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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. The theoretical basis for that relation, now called electromagnetic radiation, was developed by James Clerk Maxwell in the 1860's and 1870's. This effect occurs in most optically transparent dielectric materials (including liquids) 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.
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 relation between the angle of rotation of the polarization and the magnetic field in a diamagnetic material is:
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
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.
Some materials, such as terbium gallium garnet (TGG) have extremely high Verdet constants (~ -40 rad T-1m-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 of Faraday rotators, which are the principal component of Faraday isolators, devices which transmit light in only one direction.
Similar isolators are constructed for microwave systems by using ferrite rods in a waveguide with a surrounding magnetic field.
Further Reading
- Optics, Eugene Hecht, Addison Wesley, 4th edition 2002, hardcover, chapter 8.11.2
- Optics Amnon Yariv, Oxford University Press; 5th edition (April 1997), hardcover, Optical Electronics in Modern Communications (Oxford Series in Electrical and Computer Engineering)
- Faraday Rotation - Eric Weisstein's World of Physics
- Electro-optical measurements - Kerr, Pockels, and Faraday
- Faraday Effect Rotation for Water and Flint Glass (write-up of an experimental study of the Faraday effect)
This article is licensed under the GNU Free Documentation License. It uses material from Wikipedia Encyclopedia article "Faraday Effect"
