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<title>Electro–optic effect</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Electro–optic effect</span></span>

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<p>An <b>electro–optic effect</b> is a change in the optical properties of a material in response to an <a href="Electric_field" title="Electric field">electric field</a> that varies slowly compared with the frequency of light. The term encompasses a number of distinct phenomena, which can be subdivided into

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<ul><li>a) change of the <a href="Absorption_(optics)" class="mw-redirect" title="Absorption (optics)">absorption</a>

<ul><li>Electroabsorption: general change of the absorption constants</li>

<li><a href="Franz%E2%80%93Keldysh_effect" title="Franz–Keldysh effect">Franz–Keldysh effect</a>: change in the absorption shown in some bulk semiconductors</li>

<li><a href="Quantum-confined_Stark_effect" title="Quantum-confined Stark effect">Quantum-confined Stark effect</a>: change in the absorption in some semiconductor <a href="Quantum_well" title="Quantum well">quantum wells</a></li>

<li><a href="Electrochromism" title="Electrochromism">Electrochromic effect</a>: creation of an absorption band at some wavelengths, which gives rise to a change in colour</li></ul></li>

<li>b) change of the <a href="Refractive_index" title="Refractive index">refractive index</a> and <a href="Permittivity" title="Permittivity">permittivity</a>

<ul><li><a href="Pockels_effect" title="Pockels effect">Pockels effect</a> (or linear electro-optic effect): change in the refractive index linearly proportional to the electric field. Only certain crystalline solids show the <a href="Pockels_effect" title="Pockels effect">Pockels effect</a>, as it requires lack of inversion symmetry</li>

<li><a href="Kerr_effect" title="Kerr effect">Kerr effect</a> (or quadratic electro-optic effect, QEO effect): change in the refractive index proportional to the square of the electric field. All materials display the Kerr effect, with varying magnitudes, but it is generally much weaker than the <a href="Pockels_effect" title="Pockels effect">Pockels effect</a></li>

<li>electro-gyration: change in the <a href="Optical_activity" class="mw-redirect" title="Optical activity">optical activity</a>.</li>

<li><a href="Electron-refractive_effect" title="Electron-refractive effect">Electron-refractive effect</a> or EIPM</li></ul></li></ul>

<p>In December 2015, two further electro-optic effects of type (b) were theoretically predicted to exist <sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> but have not, as yet, been experimentally observed.

</p><p>Changes in absorption can have a strong effect on refractive index for wavelengths near the absorption edge, due to the <a href="Kramers%E2%80%93Kronig_relation" class="mw-redirect" title="Kramers–Kronig relation">Kramers–Kronig relation</a>.

</p><p>Using a less strict definition of the electro-optic effect allowing also electric fields oscillating at optical frequencies, one could also include nonlinear absorption (absorption depends on the light intensity) to category a) and the <a href="Optical_Kerr_effect" class="mw-redirect" title="Optical Kerr effect">optical Kerr effect</a> (refractive index depends on the light intensity) to category b). Combined with the <a href="Photoeffect" class="mw-redirect" title="Photoeffect">photoeffect</a> and <a href="Photoconductivity" title="Photoconductivity">photoconductivity</a>, the electro-optic effect gives rise to the <a href="Photorefractive_effect" title="Photorefractive effect">photorefractive effect</a>.

</p><p>The term <i>"electro-optic"</i> is often erroneously used as a synonym for <i>"<a href="Optoelectronic" class="mw-redirect" title="Optoelectronic">optoelectronic</a>"</i>.

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<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Electro-optic_modulators">Electro-optic modulators</h3></div>

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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Electro-optic_modulator" title="Electro-optic modulator">Electro-optic modulator</a></div>

<p>Electro-optic <a href="Modulator" class="mw-redirect" title="Modulator">modulators</a> are usually built with electro-optic crystals exhibiting the <a href="Pockels_effect" title="Pockels effect">Pockels effect</a>. The transmitted beam is <a href="Phase_modulation" title="Phase modulation">phase modulated</a> with the electric signal applied to the crystal. <a href="Amplitude_modulator" class="mw-redirect" title="Amplitude modulator">Amplitude modulators</a> can be built by putting the electro-optic crystal between two linear <a href="Polarizer" title="Polarizer">polarizers</a> or in one path of a <a href="Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder interferometer</a>.

Additionally, <a href="Amplitude_modulator" class="mw-redirect" title="Amplitude modulator">Amplitude modulators</a> can be constructed by deflecting the beam into and out of a small aperture such as a fiber. This design can be low loss (<3 dB) and polarization independent depending on the crystal configuration.

