Nonlinear electromagnetic response of bloch electrons in a magnetic field I. - One-band effective-mass approximation

Abstract

A general self-consistent method has been developed to calculate optical nonlinearities of a solid in presence of a d.c. magnetic field. This method has been used to calculate linear as well as bilinear induced current densities in the one-band effective-mass approximation for Bloch electrons in the solid. The result for the linear current density gives familiar expressions for the Faraday effect and cyclotron resonance when the incident wave is polarized in the direction other than that of the d.c. magnetic field. However, it is shown that even if two fundamental waves of frequencies ω ₁ and ω ₂ are polarized in the direction of the d.c. magnetic field, the bilinear current density induced in the solid has cyclotron resonance denominators at the combination frequencies 2ω ₁, 2ω ₂ and ω₁ ± ω₂. When the fundamental waves are polarized in arbitrary directions cyclotron resonance denominators occur in the bilinear current density also at frequencies ω ₁ and ω ₂.