956:
2409:, which become important when the intensity becomes very high. As the intensity of the self-focused spot increases beyond a certain value, the medium is ionized by the high local optical field. This lowers the refractive index, defocusing the propagating light beam. Propagation then proceeds in a series of repeated focusing and defocusing steps.
2854:
622:
2176:
1825:
515:
1442:
183:, no light will be transmitted when the electric field is turned off, while nearly all of the light will be transmitted for some optimum value of the electric field. Higher values of the Kerr constant allow complete transmission to be achieved with a smaller applied electric field.
1972:
951:{\displaystyle P_{i}=\varepsilon _{0}\sum _{j=1}^{3}\chi _{ij}^{(1)}E_{j}+\varepsilon _{0}\sum _{j=1}^{3}\sum _{k=1}^{3}\chi _{ijk}^{(2)}E_{j}E_{k}+\varepsilon _{0}\sum _{j=1}^{3}\sum _{k=1}^{3}\sum _{l=1}^{3}\chi _{ijkl}^{(3)}E_{j}E_{k}E_{l}+\cdots }
1983:
2346:
1678:
381:
1203:
2858:
1590:
In the optical or AC Kerr effect, an intense beam of light in a medium can itself provide the modulating electric field, without the need for an external field to be applied. In this case, the electric field is given by:
1302:
1117:
For materials exhibiting a non-negligible Kerr effect, the third, χ term is significant, with the even-order terms typically dropping out due to inversion symmetry of the Kerr medium. Consider the net electric field
1447:
which is similar to the linear relationship between polarization and an electric field of a wave, with an additional non-linear susceptibility term proportional to the square of the amplitude of the external field.
1294:
73:
of the electric field instead of varying linearly with it. All materials show a Kerr effect, but certain liquids display it more strongly than others. The Kerr effect was discovered in 1875 by
Scottish physicist
1650:
1523:
1836:
2379:
The optical Kerr effect manifests itself temporally as self-phase modulation, a self-induced phase- and frequency-shift of a pulse of light as it travels through a medium. This process, along with
265:
The optical Kerr effect, or AC Kerr effect is the case in which the electric field is due to the light itself. This causes a variation in index of refraction which is proportional to the local
2405:
As the beam self-focuses, the peak intensity increases which, in turn, causes more self-focusing to occur. The beam is prevented from self-focusing indefinitely by nonlinear effects such as
154:
2390:
Spatially, an intense beam of light in a medium will produce a change in the medium's refractive index that mimics the transverse intensity pattern of the beam. For example, a
545:
311:
The magneto-optic Kerr effect (MOKE) is the phenomenon that the light reflected from a magnetized material has a slightly rotated plane of polarization. It is similar to the
2171:{\displaystyle n=(1+\chi )^{1/2}=\left(1+\chi _{\mathrm {LIN} }+\chi _{\mathrm {NL} }\right)^{1/2}\simeq n_{0}\left(1+{\frac {1}{2{n_{0}}^{2}}}\chi _{\mathrm {NL} }\right)}
81:
Two special cases of the Kerr effect are normally considered, these being the Kerr electro-optic effect, or DC Kerr effect, and the optical Kerr effect, or AC Kerr effect.
373:
351:
582:
1820:{\displaystyle \mathbf {P} \simeq \varepsilon _{0}\left(\chi ^{(1)}+{\frac {3}{4}}\chi ^{(3)}|\mathbf {E} _{\omega }|^{2}\right)\mathbf {E} _{\omega }\cos(\omega t).}
997:
2217:
1109:
1082:
1051:
1024:
2753:
602:
510:{\displaystyle \mathbf {P} =\varepsilon _{0}\chi ^{(1)}\mathbf {E} +\varepsilon _{0}\chi ^{(2)}\mathbf {EE} +\varepsilon _{0}\chi ^{(3)}\mathbf {EEE} +\cdots }
230:
light, since the Kerr effect responds very quickly to changes in electric field. Light can be modulated with these devices at frequencies as high as 10
1451:
For non-symmetric media (e.g. liquids), this induced change of susceptibility produces a change in refractive index in the direction of the electric field:
2376:) on the order of 1 GW cm (such as those produced by lasers) are necessary to produce significant variations in refractive index via the AC Kerr effect.
