Resonant Nonlinear Optical Susceptibility: Electroreflectance in the Low-Field Limit

Abstract

A theory of the electric field effect on the dielectric function of solids is developed by means of a perturbation treatment similar to that used to describe nonlinear optical phenomena. The field-induced change in the dielectric function is given directly as a Brillouin-zone integral over a fourth-power resonant denominator. It is shown that electric field modulation results in spectra nearly proportional to the third derivative of the unperturbed dielectric function for common experimental conditions. The perturbation treatment is related to the standard (high-field) Franz-Keldysh theories. The differences between the two approaches is discussed in physical terms. Simplified expressions for parabolic critical points are developed and used to discuss experimental criteria for the validity of the perturbation theory. Application to band-structure analysis is discussed. In particular, critical-point parameters (energy, broadening, etc.) enter nearly independently, and the mathematical form of the fourth-rank tensorial line shape is simple enough to permit the calculation of electroreflectance spectra from existing band-structure calculations.