Parametric four-photon mixing: exact analytical solutions in Jacobi functions

Abstract

The problem with generating of new frequencies (signal and idler waves) in parametric four-photon processes without including the Raman scatter was solved only in approximation for a constant electric field or a constant intensity of the pump wave. The overall task which includes the change in intensity and the phase of the pump wave has not been studied in detail in the literature up to now. The main idea of present work is to solve the more general problem in which we have energy exchange between pump wave, signal and idler waves.