1135:
179:
when light is incident on it in a direction perpendicular to the electric field. If the material is placed between two "crossed" (perpendicular) linear
89:
The Kerr electro-optic effect, or DC Kerr effect, is the special case in which a slowly varying external electric field is applied by, for instance, a
297:, a technique that has potential applications for all-optical switching mechanisms, nanophotonic systems and low-dimensional photo-sensors devices.
1437:{\displaystyle \mathbf {P} \simeq \varepsilon _{0}\left(\chi ^{(1)}+3\chi ^{(3)}|\mathbf {E} _{0}|^{2}\right)\mathbf {E} _{\omega }\cos(\omega t),}
2662:
Hernández-Acosta, M A; Trejo-Valdez, M; Castro-Chacón, J H; Torres-San Miguel, C R; Martínez-Gutiérrez, H; Torres-Torres, C (23 February 2018).
1552:, rotating the plane of polarization of a wave travelling through it. In combination with polarizers, it can be used as a shutter or modulator.
2791:
2736:
1225:
2362:
is the intensity of the wave. The refractive index change is thus proportional to the intensity of the light travelling through the medium.
1597:
2807:
Dharmadhikari, A. K.; Dharmadhikari, J. A.; Mathur, D. (2008). "Visualization of focusing–refocusing cycles during filamentation in BaF
1114:
For a linear medium, only the first term of this equation is significant and the polarization varies linearly with the electric field.
2890:
1967:{\displaystyle \chi =\chi _{\mathrm {LIN} }+\chi _{\mathrm {NL} }=\chi ^{(1)}+{\frac {3\chi ^{(3)}}{4}}|\mathbf {E} _{\omega }|^{2},}
2777:
1457:
2869:
2863:
257:. The Kerr effect is still present, however, and in many cases can be detected independently of Pockels effect contributions.
246:, is poisonous. Some transparent crystals have also been used for Kerr modulation, although they have smaller Kerr constants.
2599:
Rashidian Vaziri, M R (2015). "Comment on "Nonlinear refraction measurements of materials using the moiré deflectometry"".
2915:
329:
2435:
2537:
Kerr, John (1875). "A new relation between electricity and light: Dielectrified media birefringent (Second paper)".
242:, which can operate at much lower voltages. Another disadvantage of Kerr cells is that the best available material,
2372:
are relatively small for most materials, on the order of 10 m W for typical glasses. Therefore, beam intensities (
2910:
306:
31:
175:
is the strength of the electric field. This difference in index of refraction causes the material to act like a
111:
30:
This article is about the Kerr nonlinear optical effect. For the magneto-optic phenomenon of the same name, see
294:
282:
1548:
in the medium in the direction of the field. A Kerr cell with a transverse field can thus act as a switchable
2564:
Melnichuk, Mike; Wood, Lowell T. (2010). "Direct Kerr electro-optic effect in noncentrosymmetric materials".
605:
2406:
234:. Because the Kerr effect is relatively weak, a typical Kerr cell may require voltages as high as 30
286:
278:
75:
66:
523:
293:. The optical Kerr effect has also been observed to dynamically alter the mode-coupling properties in
2820:
2696:
2608:
2573:
2510:
Kerr, John (1875). "A new relation between electricity and light: Dielectrified media birefringent".
2476:
2424:
98:
2395:
2380:
1665:
Combining this with the equation for the polarization, and taking only linear terms and those in χ|
2461:
356:
334:
2836:
2492:
554:
250:
2635:
2341:{\displaystyle n=n_{0}+{\frac {3\chi ^{(3)}}{8n_{0}}}|\mathbf {E} _{\omega }|^{2}=n_{0}+n_{2}I}
222:) exhibit very large Kerr constants. A glass cell filled with one of these liquids is called a
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parallel to or perpendicular to the applied field. The difference in index of refraction,
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2612:
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1830:
As before, this looks like a linear susceptibility with an additional non-linear term:
587:
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62:
58:
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1198:{\displaystyle \mathbf {E} =\mathbf {E} _{0}+\mathbf {E} _{\omega }\cos(\omega t),}
548:
243:
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207:
191:
94:
93:
on electrodes across the sample material. Under this influence, the sample becomes
2432:, which used a Kerr cell to take sub-millisecond photographs of nuclear explosions
1222:. For the DC Kerr effect, we can neglect all except the linear terms and those in
289:. This effect only becomes significant with very intense beams such as those from
2620:
1122:
produced by a light wave of frequency ω together with an external electric field
27:
Change in refractive index of a material in response to an applied electric field
2709:
2663:
2585:
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2523:
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1549:
1533:
266:
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180:
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2783:
235:
17:
2637:
Experimental
Observation of Non-Linear Mode Conversion in Few-Mode Fiber
2384:
1575:
1289:{\displaystyle \chi ^{(3)}|\mathbf {E} _{0}|^{2}\mathbf {E} _{\omega }}
90:
2394:
results in a
Gaussian refractive index profile, similar to that of a
1579:
315:
where the plane of polarization of the transmitted light is rotated.
