1152:
486:
192:
33:
1577:
1043:
1143:
Kerr rotation and Kerr ellipticity are changes in the polarization of incident light which comes in contact with a gyromagnetic material. Kerr rotation is a rotation in the plane of polarization of transmitted light, and Kerr ellipticity is the ratio of the major to minor axis of the ellipse traced
1278:
This can be better understood if we consider a wave of light that is circularly polarized (seen to the right). If this wave interacts with a material at which the horizontal component (green sinusoid) travels at a different speed than the vertical component (blue sinusoid), the two components will
481:{\displaystyle \varepsilon ={\begin{pmatrix}\varepsilon _{xx}'&\varepsilon _{xy}'+ig_{z}&\varepsilon _{xz}'-ig_{y}\\\varepsilon _{xy}'-ig_{z}&\varepsilon _{yy}'&\varepsilon _{yz}'+ig_{x}\\\varepsilon _{xz}'+ig_{y}&\varepsilon _{yz}'-ig_{x}&\varepsilon _{zz}'\\\end{pmatrix}}}
1286:
components: Left-handed circular polarized (LHCP) light and right-handed circular polarized (RHCP) light. The anisotropy of the magneto-optic material permittivity causes a difference in the speed of LHCP and RHCP light, which will cause a change in the angle of polarized light. Materials that
574:
915:
106:, left- and right-rotating elliptical polarizations can propagate at different speeds, leading to a number of important phenomena. When light is transmitted through a layer of magneto-optic material, the result is called the
1581:
781:
1118:
1204:
673:
1294:
From this rotation, we can calculate the difference in orthogonal velocity components, find the anisotropic permittivity, find the gyration vector, and calculate the applied magnetic field
511:
899:
874:
706:
602:
818:
1314:
147:
Two gyrotropic materials with reversed rotation directions of the two principal polarizations, corresponding to complex-conjugate ε tensors for lossless media, are called
1253:
1618:
1233:
1273:
1038:{\displaystyle \varepsilon ={\begin{pmatrix}\varepsilon _{1}&+ig_{z}&0\\-ig_{z}&\varepsilon _{1}&0\\0&0&\varepsilon _{2}\\\end{pmatrix}}}
1151:
179:
become complex as well, corresponding to elliptically-polarized light where left- and right-rotating polarizations can travel at different speeds (analogous to
1148:
polarized light on the plane through which it propagates. Changes in the orientation of polarized incident light can be quantified using these two properties.
1275:
is the material permeability. Because the permittivity is anisotropic, polarized light of different orientations will travel at different speeds.
730:
159:
In particular, in a magneto-optic material the presence of a magnetic field (either externally applied or because the material itself is
1464:
1474:
Jonsson, Fredrik; Flytzanis, Christos (1 November 1999). "Optical parametric generation and phase matching in magneto-optic media".
1438:
73:
1062:
1592:
1586:
1164:
1623:
171:
off-diagonal components, depending on the frequency ω of incident light. If the absorption losses can be neglected, ε is a
1568:
837:
611:
492:
136:
locally (i.e. when only the propagation of light, and not the source of the magnetic field, is considered) as well as
51:
821:
1613:
186:
More specifically, for the case where absorption losses can be neglected, the most general form of
Hermitian ε is:
1372:"Magneto-conductivity and magnetically-controlled nonlinear optical transmittance in multi-wall carbon nanotubes"
1335:
1282:
A change in Kerr rotation is most easily recognized in linearly polarized light, which can be separated into two
119:
55:
569:{\displaystyle \mathbf {D} =\varepsilon \mathbf {E} =\varepsilon '\mathbf {E} +i\mathbf {E} \times \mathbf {g} }
1279:
fall out of the 90 degree phase difference (required for circular polarization) changing the Kerr ellipticity.
