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

Faraday effect

In physics, the Faraday effect or Faraday rotation is a Magneto-optical phenomenon, that is, an interaction between light and a magnetic field in a medium...

, which in turn is based on a magneto-optic effect

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...

.

The Faraday rotator works because one polarization of the input light is in ferromagnetic resonance

Resonance

In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...

 with the material which causes its phase velocity

Phase velocity

The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...

 to be higher than the other.

The plane of linearly polarized light is rotated when a magnetic field

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

 is applied parallel

Parallel (geometry)

Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not...

 to the propagation

Wave propagation

Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....

 direction. The empirical angle of rotation

Angle of rotation

In mathematics, the angle of rotation is a measurement of the amount, the angle, that a figure is rotated about a fixed point, often the center of a circle....

 is given by:


Where is the angle of rotation (in radian

Radian

Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...

s).

is the magnetic flux density in the direction of propagation (in tesla

Tesla (unit)

The tesla is the SI derived unit of magnetic field B . One tesla is equal to one weber per square meter, and it was defined in 1960 in honour of the inventor, physicist, and electrical engineer Nikola Tesla...

s).

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

Then is the Verdet constant

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...

 for the material. This empirical proportionality constant (in units of radians per tesla per metre, rad/(T·m)) varies with wavelength and temperature and is tabulated for various materials.

Faraday rotation is an example of non-reciprocal optical propagation. Unlike what happens in an optically active medium such as a sugar solution, reflecting a polarized beam back through the same Faraday medium does not undo the polarization change the beam underwent in its forward pass through the medium. This allows Faraday rotators to be used to construct devices such as optical isolator

Optical isolator

An optical isolator, or optical diode, is an optical component which allows the transmission of light in only one direction. It is typically used to prevent unwanted feedback into an optical oscillator, such as a laser cavity...

s to prevent undesired back propagation of light from disrupting or damaging an optical system.

The geometry of nonreciprocal propagation may at first appear paradoxical. In an optically active medium, the polarization direction twists in the same sense (e.g. like a right-handed screw) during the forward and backward passes, whereas in a Faraday medium, because the light reverses its propagation direction with respect to the magnetic field, the helicity of the propagation also reverses. But because the propagation axis has also reversed, this reversal of helicity is just what is needed cause the back-reflected light to have different polarization from the incident light. If the Faraday medium is of such thickness as to cause a 45 degree rotation on the way in, the back-reflected beam will have polarization perpendicular to the incident beam, allowing it to be cleanly blocked.

Faraday rotators may be enhanced by the Zeeman effect

Zeeman effect

The Zeeman effect is the splitting of a spectral line into several components in the presence of a static magnetic field. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field...

.