269:
of the light. This refractive index variation is responsible for the
1645:{\displaystyle \mathbf {E} =\mathbf {E} _{\omega }\cos(\omega t),}
1564:
290:
2897:(Scroll down the page for several early articles on Kerr cells.)
2722:
2720:
1560:
1218:
Combining these two equations produces a complex expression for
2398:. This causes the beam to focus itself, a phenomenon known as
1582:, and the Kerr effect produces a modification of this tensor.
608:
of the medium. We can write that relationship explicitly; the
1518:{\displaystyle \Delta n=\lambda _{0}K|\mathbf {E} _{0}|^{2},}
253:, the Kerr effect is generally masked by the much stronger
238:
to achieve complete transparency. This is in contrast to
1578:, the susceptibility of the medium will in general be a
65:
in that the induced index change for the Kerr effect is
2220:
1986:
1839:
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1005:
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114:
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is the second-order nonlinear refractive index, and
2462:"John Kerr and his Effects Found in 1877 and 1878"
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1966:
1819:
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1103:
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148:
97:, with different indices of refraction for light
2685:nanostructures explored by Lorenz attractors"
8:
1559:depend on the medium and are about 9.4×10 m·
1544:for the medium. The applied field induces
2192:) is the linear refractive index. Using a
149:{\displaystyle \Delta n=\lambda KE^{2},\ }
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360:
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134:
113:
1662:is the amplitude of the wave as before.
57:of a material in response to an applied
2779:Physics of Dielectrics for the Engineer
2664:"Chaotic signatures of photoconductive
2452:
61:. The Kerr effect is distinct from the
1215:is the vector amplitude of the wave.
7:
2209:intensity dependent refractive index
2421:, an early acousto-optic modulator
2157:
2154:
2068:
2065:
2050:
2047:
2044:
1876:
1873:
1858:
1855:
1852:
1461:
1053:, i.e., the component parallel to
353:will depend on the electric field
115:
25:
2857: This article incorporates
2852:
2729:Introduction to Nonlinear Optics
2287:
1939:
1786:
1757:
1683:
1611:
1602:
1490:
1403:
1374:
1307:
1276:
1252:
1164:
1149:
1140:
540:{\displaystyle \varepsilon _{0}}
497:
494:
491:
457:
454:
420:
386:
361:
339:
163:is the wavelength of the light,
2870:General Services Administration
2752:Moreno, Michelle (2018-06-14).
226:. These are frequently used to
2888:Kerr cells in early television
2731:. Cambridge University Press.
2469:Philosophical Magazine Letters
2299:
2281:
2257:
2251:
2006:
1993:
1951:
1933:
1921:
1915:
1896:
1890:
1811:
1802:
1769:
1751:
1745:
1739:
1716:
1710:
1636:
1627:
1502:
1484:
1428:
1419:
1386:
1368:
1362:
1356:
1340:
1334:
1264:
1246:
1240:
1234:
1189:
1180:
907:
901:
781:
775:
689:
683:
569:
563:
485:
479:
448:
442:
414:
408:
328:For a nonlinear material, the
1:
2621:10.1016/j.optcom.2014.09.017
2436:Optical heterodyne detection
999:. It is often assumed that
612:th component for the vector
368:{\displaystyle \mathbf {E} }
346:{\displaystyle \mathbf {P} }
1057:of the polarization field;
604:-th order component of the
577:{\displaystyle \chi ^{(n)}}
2932:
2586:10.1103/PhysRevA.82.013821
304:
29:
2833:10.1007/s00340-008-3317-7
2551:10.1080/14786447508641319
2524:10.1080/14786447508641302
2489:10.1080/09500830802526604
307:Magneto-optic Kerr effect
301:Magneto-optic Kerr effect
85:Kerr electro-optic effect
32:magneto-optic Kerr effect
2710:10.1088/1367-2630/aaad41
2643:. San Jose. pp. 1–3
283:modulational instability
2776:Coelho, Roland (2012).
2460:Weinberger, P. (2008).