1145:
1417:
133:
43:
1283:
1121:
1549:
1520:
1483:
1383:
1350:
1128:
111:
91:
1127:
For light propagating purely perpendicular to the axis of gyration, the properties are known as the
1371:
879:
854:
789:
686:
582:
137:
1297:
1238:
1159:
According to classical physics, the speed of light varies with the permittivity of a material:
1499:
1460:
1434:
1401:
1557:
1528:
1491:
1391:
833:
825:
605:
172:
141:
123:
1211:
1258:
115:
1553:
1524:
1487:
1387:
1340:
1057:
841:
721:
499:
168:
160:
148:
107:
95:
1607:
1325:
1288:
1056:). In this case the solutions are elliptically polarized electromagnetic waves with
180:
832:). If this susceptibility itself depends upon the electric field, one can obtain a
1596:
1345:
676:
176:
164:
94:
propagates through a medium that has been altered by the presence of a quasistatic
1428:
1421:
126:
1561:
1330:
1132:
17:
118:. The results of reflection from a magneto-optic material are known as the
1503:
1405:
1495:
1396:
167:
tensor ε of the material. The ε becomes anisotropic, a 3×3 matrix, with
1532:
1124:). This difference in phase velocities leads to the Faraday effect.
829:
776:{\displaystyle \mathbf {g} =\varepsilon _{0}\chi ^{(m)}\mathbf {H} }
683:, whose magnitude is generally small compared to the eigenvalues of
1150:
144:(through which light passes in one direction but not the other).
1540:
Freiser, M. (1 June 1968). "A survey of magnetooptic effects".
1427:
Lev Davídovich Landau; Evgeniĭ Mikhaĭlovich
Lifshit︠s︡ (1960).
909:
direction for simplicity, the ε tensor simplifies to the form:
140:, which is a necessary condition to construct devices such as
26:
844:
whose strength is controlled by the applied magnetic field).
1511:
Pershan, P. S. (1 January 1967). "Magneto-Optical
Effects".
1113:{\displaystyle 1/{\sqrt {\mu (\varepsilon _{1}\pm g_{z})}}}
1199:{\displaystyle v_{p}={\frac {1}{\sqrt {\epsilon \mu }}}}
1048:
Most commonly, one considers light propagating in the
930:
207:
1300:
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1241:
1214:
1167:
1065:
918:
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792:
733:
689:
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514:
195:
1308:
1267:
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1112:
1037:
893:
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812:
775:
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667:
596:
568:
480:
847:The simplest case to analyze is the one in which
809:
1459:(3rd ed.). New York: Wiley. pp. 6–10.
668:{\displaystyle \mathbf {g} =(g_{x},g_{y},g_{z})}
90:is any one of a number of phenomena in which an
1235:is the velocity of light through the material,
491:or equivalently the relationship between the
8:
54:. There might be a discussion about this on
98:. In such a medium, which is also called
1395:
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1219:
1213:
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1172:
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1099:
1086:
1074:
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1021:
992:
980:
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917:
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856:
828:in isotropic media, but more generally a
797:
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74:Learn how and when to remove this message
132:In general, magneto-optic effects break
1569:Broad band magneto-optical spectroscopy
1362:
1619:Electric and magnetic fields in matter
851:is a principal axis (eigenvector) of
838:magneto-optical parametric generation
7:
1430:Electrodynamics of continuous media
1287:exhibit this property are known as
876:, and the other two eigenvalues of
1255:is the material permittivity, and
1139:Kerr rotation and Kerr ellipticity
716:of the material. To first order,
25:
1580: This article incorporates
1575:
1302:
901:are identical. Then, if we let
769:
735:
616:
562:
554:
543:
527:
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31:
1593:General Services Administration
720:is proportional to the applied
1542:IEEE Transactions on Magnetics
1433:. Pergamon Press. p. 82.
1105:
1079:
822:magneto-optical susceptibility
804:
798:
763:
757:
662:
623:
1:
1370:Garcia-Merino, J. A. (2016).
894:{\displaystyle \varepsilon '}
869:{\displaystyle \varepsilon '}
813:{\displaystyle \chi ^{(m)}\!}
701:{\displaystyle \varepsilon '}
597:{\displaystyle \varepsilon '}
122:(not to be confused with the
1455:Jackson, John David (1998).
