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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 A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
. 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 Polarization or polarisation may refer to: Mathematics *Polarization of an Abelian variety, in the mathematics of complex manifolds *Polarization of an algebraic form, a technique for expressing a homogeneous polynomial in a simpler fashion by ...
can be rotated, forming a Faraday rotator. The results of reflection from a magneto-optic material are known as the magneto-optic Kerr effect (not to be confused with the nonlinear
Kerr effect The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index chang ...
). In general, magneto-optic effects break
time reversal symmetry T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal, : T: t \mapsto -t. Since the second law of thermodynamics states that entropy increases as time flows toward the future ...
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.


Gyrotropic permittivity

In particular, in a magneto-optic material the presence of a magnetic field (either externally applied or because the material itself is
ferromagnetic Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
) can cause a change in the permittivity tensor ε of the material. The ε becomes anisotropic, a 3×3 matrix, with complex off-diagonal 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 elliptically-polarized light where left- and right-rotating polarizations can travel at different speeds (analogous to
birefringence Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...
). More specifically, for the case where absorption losses can be neglected, the most general form of Hermitian ε is: :\varepsilon = \begin \varepsilon_' & \varepsilon_' + i g_z & \varepsilon_' - i g_y \\ \varepsilon_' - i g_z & \varepsilon_' & \varepsilon_' + i g_x \\ \varepsilon_' + i g_y & \varepsilon_' - i g_x & \varepsilon_' \\ \end or equivalently the relationship between the displacement field D and the
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
E is: :\mathbf = \varepsilon \mathbf = \varepsilon' \mathbf + i \mathbf \times \mathbf where \varepsilon' is a real symmetric matrix and \mathbf = (g_x,g_y,g_z) is a real
pseudovector In physics and mathematics, a pseudovector (or axial vector) is a quantity that is defined as a function of some vectors or other geometric shapes, that resembles a vector, and behaves like a vector in many situations, but is changed into its o ...
called the gyration vector, whose magnitude is generally small compared to the eigenvalues of \varepsilon'. The direction of g is called the axis of gyration of the material. To first order, g is proportional to the applied
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
: :\mathbf = \varepsilon_0 \chi^ \mathbf where \chi^ \! 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 Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in ''nonlinear media'', that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typica ...
effect of magneto-optical 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 \varepsilon', and the other two eigenvalues of \varepsilon' are identical. Then, if we let g lie in the ''z'' direction for simplicity, the ε tensor simplifies to the form: :\varepsilon = \begin \varepsilon_1 & + i g_z & 0 \\ - i g_z & \varepsilon_1 & 0 \\ 0 & 0 & \varepsilon_2 \\ \end 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 1 / \sqrt (where μ is the
magnetic permeability In electromagnetism, permeability is the measure of magnetization that a material obtains in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. The term was coined by William ...
). 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 Cotton-Mouton 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 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: v_p = \frac where v_p is the velocity of light through the material, \epsilon is the material permittivity, and \mu 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: 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 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 \mathbf.


See also

* Zeeman effect *
QMR effect Quadratic magnetic rotation (also known as QMR or QMR effect) is a type of magneto-optic effect, discovered in the mid 1980s by a team of Ukrainian physicists. QMR, like the Faraday effect, establishes a relationship between the magnetic field and ...
* Magneto-optic Kerr effect * Faraday effect * Voigt Effect * Photoelectric effect


References

* Federal Standard 1037C and from MIL-STD-188 * * * * *
Broad band magneto-optical spectroscopy
{{Authority control Optical phenomena Electric and magnetic fields in matter de:Magnetooptik#Magnetooptische Effekte