- Faraday effect
In

physics , the**Faraday effect**or**Faraday rotation**is amagneto-optic al phenomenon, or an interaction betweenlight and amagnetic field in a dielectric material. The rotation of the plane ofpolarization is proportional to the intensity of the component of the magnetic field in the direction of the beam of light.The Faraday effect, discovered by

Michael Faraday in 1845, was the first experimental evidence that light and electromagnetism are related. The theoretical basis for that relation, now calledelectromagnetic radiation , was further developed byJames Clerk Maxwell in the 1860s and 1870s. This effect occurs in most optically transparentdielectric materials (including liquids) when they are subject to strongmagnetic field s.The Faraday effect is a result of

ferromagnetic resonance when thepermittivity of a material is represented by atensor . 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.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. The Faraday effect is used in

spintronics research to study the polarization of electron spins in semiconductors.The relation between the angle of rotation of the polarization and the magnetic field in a diamagnetic material is:

:$eta\; =\; mathcal\{V\}Bd$

where

:β is the angle of rotation (in

radian s):"B" is the magnetic flux density in the direction of propagation (in teslas)

:"d" is the length of the path (in

meter s) where the light and magnetic field interact:$mathcal\{V\}$ is the

Verdet constant for the material. This empirical proportionality constant (in units of radians per tesla per meter) 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.

Some materials, such as

terbium gallium garnet (TGG) have extremely high Verdet constants (≈ −40 rad T^{-1}m^{-1}). By placing a rod of this material in a strong magnetic field, Faraday rotation angles of over 0.78 rad (45°) can be achieved. This allows the construction ofFaraday rotator s, which are the principal component ofFaraday isolator s, devices which transmit light in only one direction.Similar isolators are constructed for microwave systems by using

ferrite rods in awaveguide with a surrounding magnetic field.**Faraday rotation in the interstellar medium**The Faraday effect is imposed on light over the course of its propagation from its origin to the

Earth , through theinterstellar medium . Here, the effect is caused by freeelectrons and can be characterized as a difference in therefractive index seen by the two circularly polarized propagation modes. Hence, in contrast to the Faraday effect in solids or liquids, interstellar Faraday rotation has a profoundly simple dependence on the wavelength of light (λ), namely::$eta\; =\; mathrm\{RM\}\; lambda^2\; ,$

where the overall strength of the effect is characterized by RM, the rotation measure. This in turn depends on "B", and the number density of electrons, "n

_{e}", both of which may vary along the propagation path, to give (incgs units)::$mathrm\{RM\}\; =\; frac\{e^3\}\{2pi\; m^2c^4\}int\_0^d\; n\_e\; B\; ;mathrm\{d\}s,$

where

:"e" is the charge of an electron;:"m" is the

mass of an electron;:"c" is the speed of light in a vacuum.(In

SI units, $mathrm\{RM\}^\{(SI)\}\; =\; frac\{e^3\}\{8pi^2\; varepsilon\_0\; m^2c^3\}int\_0^d\; n\_e\; B\; ;mathrm\{d\}s\; =\; 2.62\; imes\; 10^\{-13\}\; int\_0^d\; n\_e\; B\; ;mathrm\{d\}s,$where $epsilon\_0$ is thevacuum permittivity ; with $B$ in teslas (T), and $n\_e$ in m$^\{-3\}$ (electrons per cubic meter), $mathrm\{RM\}^\{(SI)\}$ is in radians per square meter (rad/m²).)Faraday rotation is an important tool in

astronomy for the measurement of magnetic fields, which can be estimated from rotation measures given a knowledge of the electron number density [*cite book|last=Longair|first=Malcolm | authorlink=Malcolm Longair|title=High Energy Astrophysics|publisher=Cambridge University Press|year = 1992|isbn=ISBN 0521435846*] . In the case ofradio pulsar s, the dispersion caused by these electrons results in a time delay between pulses received at different wavelengths, which can be measured in terms of the electron column density, ordispersion measure . A measurement of both the dispersion measure and the rotation measure therefore yields the weighted mean of the magnetic field along the line of sight. The same information can be obtained from objects other than pulsars, if the dispersion measure can be estimated based on reasonable guesses about the propagation path length and typical electron densities.Radio wave s passing through the Earth'sionosphere are also subject to Faraday rotation; as the above equation indicates, the effect is proportional to the square of the wavelength. At 435 MHz (UHF), one should expect in the order of 1.5 complete rotations of the wavefront as it transits the ionosphere, whereas at 1.2 GHz less than a quarter of one rotation is likely.**ee also***

Magneto-optic Kerr effect

* Electro-optic Kerr effect

*Faraday rotator

*Scientific phenomena named after people

*Inverse Faraday effect

*Optical rotation

*QMR effect

*Voigt effect

*Polarization spectroscopy

*Magnetic circular dichroism **External links*** [

*http://scienceworld.wolfram.com/physics/FaradayRotation.html Faraday Rotation*] "(at Eric W. Weisstein's World of Physics)"

* [*http://home.earthlink.net/~jimlux/hv/eo.htm Electro-optical measurements (Kerr, Pockels, and Faraday)*]

* [*http://www.wooster.edu/physics/JrIS/Files/kash-webarticle.pdf Faraday Effect Rotation for Water and Flint Glass*] "(write-up of an experimental study of the Faraday effect)"

* [*http://www.classicistranieri.com/american/1/6/6/7/16671/16671-h/16671-h.htm#art16 "Scientific American Supplement" Vol. XXV, No. 643*] from 1888, article "The direct optical projection of electro-dynamic lines of force and other electro-dynamic phenomena" describing an experiment which apparently uses the Faraday Effect in order to directly visualise lines of force in a magnetic field (without the mess normally associated with using iron filings) ... unfortunately the first part of the article is not available online, so the exact materials and methods are not clear.**References**

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