992:{\displaystyle i=1,2,3}
606:electric susceptibility
285:, and is the basis for
43:quadratic electro-optic
2865:Federal Standard 1037C
2859:public domain material
2727:New, Geoffery (2011).
2689:New Journal of Physics
2539:Philosophical Magazine
2512:Philosophical Magazine
2407:multiphoton ionization
2383:, can produce optical
2342:
2172:
1968:
1821:
1646:
1519:
1438:
1290:
1199:
1105:
1078:
1047:
1020:
993:
952:
881:
860:
839:
758:
737:
669:
598:
578:
541:
511:
369:
347:
150:
2634:Xu, Jing (May 2015).
2601:Optics Communications
2343:
2173:
1969:
1822:
1647:
1567:, and 4.4×10 m·V for
1520:
1439:
1291:
1200:
1106:
1104:{\displaystyle E_{y}}
1079:
1077:{\displaystyle E_{2}}
1048:
1046:{\displaystyle P_{x}}
1021:
1019:{\displaystyle P_{1}}
994:
953:
861:
840:
819:
738:
717:
649:
616:can be expressed as:
599:
579:
542:
512:
370:
348:
330:electric polarization
287:Kerr-lens modelocking
279:self-phase modulation
151:
67:directly proportional
53:, is a change in the
2916:Polarization (waves)
2425:Filament propagation
2218:
1984:
1837:
1679:
1598:
1458:
1303:
1226:
1136:
1088:
1061:
1030:
1003:
965:
623:
588:
555:
524:
382:
357:
335:
112:
2825:2009ApPhB..94..259D
2701:2018NJPh...20b3048H
2613:2015OptCo.357..200R
2578:2010PhRvA..82a3821M
2481:2008PMagL..88..897W
2396:gradient-index lens
911:
785:
693:
261:Optical Kerr effect
249:In media that lack
2893:2016-10-01 at the
2338:
2168:
1964:
1817:
1642:
1515:
1434:
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1074:
1043:
1016:
989:
948:
882:
759:
670:
594:
574:
537:
507:
365:
343:
251:inversion symmetry
146:
41:, also called the
2813:Applied Physics B
2793:978-0-444-60180-3
2738:978-0-521-87701-5
2430:Rapatronic camera
2278:
2146:
1930:
1732:
597:{\displaystyle n}
271:nonlinear optical
190:liquids, such as
145:
16:(Redirected from
2923:
2911:Nonlinear optics
2878:
2877:
2872:. Archived from
2856:
2855:
2845:
2844:
2804:
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2797:
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2650:
2648:
2642:
2631:
2625:
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2596:
2590:
2589:
2561:
2555:
2554:
2545:(333): 446–458.
2534:
2528:
2527:
2518:(332): 337–348.
2507:
2501:
2500:
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2284:
2279:
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2241:
2236:
2235:
2207:, this gives an
2194:Taylor expansion
2177:
2175:
2174:
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2163:
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2161:
2160:
2147:
2145:
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1371:
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1344:
1343:
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1023:
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1017:
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998:
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583:
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401:
389:
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371:
366:
364:
352:
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349:
344:
342:
155:
153:
152:
147:
143:
139:
138:
55:refractive index
21:
2931:
2930:
2926:
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2924:
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2921:
2920:
2901:
2900:
2895:Wayback Machine
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2504:
2475:(12): 897–907.
2464:
2459:
2458:
2454:
2449:
2415:
2371:
2357:
2325:
2312:
2297:
2285:
2267:
2263:
2246:
2242:
2227:
2216:
2215:
2206:
2199:
2191:
2187:
2148:
2128:
2126:
2122:
2110:
2106:
2096:
2059:
2038:
2031:
2027:
2026:
2005:
1982:
1981:
1949:
1937:
1910:
1906:
1885:
1867:
1846:
1835:
1834:
1784:
1767:
1755:
1734:
1705:
1704:
1700:
1690:
1677:
1676:
1671:
1661:
1609:
1596:
1595:
1588:
1531:
1500:
1488:
1470:
1456:
1455:
1401:
1384:
1372:
1351:
1329:
1328:
1324:
1314:
1301:
1300:
1274:
1262:
1250:
1229:
1224:
1223:
1214:
1162:
1147:
1134:
1133:
1128:
1091:
1086:
1085:
1064:
1059:
1058:
1033:
1028:
1027:
1006:
1001:
1000:
963:
962:
932:
922:
912:
809:
796:
786:
707:
694:
639:
626:
621:
620:
586:
585:
558:
553:
552:
527:
522:
521:
474:
464:
437:
427:
403:
393:
380:
379:
355:
354:
333:
332:
326:
321:
309:
303:
295:multimode fiber
263:
221:
217:
213:
205:
201:
197:
130:
110:
109:
87:
35:
28:
23:
22:
15:
12:
11:
5:
2929:
2927:
2919:
2918:
2913:
2903:
2902:
2899:
2898:
2883:
2882:External links
2880:
2876:on 2022-01-22.
