what is the relationship between the optical and magnetic properties?
The interaction of the magnetic field H of light with matter is very small at normal intensities and can be neglected.
But matter in a strong static fields Bs becomes birefringent. Two effects are of interest:
1.) Cotton-Mouton effect (also Voigt effect)
If the light propergates perpendicular to a static magnetic Bs the refractive indices of tjhe electric field parallel and perpendicular to Bs are different. It holds ne-neo= MlwBs2, with lw the wavelength and M the Cotton-Mouton constant. Example: nitrobenzene M = 2.5 x10-2 [m3V-2s-2 ]. The Cotton-Mouton effect is a quadratic effect and matter (glass, liquids, gases) becomes uniaxial birefringent.
2.) Faraday-effect
If the light propagates parallel to Bs matter becomes circular birefringent. The E-vector of linearly polarized light is rotated by an angle ß. it holds: ß=VdBs with d the length of the interacting region, V the Verdet constant. Example. glass V = 270 [degree m V-1s-1]; terbium doped glass V = 4000 [degree m V-1s-1]. The Faraday effect is a linear effect and is used for optical diodes (system with unidirectional transmission of light).
This can be understood by magneto optic kerr effect(Reflection mode) and faraday effect(transmission mode) in which incident light polarization can be controlled by the application of magnetic field......................
Vinay Sharma is right. The Cotton-mouton effect corresponds to the eelctrical Kerr effect. By a static (or slowly varying) electric field Es isotropic crystals or liquids become birefringent. Now holds for the refractive indices ne-neo=KlwEs2.
Example nitrobenzene K = 4x10-12 mV-2. The elctrical kerr-effect is used to modulate light. E.g in former times the analogous movie films had a special trace for the sound, generated by a Kerr-cell modulated light beam.
In my opinion the relationship between the optical and magnetic properties can be interpreted in two quite distinct ways, according to the scientific framework.
The magneto-optic effect was discovered in 1845 by Faraday, who was searching for an optical effect analogous to the electrical one discovered by Oersted, i.e. the rotation of a magnetic needle subject to an electric current. The optical rotation is not as easily seen as the electrical one, and Faraday had to enhance its visibility to prove it. As both researches were conducted in the framework of the conservation and transformation of energy, matter was not considered. In fact, according to Faraday's interpretation, a magnetic field B causes the polarization plane of light to rotate by an angle w = V B l, where l is the thickness of a transparent – i.e. optically inert – and diamagnetic substance such as glass or common salt, and the B-field is supposed to be oriented as the thickness of the sample. V is the Verdet constant.
However, it is known that there are also substances which exhibit optical activity, in the sense of changing the polarization of light, without the need to apply any B-field. Therefore the Faraday effect was interpreted as a property of substances, of becoming optically active when subject to magnetism. Today the Faraday effect is closely associated with the inverse Zeeman effect, and is explained accordingly.
As already told by Horst Weber and Vinay Sharma, later on also other magneto-optical effects were discovered. There are also less studied effects, as reported by J. Lamarsh in "Forgotten Magneto-Optical Effect".
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