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<div class="mw-heading mw-heading3"><h3 id="Electro-optic_deflectors">Electro-optic deflectors</h3></div>

<p>Electro-optic deflectors utilize <a href="Prism_(optics)" title="Prism (optics)">prisms</a> of electro-optic crystals. The index of refraction is changed by the <a href="Pockels_effect" title="Pockels effect">Pockels effect</a>, thus changing the direction of propagation of the beam inside the prism. Electro-optic deflectors have only a small number of resolvable spots, but possess a fast response time. There are few commercial models available at this time. This is because of competing <a href="Acousto-optic_effect" class="mw-redirect" title="Acousto-optic effect">acousto-optic</a> deflectors, the small number of resolvable spots and the relatively high price of electro-optic crystals.

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<div class="mw-heading mw-heading3"><h3 id="Electro-optic_field_sensors">Electro-optic field sensors</h3></div>

<p>The electro-optic <a href="Pockels_effect" title="Pockels effect">Pockels effect</a> in nonlinear crystals (e.g. KDP, BSO, K*DP) can be used for electric field sensing via polarisation state modulation techniques. In this scenario, an unknown electric field results in polarisation rotation of a laser beam propagating through the electro-optic crystal; through inclusion of polarisers to modulate the light intensity incident on a photodiode, a time-resolved electric field measurement can be reconstructed from the obtained voltage trace. As the signals obtained from the crystalline probes are optical, they are inherently resistant to electrical noise pickup, hence can be used for low-noise field measurement even in areas with high levels of electromagnetic noise in the vicinity of the probe. Furthermore, as the polarisation rotation due to the <a href="Pockels_effect" title="Pockels effect">Pockels effect</a> scales linearly with electric field, <i>absolute</i> field measurements are obtained, with no need for numerical integration to reconstruct electric fields, as is the case with conventional probes sensitive to the time-derivative of the electric field.

</p><p>Electro-optic measurements of strong electromagnetic pulses from intense laser-matter interactions have been demonstrated in both the nanosecond and picosecond (sub-petawatt) laser pulse driver regimes. <sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><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>

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<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFCastles2015" class="citation journal cs1">Castles, F. (2015-12-03). "Linear electro-optic effects due to high-order spatial dispersion". <i>Physical Review A</i>. <b>92</b> (6) 063804. American Physical Society (APS). <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1503.04103">1503.04103</a></span>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2015PhRvA..92f3804C">2015PhRvA..92f3804C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysreva.92.063804">10.1103/physreva.92.063804</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1050-2947">1050-2947</a>.</cite></span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFConsoliDe_AngelisDuvillaretAndreoli2016" class="citation journal cs1">Consoli, F.; De Angelis, R.; Duvillaret, L.; Andreoli, P. L.; Cipriani, M.; Cristofari, G.; Di Giorgio, G.; Ingenito, F.; Verona, C. (15 June 2016). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4908660">"Time-resolved absolute measurements by electro-optic effect of giant electromagnetic pulses due to laser-plasma interaction in nanosecond regime"</a>. <i>Scientific Reports</i>. <b>6</b> (1): 27889. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2016NatSR...627889C">2016NatSR...627889C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fsrep27889">10.1038/srep27889</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4908660">4908660</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/27301704">27301704</a>.</cite></span>

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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFRobinsonConsoliGiltrapEardley2017" class="citation journal cs1">Robinson, T. S.; Consoli, F.; Giltrap, S.; Eardley, S. J.; Hicks, G. S.; Ditter, E. J.; Ettlinger, O.; Stuart, N. H.; Notley, M.; De Angelis, R.; Najmudin, Z.; Smith, R. A. (20 April 2017). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5430545">"Low-noise time-resolved optical sensing of electromagnetic pulses from petawatt laser-matter interactions"</a>. <i>Scientific Reports</i>. <b>7</b> (1): 983. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017NatSR...7..983R">2017NatSR...7..983R</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41598-017-01063-1">10.1038/s41598-017-01063-1</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5430545">5430545</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/28428549">28428549</a>.</cite></span>

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</style><span class="citation FS1037C MS188"><span class="noviewer" typeof="mw:File"><span></span></span> This article incorporates <a href="Copyright_status_of_works_by_the_federal_government_of_the_United_States" title="Copyright status of works by the federal government of the United States">public domain material</a> from <cite class="citation cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20220122224547/https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm"><i>Federal Standard 1037C</i></a>. <a href="General_Services_Administration" title="General Services Administration">General Services Administration</a>. Archived from <a rel="nofollow" class="external text" href="https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm">the original</a> on 2022-01-22.</cite> (in support of <a href="MIL-STD-188" title="MIL-STD-188">MIL-STD-188</a>).</span>

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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="http://www.advr-inc.com/research.html">AdvR - Electro-optic Devices & Research</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150507023623/http://www.advr-inc.com/research.html">Archived</a> 2015-05-07 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul>

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