2847:
2846:
2808:
2799:
2792:
2786:. p. 52.
2768:
2744:
2737:
2716:
2679:
2670:
2654:
2626:
2591:
2556:
2529:
2502:
2451:
2450:
2448:
2445:
2444:
2443:
2438:
2433:
2427:
2422:
2414:
2411:
2369:
2365:The values of
2355:
2349:
2348:
2337:
2332:
2328:
2324:
2319:
2315:
2311:
2306:
2301:
2294:
2289:
2283:
2274:
2270:
2266:
2259:
2256:
2253:
2249:
2245:
2239:
2234:
2230:
2226:
2223:
2204:
2197:
2189:
2185:
2179:
2178:
2166:
2159:
2156:
2151:
2142:
2135:
2131:
2125:
2121:
2116:
2113:
2109:
2103:
2099:
2095:
2090:
2086:
2082:
2077:
2070:
2067:
2062:
2058:
2052:
2049:
2046:
2041:
2037:
2034:
2030:
2025:
2020:
2016:
2012:
2008:
2004:
2001:
1998:
1995:
1992:
1989:
1975:
1974:
1963:
1958:
1953:
1946:
1941:
1935:
1929:
1923:
1920:
1917:
1913:
1909:
1903:
1898:
1895:
1892:
1888:
1884:
1878:
1875:
1870:
1866:
1860:
1857:
1854:
1849:
1845:
1842:
1828:
1827:
1816:
1813:
1810:
1807:
1804:
1801:
1798:
1793:
1788:
1782:
1776:
1771:
1764:
1759:
1753:
1747:
1744:
1741:
1737:
1731:
1728:
1723:
1718:
1715:
1712:
1708:
1703:
1697:
1693:
1689:
1685:
1669:
1659:
1653:
1652:
1641:
1638:
1635:
1632:
1629:
1626:
1623:
1618:
1613:
1608:
1604:
1587:
1586:AC Kerr effect
1584:
1555:The values of
1532:is the vacuum
1529:
1526:
1525:
1514:
1509:
1504:
1497:
1492:
1486:
1482:
1477:
1473:
1469:
1466:
1463:
1445:
1444:
1433:
1430:
1427:
1424:
1421:
1418:
1415:
1410:
1405:
1399:
1393:
1388:
1381:
1376:
1370:
1364:
1361:
1358:
1354:
1350:
1347:
1342:
1339:
1336:
1332:
1327:
1321:
1317:
1313:
1309:
1283:
1278:
1271:
1266:
1259:
1254:
1248:
1242:
1239:
1236:
1232:
1212:
1206:
1205:
1194:
1191:
1188:
1185:
1182:
1179:
1176:
1171:
1166:
1161:
1156:
1151:
1146:
1142:
1126:
1098:
1094:
1071:
1067:
1040:
1036:
1013:
1009:
988:
985:
982:
979:
976:
973:
970:
959:
958:
947:
944:
939:
935:
929:
925:
919:
915:
909:
906:
903:
898:
895:
892:
889:
885:
879:
874:
871:
868:
864:
858:
853:
850:
847:
843:
837:
832:
829:
826:
822:
816:
812:
808:
803:
799:
793:
789:
783:
780:
777:
772:
769:
766:
762:
756:
751:
748:
745:
741:
735:
730:
727:
724:
720:
714:
710:
706:
701:
697:
691:
688:
685:
680:
677:
673:
667:
662:
659:
656:
652:
646:
642:
638:
633:
629:
593:
571:
568:
565:
561:
547:is the vacuum
534:
530:
518:
517:
506:
503:
499:
496:
493:
487:
484:
481:
477:
471:
467:
463:
459:
456:
450:
447:
444:
440:
434:
430:
426:
422:
416:
413:
410:
406:
400:
396:
392:
388:
363:
341:
325:
324:DC Kerr effect
322:
320:
317:
313:Faraday effect
305:Main article:
302:
299:
262:
259:
255:Pockels effect
219:
215:
211:
203:
199:
195:
157:
156:
142:
137:
133:
129:
126:
123:
120:
117:
105:, is given by
86:
83:
63:Pockels effect
59:electric field
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2928:
2917:
2914:
2912:
2909:
2908:
2906:
2896:
2892:
2889:
2886:
2885:
2881:
2879:
2875:
2871:
2867:
2866:
2860:
2842:
2838:
2834:
2830:
2826:
2822:
2818:
2814:
2803:
2800:
2795:
2789:
2785:
2781:
2780:
2772:
2769:
2755:
2754:"Kerr Effect"
2748:
2745:
2740:
2734:
2730:
2723:
2721:
2717:
2711:
2706:
2702:
2698:
2695:(2): 023048.
