Coherent propagation of waves in random media with weak nonlinearity

TL;DR

This paper develops a diagrammatic theory to analyze how weak nonlinearity affects wave transport and coherent backscattering in disordered media, revealing that nonlinearity can enhance or suppress the backscattering effect.

Contribution

It introduces a nonperturbative diagrammatic approach to describe nonlinear wave transport and coherent backscattering in disordered media, extending linear theories.

Findings

Nonlinearity significantly alters the magnitude of coherent backscattering.

Depending on the nonlinearity type, backscattering can be enhanced or suppressed.

The theory provides integral equations for nonlinear diffusive transport and coherent backscattering.

Abstract

We develop a diagrammatic theory for transport of waves in disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and crossed diagrams for the average wave intensity. Then, we sum up the diagrammatic series completely, i.e. nonperturbatively in the strength of the nonlinearity, and thereby obtain integral equations describing both nonlinear diffusive transport and coherent backscattering of the average intensity. As main result, we find that the nonlinearity significantly influences the magnitude of the coherent backscattering effect. Depending on the type of nonlinearity, coherent backscattering is either enhanced or suppressed, as compared to the linear case.