The Theory of the Faraday Effect in Anisotropic Semiconductors

A formal treatment of the Faraday effect, due to free charge carriers, is developed for arbitrary directions of propagation in anisotropic semiconductors. General expressions for the Faraday rotation and the ellipticity are derived, in terms of four quantities which involve components of the tensors representing the dielectric constant and the high frequency conductivity in the presence of a magnetic field. It is found that, in contrast to the isotropic case, both the rotation and ellipticity depend upon the real and also the imaginary parts of the complex propagation constants. An examination is also made of the two elliptically polarized component waves into which the initially plane polarized radiation is resolved. Two special cases are discussed, of particular relevance to crystals with cubic symmetry, in which a simplification of the general expressions may be effected.