2694:
2690:
2686:
2658:
2655:
2639:
2638:
2630:
2627:
2622:
2618:
2614:
2610:
2606:
2602:
2595:
2592:
2587:
2583:
2579:
2575:
2572:(1): 013821.
2571:
2567:
2560:
2557:
2552:
2548:
2544:
2540:
2533:
2530:
2525:
2521:
2517:
2513:
2506:
2503:
2498:
2494:
2490:
2486:
2482:
2478:
2474:
2470:
2463:
2456:
2453:
2446:
2442:
2441:Zeeman effect
2439:
2437:
2434:
2431:
2428:
2426:
2423:
2420:
2417:
2416:
2412:
2410:
2408:
2403:
2401:
2400:self-focusing
2397:
2393:
2392:Gaussian beam
2388:
2386:
2382:
2377:
2375:
2368:
2363:
2361:
2354:
2335:
2330:
2326:
2322:
2317:
2313:
2309:
2304:
2292:
2272:
2268:
2264:
2254:
2247:
2243:
2237:
2232:
2228:
2224:
2221:
2214:
2213:
2212:
2210:
2203:
2195:
2184:
2164:
2149:
2140:
2133:
2129:
2123:
2119:
2114:
2111:
2107:
2101:
2097:
2093:
2088:
2084:
2080:
2075:
2060:
2056:
2039:
2035:
2032:
2028:
2023:
2018:
2014:
2010:
2002:
1999:
1996:
1990:
1987:
1980:
1979:
1978:
1961:
1956:
1944:
1927:
1918:
1911:
1907:
1901:
1893:
1886:
1882:
1868:
1864:
1847:
1843:
1840:
1833:
1832:
1831:
1814:
1808:
1805:
1799:
1796:
1791:
1780:
1774:
1762:
1742:
1735:
1729:
1726:
1721:
1713:
1706:
1701:
1695:
1691:
1687:
1675:
1674:
1673:
1668:
1663:
1658:
1639:
1633:
1630:
1624:
1621:
1616:
1606:
1594:
1593:
1592:
1585:
1583:
1581:
1577:
1572:
1570:
1566:
1562:
1558:
1553:
1551:
1547:
1546:birefringence
1543:
1542:Kerr constant
1539:
1535:
1512:
1507:
1495:
1480:
1475:
1471:
1467:
1464:
1454:
1453:
1452:
1449:
1431:
1425:
1422:
1416:
1413:
1408:
1397:
1391:
1379:
1359:
1352:
1348:
1345:
1337:
1330:
1325:
1319:
1315:
1311:
1299:
1298:
1297:
1281:
1269:
1257:
1237:
1230:
1221:
1216:
1211:
1192:
1186:
1183:
1177:
1174:
1169:
1159:
1154:
1144:
1132:
1131:
1130:
1125:
1121:
1115:
1112:
1096:
1092:
1069:
1065:
1056:
1038:
1034:
1011:
1007:
986:
983:
980:
977:
974:
971:
968:
945:
942:
937:
933:
927:
923:
917:
913:
904:
896:
893:
890:
887:
883:
877:
872:
869:
866:
862:
856:
851:
848:
845:
841:
835:
830:
827:
824:
820:
814:
810:
806:
801:
797:
791:
787:
778:
770:
767:
764:
760:
754:
749:
746:
743:
739:
733:
728:
725:
722:
718:
712:
708:
704:
699:
695:
686:
678:
675:
671:
665:
660:
657:
654:
650:
644:
640:
636:
631:
627:
619:
618:
617:
615:
611:
607:
591:
566:
559:
550:
532:
528:
504:
501:
482:
475:
469:
465:
461:
445:
438:
432:
428:
424:
411:
404:
398:
394:
390:
378:
377:
376:
331:
323:
318:
316:
314:
308:
300:
298:
296:
292:
288:
284:
280:
276:
275:self-focusing
272:
268:
260:
258:
256:
252:
247:
245:
241:
240:Pockels cells
237:
233:
229:
225:
