Quantum Theory of Interband Faraday and Voigt Effects

A quantum-mechanical analysis of the Faraday rotation and the Voigt effect has been carried out for both the oscillatory and long-wavelength regions. Expressions have been developed for these effects from the offdiagonal and diagonal components, respectively, of the conductivity tensor; the latter has been obtained in the form of the Kramers-Heisenberg dispersion relations through the use of first-order time-dependent perturbation theory. The results, which have been calculated for a simplified two-bandmodel, are generalized to apply in the high-field case as well as the low-field limit. Through the introduction of a phenomenological relaxation time, $\tau$, line shapes have been calculated for both the direct and indirect transition for the Faraday and Voigt effects. These have been obtained as a function of frequency for various values of magnetic field and relaxation times. The results obtained enable the evaluation of $g$ factors from experimantal line shapes.