Dispersive Magneto-Optical Phenomena in Semiconductors in Crossed Magnetic and Electric Fields

The semiclassical and quantum theories of the Faraday and Voigt effects due to transitions between two simple energy bands in the presence of crossed magnetic and electric fields are developed. The dispersive phenomena are found to complement and augment the information obtained from absorption. The decrease of instensity of $\Delta n=0\mathrm{}$ transitions, the finite probability of transitions with $\Delta n\ne 0$, and the shift of transitions to lower energies are found here, as they were in the optical absorption. The absorption constant due to second-order (forbidden) transitions is calculated and anisotropy with respect to electric-field direction is predicted. The experimental results of crossed-field Faraday rotation in gemanium are presented, and comparison with the theory is carried out, taking into account the degeneracy of the valence band. Good correlation between the theory and the experiment is obtained.