Calculation of the nonlinear optical conductivity by a quantum-statistical method

Abstract

Utilizing the operator algebra technique, we derive a nonlinear conductivity formula for a system of electrons interacting with phonons. We present a method to obtain the general formula for a nonlinear optical conductivity of general rank, and calculate the linear and lowest-order nonlinear conductivities with the damping factors, which are known to be a combination of Suzuki's and Bloembergen's results. The present result includes the electron and phonon distribution functions properly, and thus it is possible to explain the phonon emissions and absorptions in all electron transition processes.