt">Kerr-Effekt</a>.
</p>
<div class="mw-heading mw-heading2"><h2 id="Erklärung"><span id="Erkl.C3.A4rung"></span>Erklärung</h2></div>
<p>Hängt in einem nichtlinearen Medium der <a href="Brechungsindex" title="Brechungsindex">Brechungsindex</a> <span class="mwe-math-element mwe-math-element-inline"><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="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a601995d55609f2d9f5e233e36fbe9ea26011b3b.svg" 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}" loading="lazy"></span> linear von der <a href="Intensit%C3%A4t_(Physik)" title="Intensität (Physik)">Intensität</a> <span class="mwe-math-element mwe-math-element-inline"><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}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>I</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle I}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/535ea7fc4134a31cbe2251d9d3511374bc41be9f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}" loading="lazy"></span> des Lichtes ab, so gilt (Kerr-Effekt):
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><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(I)=n_{0}+n_{2}\cdot I}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>n</mi>
<mo stretchy="false">(</mo>
<mi>I</mi>
<mo stretchy="false">)</mo>
<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>
<mo>⋅<!-- ⋅ --></mo>
<mi>I</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle n(I)=n_{0}+n_{2}\cdot I}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d16298fa2347b33341c801e2980b5caef9d3e665.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.063ex; height:2.843ex;" alt="{\displaystyle n(I)=n_{0}+n_{2}\cdot I}" loading="lazy"></span></dd></dl>
<p>mit
</p>
<ul><li><span class="mwe-math-element mwe-math-element-inline"><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_{0}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>n</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle n_{0}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/63584d203ecb012a7bcb90f422408bbfe4018956.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{0}}" loading="lazy"></span>: Brechungsindex bei Abwesenheit von Licht</li>
<li><span class="mwe-math-element mwe-math-element-inline"><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_{2}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>n</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle n_{2}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/840e456e3058bc0be28e5cf653b170cdbfcc3be4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{2}}" loading="lazy"></span>: Kerr-Koeffizient.</li></ul>
<p>Fällt nun ein Laserstrahl hoher Intensität, dessen Strahlprofil in der Mitte am stärksten ist, auf das Medium, so ist die Phasenänderung an dieser Stelle entsprechend dem Brechungsindex am höchsten, während sie in den Randbereichen kleiner ist. Für positives <span class="mwe-math-element mwe-math-element-inline"><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_{2}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>n</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle n_{2}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/840e456e3058bc0be28e5cf653b170cdbfcc3be4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{2}}" loading="lazy"></span> führt dies zu <i>Selbstfokussierung</i>, für negatives <span class="mwe-math-element mwe-math-element-inline"><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_{2}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>n</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle n_{2}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/840e456e3058bc0be28e5cf653b170cdbfcc3be4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{2}}" loading="lazy"></span> zu <i>Selbstdefokussierung</i>.
</p>
<div class="mw-heading mw-heading2"><h2 id="Beispiel:_Gauß'scher_Strahl"><span id="Beispiel:_Gau.C3.9F.27scher_Strahl"></span>Beispiel: Gauß'scher Strahl</h2></div>
<p>Ist das Strahlprofil <a href="Gau%C3%9Fkurve" class="mw-redirect" title="Gaußkurve">gaußförmig</a>, lässt sich für das Medium eine <a href="Brennweite" title="Brennweite">Brennweite</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>f</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle f}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/132e57acb643253e7810ee9702d9581f159a1c61.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" loading="lazy"></span> angeben:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f={\frac {\pi }{8}}\cdot {\frac {w^{4}}{n_{2}\cdot d\cdot P}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>f</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>π<!-- π --></mi>
<mn>8</mn>
</mfrac>
</mrow>
<mo>⋅<!-- ⋅ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msup>
<mi>w</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msup>
<mrow>
<msub>
<mi>n</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mo>⋅<!-- ⋅ --></mo>
<mi>d</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>P</mi>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle f={\frac {\pi }{8}}\cdot {\frac {w^{4}}{n_{2}\cdot d\cdot P}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6a3552697c61c51595174c3b33f52fd72b61cd87.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.829ex; height:6.176ex;" alt="{\displaystyle f={\frac {\pi }{8}}\cdot {\frac {w^{4}}{n_{2}\cdot d\cdot P}}}" loading="lazy"></span></dd></dl>
<p>mit
</p>
<ul><li><span class="mwe-math-element mwe-math-element-inline"><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="./_assets_/eb734a37dd21ce173a46342d1cc64c92/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6.svg" 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}" loading="lazy"></span>: Strahlradius</li>
<li><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>d</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle d}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e85ff03cbe0c7341af6b982e47e9f90d235c66ab.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}" loading="lazy"></span>: Dicke des Mediums</li>
<li><span class="mwe-math-element mwe-math-element-inline"><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}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>P</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle P}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span>: <a href="Leistung_(Physik)" title="Leistung (Physik)">Leistung</a> des Lasers.</li></ul>
<div class="mw-heading mw-heading2"><h2 id="Anwendung">Anwendung</h2></div>
<p>Die Kerr-Linse im <a href="Titan-Saphir-Laser" class="mw-redirect" title="Titan-Saphir-Laser">Titan-Saphir-Laser</a> sorgt für den stabilen <a href="Ultrakurzpulslaser" title="Ultrakurzpulslaser">Ultrakurzpuls</a>-Betrieb. Mit Linsen wird das Licht im <a href="Resonator" title="Resonator">Resonator</a> gezielt so aufgeweitet, dass nur die von der Kerrlinse fokussierten ultrakurzen Pulse mit hoher Intensität verlustfrei von Endspiegel zu Endspiegel reflektiert werden. Die <a href="Continuous_wave" title="Continuous wave">cw</a>-Anteile werden dagegen aufgeweitet und erfahren dadurch höhere Verluste, weshalb sich die Pulse im Resonator durchsetzen.
</p>
<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>
<ul><li><a rel="nofollow" class="external text" href="https://www.rp-photonics.com/kerr_lens.html"><i>Kerr Lens</i></a> in der <i>Encyclopedia of Laser Physics and Technology</i> (englisch)</li></ul></div><!--htdig_noindex--><div><div class="zim-footer">
Dieser Artikel wurde von <a class="external text" title="Zuletzt bearbeitet am 2022-09-11" href="https://de.wikipedia.org/wiki/?title=Kerr-Linse&oldid=226075654">Wikipedia</a> herausgegeben. Der Text ist unter <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.de">Creative Commons Attribution-Share Alike 4.0</a> verfügbar, sofern nicht anders angegeben. Für die Mediendateien können zusätzliche Bedingungen gelten.
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