Faraday rotation
In physics, 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. 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.
Faraday rotation caused by the earth's magnetic field is one phenomenon that affects the polarization of radio waves propagating through the atmosphere.
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:
- <math> \beta = \mathcal{V}Bd <math>
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 <math>\mathcal{V}<math> 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 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 45° can be achieved. This allows the construction of Faraday rotators, which are the principle 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, ISBN 0-8053-8566-5, chapter 8.11.2
- Optics Amnon Yariv, Oxford University Press; 5th edition (April 1997), hardcover, ISBN 0195106261, Optical Electronics in Modern Communications (Oxford Series in Electrical and Computer Engineering)
See also
