Faraday rotator is a device that exploits the magnetic optical effect in certain crystals.

When magnetic field is applied to the crystal, it changes the refractive index of the crystal. When a linearly polarized light passes through the crystal at the same direction of the magnetic field lines, and we know that the linearly polarized light can be treated as the superposition of two circularly polarized components (with opposite circular directions), those two components experiences different refractive index, and hence their optical delay is different. This difference causes a phase change between those two components, which means the linearly polarized light is rotated to a degree.

The degree of the rotation is in proportion to the phase difference, and hence the index difference caused by the magnetic field. This effect is called Faraday rotation. Different materials have different degrees of Faraday rotation under the same magnetic field. This is indicated by a coefficient called Verdet constant of the material.

The Verdet coefficient is also wavelength dependent. It decreases in value when the wavelength is increased. This puts a limit on the bandwidth of Faraday rotator (and the devices based on it), in addition to other factors.

The angle of the Faraday rotation (caused by the change of refractive index of the two circularly polarized components) is only determined by the direction of the magnetic field, and it is not affected by the direction of the light. Therefore, if the light is reflected back into the optical medium again, the rotation angle is added up.

Optical Faraday rotator is the key sub-component used in devices such as optical isolators, circulators, etc. Faraday rotator itself is also very useful in polarization manipulate of the light.