Analytic structure of the four-wave mixing model in photorefractive materials

TL;DR

This paper analyzes the singularity structure of the four-wave mixing model in photorefractive materials, revealing that solutions depend on a specific reduced variable, which aids in finding explicit analytic solutions.

Contribution

It identifies the singularity structure of the four-wave mixing model and introduces a reduced variable for explicit analytic solutions, linking it to the cubic complex Ginzburg-Landau equation.

Findings

Solutions depend on the reduced variable xi = sqrt(z) exp(-t / tau)

Singularity analysis parallels that of the cubic complex Ginzburg-Landau equation

Provides insight into explicit analytic solutions in nonlinear optics

Abstract

In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space variable z. This structure is quite similar, and this is not a surprise, to that of the cubic complex Ginzburg-Landau equation. The main result is that, in order to be single valued, time-dependent solutions should depend on the space-time coordinates through the reduced variable xi=\sqrt{z} exp(-t / tau), in which tau is the relaxation time.