209:
193:
189:
184:
182:
178:
174:
170:
169:Kerr constant
166:
162:
140:
135:
131:
127:
124:
121:
118:
108:
107:
106:
104:
100:
96:
92:
84:
82:
79:
77:
72:
68:
64:
60:
56:
52:
48:
44:
40:
33:
19:
2874:the original
2864:
2850:
2816:
2812:
2802:
2778:
2771:
2760:. Retrieved
2747:
2728:
2692:
2688:
2657:
2645:. Retrieved
2636:
2629:
2604:
2600:
2594:
2569:
2566:Phys. Rev. A
2565:
2559:
2542:
2538:
2532:
2515:
2511:
2505:
2472:
2468:
2455:
2419:Jeffree cell
2404:
2389:
2378:
2366:
2364:
2359:
2352:
2350:
2208:
2201:
2182:
2180:
1976:
1829:
1666:
1664:
1656:
1654:
1589:
1573:
1569:nitrobenzene
1556:
1554:
1541:
1537:
1527:
1450:
1446:
1219:
1217:
1209:
1207:
1123:
1119:
1116:
1113:
1054:
960:
613:
609:
549:permittivity
519:
327:
310:
264:
248:
244:nitrobenzene
223:
208:nitrobenzene
192:nitrotoluene
185:
172:
168:
164:
160:
158:
102:
95:birefringent
88:
80:
70:
50:
46:
42:
38:
36:
2607:: 200–201.
2374:irradiances
2211:(IDRI) of:
1977:and since:
1111:and so on.
273:effects of
39:Kerr effect
2905:Categories
2819:(2): 259.
2762:2023-11-17
2447:References
2381:dispersion
1550:wave plate
1534:wavelength
267:irradiance
181:polarizers
2841:122865446
2497:119771088
2293:ω
2248:χ
2150:χ
2094:≃
2061:χ
2040:χ
2003:χ
1945:ω
1912:χ
1887:χ
1869:χ
1848:χ
1841:χ
1806:ω
1800:
1792:ω
1763:ω
1736:χ
1707:χ
1692:ε
1688:≃
1631:ω
1625:
1617:ω
1472:λ
1462:Δ
1423:ω
1417:
1409:ω
1353:χ
1331:χ
1316:ε
1312:≃
1282:ω
1231:χ
1184:ω
1178:
1170:ω
946:⋯
884:χ
863:∑
842:∑
821:∑
811:ε
761:χ
740:∑
719:∑
709:ε
672:χ
651:∑
641:ε
560:χ
529:ε
505:⋯
476:χ
466:ε
439:χ
429:ε
405:χ
395:ε
224:Kerr cell
177:waveplate
125:λ
116:Δ
99:polarized
76:John Kerr
18:Kerr cell
2891:Archived
2784:Elsevier
2413:See also
2385:solitons
1576:crystals
228:modulate
2821:Bibcode
2697:Bibcode
2609:Bibcode
2574:Bibcode
2477:Bibcode
2196:since χ
1540:is the
1528:where λ
584:is the
167:is the
91:voltage
69:to the
2839:
2790:
2735:
2647:24 Feb
2495:
2351:where
2181:where
1655:where
1580:tensor
1208:where
961:where
520:where
319:Theory
291:lasers
206:) and
171:, and
159:where
144:
71:square
51:effect
2861:from
2837:S2CID
2757:(PDF)
2675:ZnSnS
2641:(PDF)
2541:. 4.
2514:. 4.
2493:S2CID
2465:(PDF)
2188:=(1+χ
1565:water
188:polar
186:Some
2788:ISBN
2733:ISBN
2649:2016
1574:For
1563:for
1536:and
551:and
281:and
37:The
2829:doi
2811:".
2705:doi
2617:doi
2605:357
2582:doi
2547:doi
2520:doi
2485:doi
2190:LIN
1797:cos
1672:|:
1622:cos
1414:cos
1175:cos
232:GHz
47:QEO
2907::
2868:.
2835:.
2827:.
2817:94
2815:.
2782:.
