Magneto-optic effect

A magneto-optic 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 medium, which is also called gyrotropic or gyromagnetic, 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 Faraday effect: the plane of polarization can be rotated, forming a Faraday rotator.

In general, magneto-optic 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).

Two gyrotropic materials with reversed rotation directions of the two principal polarizations, corresponding to complex-conjugate ε tensors for lossless media, are called optical isomers.

The ε becomes anisotropic, a 3×3 matrix, with complex off-diagonal components, depending on the frequency ω of incident light.

The resulting principal axes become complex as well, corresponding to elliptically-polarized light where left- and right-rotating polarizations can travel at different speeds (analogous to birefringence).

is a real pseudovector called the gyration vector, whose magnitude is generally small compared to the eigenvalues of

is the magneto-optical 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 magneto-optical parametric generation (somewhat analogous to a Pockels effect whose strength is controlled by the applied magnetic field).

In this case the solutions are elliptically polarized electromagnetic waves with phase velocities

For light propagating purely perpendicular to the axis of gyration, the properties are known as the Cotton-Mouton effect and used for a Circulator.

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 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:

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.

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[1]

This article incorporates public domain material from Federal Standard 1037C.