1309:{\displaystyle \mathbf {H} }
163:) can cause a change in the
1640:
1513:Journal of Applied Physics
114:can be rotated, forming a
1562:10.1109/TMAG.1968.1066210
1457:Classical electrodynamics
1336:Magneto-optic Kerr effect
1248:{\displaystyle \epsilon }
840:(somewhat analogous to a
120:magneto-optic Kerr effect
1155:Circular Polarized Light
1052:direction (parallel to
155:Gyrotropic permittivity
1588:Federal Standard 1037C
1582:public domain material
1418:Federal Standard 1037C
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134:time reversal symmetry
1624:Magneto-optic effects
1311:
1270:
1250:
1230:
1228:{\displaystyle v_{p}}
1201:
1154:
1122:magnetic permeability
1115:
1040:
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871:
815:
778:
703:
670:
599:
571:
483:
1496:10.1364/OL.24.001514
1397:10.1364/OE.24.019552
1351:Photoelectric effect
1298:
1284:circularly polarized
1268:{\displaystyle \mu }
1259:
1239:
1212:
1165:
1129:Cotton-Mouton effect
1063:
916:
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790:
731:
687:
612:
583:
512:
193:
92:electromagnetic wave
88:magneto-optic effect
44:confusing or unclear
1554:1968ITM.....4..152F
1525:1967JAP....38.1482P
1488:1999OptL...24.1514J
1388:2016OExpr..2419552G
1382:(17): 19552–19557.
708:. The direction of
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365:
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138:Lorentz reciprocity
52:clarify the article
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493:displacement field
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1614:Optical phenomena
1533:10.1063/1.1709678
1482:(21): 1514–1516.
1194:
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1108:
834:nonlinear optical
175:. The resulting
142:optical isolators
84:
83:
76:
16:(Redirected from
1631:
1601:
1600:
1595:. Archived from
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1519:(3): 1482–1490.
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1234:
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1120:(where μ is the
1119:
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1058:phase velocities
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714:axis of gyration
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606:symmetric matrix
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173:Hermitian matrix
79:
72:
68:
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59:
35:
34:
27:
21:
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1322:
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1257:
1256:
1237:
1236:
1215:
1210:
1209:
1168:
1163:
1162:
1141:
1131:and used for a
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852:
793:
788:
787:
752:
742:
729:
728:
690:
685:
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681:gyration vector
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639:
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586:
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471:
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348:
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149:optical isomers
116:Faraday rotator
110:: the plane of
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36:
32:
23:
22:
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12:
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1605:
1599:on 2022-01-22.
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1548:(2): 152–161.
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1476:Optics Letters
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1376:Optics Express
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1341:Faraday effect
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842:Pockels effect
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722:magnetic field
712:is called the
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96:magnetic field
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56:the talk page
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40:This article
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19:
18:Magneto-optic
1597:the original
1587:
1573:
1545:
1541:
1516:
1512:
1479:
1475:
1456:
1444:. Retrieved
1429:
1379:
1375:
1365:
1346:Voigt Effect
1293:
1289:birefringent
1281:
1277:
1207:
1161:
1158:
1146:elliptically
1142:
1126:
1053:
1049:
1047:
906:
902:
848:
846:
785:
717:
713:
709:
680:
677:pseudovector
578:
502:
495:
490:
185:
165:permittivity
158:
146:
131:
112:polarization
104:gyromagnetic
103:
99:
87:
85:
70:
61:
50:Please help
41:
1422:MIL-STD-188
905:lie in the
679:called the
127:Kerr effect
1608:Categories
1357:References
1331:QMR effect
1133:Circulator
836:effect of
675:is a real
604:is a real
100:gyrotropic
46:to readers
1420:and from
1263:μ
1243:ϵ
1191:μ
1188:ϵ
1093:±
1084:ε
1077:μ
1019:ε
990:ε
971:−
935:ε
920:ε
885:ε
860:ε
795:χ
754:χ
744:ε
692:ε
588:ε
559:×
536:ε
524:ε
456:ε
437:−
422:ε
388:ε
352:ε
334:ε
315:−
300:ε
279:−
264:ε
230:ε
212:ε
197:ε
124:nonlinear
64:July 2010
1504:18079850
1406:27557232
1320:See also
888:′
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591:′
539:′
498:and the
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241:′
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1550:Bibcode
1521:Bibcode
1484:Bibcode
1384:Bibcode
1144:out by
820:is the
169:complex
42:may be
1502:
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1446:3 June
1437:
1404:
1208:where
830:tensor
826:scalar
786:where
579:where
1584:from
1500:PMID
1461:ISBN
1448:2012
1435:ISBN
1402:PMID
608:and
505:is:
1558:doi
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555:E
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528:E
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503:E
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