 Magnetooptic effect

A magnetooptic effect is any one of a number of phenomena in which an electromagnetic wave propagates through a medium that has been altered by the presence of a quasistatic magnetic field. In such a material, which is also called gyrotropic or gyromagnetic, left and rightrotating elliptical polarizations can propagate at different speeds, leading to a number of important phenomena. When light is transmitted through a layer of magnetooptic material, the result is called the Faraday effect: the plane of polarization can be rotated, forming a Faraday rotator. The results of reflection from a magnetooptic material are known as the magnetooptic Kerr effect (not to be confused with the nonlinear Kerr effect).
In general, magnetooptic effects break time reversal symmetry locally (i.e. when only the propagation of light, and not the source of the magnetic field, is considered) as well as Lorentz reciprocity, which is a necessary condition to construct devices such as optical isolators (through which light passes in one direction but not the other). (The other, less useful, way to break time reversal symmetry is to rely upon absorption loss.)
Two gyrotropic materials with reversed rotation directions of the two principal polarizations, corresponding to complexconjugate ε tensors for lossless media, are called optical isomers.
Contents
Gyrotropic permittivity
In particular, in a magnetooptic material the presence of a magnetic field (either externally applied or because the material itself is ferromagnetic) can cause a change in the permittivity tensor ε of the material. The ε becomes anisotropic, a 3×3 matrix, with complex offdiagonal components, depending of course on the frequency ω of incident light. If the absorption losses can be neglected, ε is a Hermitian matrix. The resulting principal axes become complex as well, corresponding to ellipticallypolarized light where left and rightrotating polarizations can travel at different speeds (analogous to birefringence).
More specifically, for the case where absorption losses can be neglected, the most general form of Hermitian ε is:
or equivalently the relationship between the displacement field D and the electric field E is:
where ε' is a real symmetric matrix and is a real pseudovector called the gyration vector, whose magnitude is generally small compared to the eigenvalues of ε'. The direction of g is called the axis of gyration of the material. To first order, g is proportional to the applied magnetic field:
where is the magnetooptical susceptibility (a scalar in isotropic media, but more generally a tensor). If this susceptibility itself depends upon the electric field, one can obtain a nonlinear optical effect of magnetooptical parametric generation (somewhat analogous to a Pockels effect whose strength is controlled by the applied magnetic field).
The simplest case to analyze is the one in which g is a principal axis (eigenvector) of ε', and the other two eigenvalues of ε' are identical. Then, if we let g lie in the z direction for simplicity, the ε tensor simplifies to the form:
Most commonly, one considers light propagating in the z direction (parallel to g). In this case the solutions are elliptically polarized electromagnetic waves with phase velocities (where μ is the magnetic permeability). This difference in phase velocities leads to the Faraday effect.
For light propagating purely perpendicular to the axis of gyration, the properties are known as the CottonMouton effect and used for a Circulator.
Kerr Rotation and Kerr Ellipticity
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 angle of transmitted light, and Kerr Ellipticity is the ratio of the major to minor axis of the ellipse traced out by elliptically polarized light on the plane through which it propagates. Changes in the orientation of polarized incident light can be quantified using these two properties.
According to classical physics, the speed of light varies with the permittivity of a material:
where v_{p} is the velocity of light through the material, is the material permittivity, and μ is the material permeability. Because the permittivity is anisotropic, polarized light of different orientations will travel at different speeds.
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 fall out of the 90 degree phase difference (required for circular polarization) changing the Kerr Ellipticity.
A change in Kerr Rotation is most easily recognized in linearly polarized light, which can be separated into two Circularly polarized components: LeftHanded Circular Polarized (LCP) light and RightHanded Circular Polarized (RCP) light. The anisotropy of the Magneto Optic material permittivity causes a difference in the speed of LCP and RCP light, which will cause a change in the angle of polarized light. Materials that exhibit this property are known as Birefringent
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 .
See also
References
 Federal Standard 1037C and from MILSTD188
 L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (AddisonWesley: Reading, MA, 1960). §82.
 J. D. Jackson, Classical Electrodynamics (3rd. ed) (Wiley: New York, 1998). §6.10.
 F. Jonsson and C. Flytzanis, "Optical parametric generation and phase matching in magnetooptic media," Optics Letters 24 (21), 15141516 (1999).
 P. S. Pershan, "Magnetooptical effects," J. Applied Physics 38 (3), 1482–1490 (1967). (Review article.)
 Marvin J. Freiser, "A survey of magnetooptic effects," IEEE Transactions on Magnetics MAG4 (2), 152–161 (1968). (Review article.)
This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".
Categories: Optical phenomena
 Electric and magnetic fields in matter
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