 The Faraday effect or Faraday rotation is an interaction between light and a magnetic field. The rotation of the plane of polarization is proportional to the intensity of the component of the magnetic field in the direction of the beam of light.

The Faraday effect, also called the Magneto-Optic Effect, discovered by Michael Faraday in 1845, was the first experimental evidence that light and magnetism are related. This effect occurs in most optically transparent dielectric materials when they are subject to strong magnetic fields.

The Faraday effect is a result of ferromagnetic resonance when the permeability of a material is represented by a tensor. This resonance causes waves to be decomposed into two circularly polarized rays which propagate at different speeds, a property known as circular birefringence. The rays can be considered to re-combine upon emergence from the medium, however owing to the difference in propagation speed they do so with a net phase offset, resulting in a rotation of the angle of linear polarization.

The relation between the angle of rotation of the polarization and the magnetic field in a diamagnetic material is:

β =  VB d

where β is the angle of rotation (in radians)

B is the magnetic flux density in the direction of propagation (in teslas)

d is the length of the path (in metres) where the light and magnetic field interact

Then V is the Verdet constant for the material. This empirical proportionality constant (in units of radians per tesla per metre) varies with wavelength and temperature and is tabulated for various materials.

A positive Verdet constant corresponds to L-rotation (anticlockwise) when the direction of propagation is parallel to the magnetic field and to R-rotation (clockwise) when the direction of propagation is anti-parallel. Thus, if a ray of light is passed through a material and reflected back through it, the rotation doubles.

One of the most familiar optical instruments utilizing this effect is the Faraday rotator; one well-know present-day application is in the protective device used to prevent the destruction of high- power laser system by backreflections from the target or other " downstream " system points.

There are a few applications of Faraday rotation in measuring instruments. For instance, the Faraday effect has been used to measure optical rotatory power, for amplitude modulation of light, and for remote sensing of magnetic fields.

Also known as Kundt effect or magnetic rotation.

Verdet constant
The Verdet constant is an optical "constant" that describes the strength of the Faraday effect for a particular material.

The Verdet constant for most materials is extremely small and is wavelength dependent. It is strongest in substances containing paramagnetic ions such as terbium. The highest Verdet constants are found in terbium doped dense flint glasses or in crystals of terbium gallium garnet.This material has excellent transparency properties and is very resistant to laser damage.

Although the Faraday effect is not chromatic (i.e. it doesn't depend on wavelength), the Verdet constant is quite strongly a function of wavelength. At 632.8 nm, the Verdet constant for MR4 is reported to be -110 rad/T·m, whereas at 1064 nm, it has fallen to -37 rad/T·m. This behavior means that the devices manufactured with a certain degree of rotation at one wavelength, will produce much less rotation at longer wavelengths. Many Faraday rotators and isolators are adjustable by varying the degree to which the active terbium doped glass or TGG rod are inserted into the magnetic field of the device. In this way, the device can be tuned for use with a range of lasers within the design range of the device. Truly broadband sources (such as ultra-short pulse lasers and the tunable vibronic lasers) will not see the same rotation across the whole wavelength band.

The Verdet constant is named after the French physicist Émile Verdet

V is the Verdet constant for the material. This empirical proportionality constant (in units of minutes of arc per gauss per cm of path, or in SI units, radians per tesla per metre) varies with wavelength and temperature and is tabulated for various materials.

A Faraday rotator is an optical device that rotates the polarization of light due to the Faraday Effect.

The Faraday rotator works because one polarization of the input light is in ferromagnetic resonance with the material which causes its phase velocity to be higher than the other. Specifically, given two rays of circularly polarized light, one with left-hand and the other with right-hand polarization, the phase velocity of the one with the polarization in the same sense as the precessing magnetization is greater.

Linearly polarized light can always be represented as a linear combination of circularly polarized light of left and right-handedness and equal amplitude. (See Jones calculus).

In other words, the plane of linearly polarized light is rotated when a magnetic field is applied parallel to the propagation direction. The empirical angle of rotation is given by:

β=νB

Where β is the angle of rotation (in minutes of arc).

B is the magnetic flux density in the direction of propagation (in gauss).

d is the length of the path (in cm) where the light and magnetic field interact.

Then is the Verdet constant for the material. This empirical proportionality constant (in units of minutes of arc per gauss per cm of path, or in SI units, radians per tesla per metre) varies with wavelength and temperature and is tabulated for various materials.

Faraday rotators are used in Faraday isolators to prevent undesired back propagation of light from disrupting or damaging an optical system.