2719:^
2703:.
2693:20
2691:.
2687:.
2666:Cu
2615:.
2603:.
2580:.
2570:82
2568:.
2543:50
2516:50
2491:.
2483:.
2473:88
2471:.
2467:.
2402:.
2387:.
2200:≪
2198:NL
1571:.
1296::
1129::
1084:∥
1026:∥
610:i-
375::
277:,
236:kV
218:NO
210:(C
202:NO
194:(C
103:Δn
78:.
49:)
2843:.
2831::
2823::
2809:2
2796:.
2765:.
2741:.
2713:.
2707::
2699::
2680:4
2671:2
2651:.
2623:.
2619::
2611::
2588:.
2584::
2576::
2553:.
2549::
2526:.
2522::
2499:.
2487::
2479::
2370:2
2367:n
2360:I
2356:2
2353:n
2336:I
2331:2
2327:n
2323:+
2318:0
2314:n
2310:=
2305:2
2300:|
2288:E
2282:|
2273:0
2269:n
2265:8
2258:)
2255:3
2252:(
2244:3
2238:+
2233:0
2229:n
2225:=
2222:n
2205:0
2202:n
2186:0
2183:n
2165:)
2158:L
2155:N
2141:2
2134:0
2130:n
2124:2
2120:1
2115:+
2112:1
2108:(
2102:0
2098:n
2089:2
2085:/
2081:1
2076:)
2069:L
2066:N
2057:+
2051:N
2048:I
2045:L
2036:+
2033:1
2029:(
2024:=
2019:2
2015:/
2011:1
2007:)
2000:+
1997:1
1994:(
1991:=
1988:n
1962:,
1957:2
1952:|
1940:E
1934:|
1928:4
1922:)
1919:3
1916:(
1908:3
1902:+
1897:)
1894:1
1891:(
1883:=
1877:L
1874:N
1865:+
1859:N
1856:I
1853:L
1844:=
1815:.
1812:)
1809:t
1803:(
1787:E
1781:)
1775:2
1770:|
1758:E
1752:|
1746:)
1743:3
1740:(
1730:4
1727:3
1722:+
1717:)
1714:1
1711:(
1702:(
1696:0
1684:P
1670:ω
1667:E
1660:ω
1657:E
1640:,
1637:)
1634:t
1628:(
1612:E
1607:=
1603:E
1561:V
1557:K
1538:K
1530:0
1513:,
1508:2
1503:|
1496:0
1491:E
1485:|
1481:K
1476:0
1468:=
1465:n
1432:,
1429:)
1426:t
1420:(
1404:E
1398:)
1392:2
1387:|
1380:0
1375:E
1369:|
1363:)
1360:3
1357:(
1349:3
1346:+
1341:)
1338:1
1335:(
1326:(
1320:0
1308:P
1277:E
1270:2
1265:|
1258:0
1253:E
1247:|
1241:)
1238:3
1235:(
1220:P
1213:ω
1210:E
1193:,
1190:)
1187:t
1181:(
1165:E
1160:+
1155:0
1150:E
1145:=
1141:E
1127:0
1124:E
1120:E
1097:y
1093:E
1070:2
1066:E
1055:x
1039:x
1035:P
1012:1
1008:P
987:3
984:,
981:2
978:,
975:1
972:=
969:i
943:+
938:l
934:E
928:k
924:E
918:j
914:E
908:)
905:3
902:(
897:l
894:k
891:j
888:i
878:3
873:1
870:=
867:l
857:3
852:1
849:=
846:k
836:3
831:1
828:=
825:j
815:0
807:+
802:k
798:E
792:j
788:E
782:)
779:2
776:(
771:k
768:j
765:i
755:3
750:1
747:=
744:k
734:3
729:1
726:=
723:j
713:0
705:+
700:j
696:E
690:)
687:1
684:(
679:j
676:i
666:3
661:1
658:=
655:j
645:0
637:=
632:i
628:P
614:P
592:n
570:)
567:n
564:(
533:0
502:+
498:E
495:E
492:E
486:)
483:3
480:(
470:0
462:+
458:E
455:E
449:)
446:2
443:(
433:0
425:+
421:E
415:)
412:1
409:(
399:0
391:=
387:P
362:E
340:P
220:2
216:5
214:H
212:6
204:2
200:7
198:H
196:7
173:E
165:K
161:λ
141:,
136:2
132:E
128:K
122:=
119:n
45:(
34:.
20:)
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