Langevin description of speckle dynamics in nonlinear disordered media

TL;DR

This paper develops a Langevin framework to describe speckle pattern dynamics in nonlinear disordered media, predicting instability, transition to chaos, and characteristic fluctuation times based on nonlinearity and frequency thresholds.

Contribution

It introduces a novel Langevin-based model for speckle dynamics in nonlinear disordered systems, revealing conditions for instability and chaos transition.

Findings

Speckle pattern becomes unstable below a certain frequency threshold.

Transition from stationary to chaotic speckle patterns with increasing nonlinearity.

Characteristic fluctuation time scales inversely with the maximum frequency threshold.

Abstract

We formulate a Langevin description of dynamics of a speckle pattern resulting from the multiple scattering of a coherent wave in a nonlinear disordered medium. The speckle pattern exhibits instability with respect to periodic excitations at frequencies $\Omega$ below some $\Omega_{\mathrm{max}}$, provided that the nonlinearity exceeds some $\Omega$-dependent threshold. A transition of the speckle pattern from a stationary state to the chaotic evolution is predicted upon increasing nonlinearity. The shortest typical time scale of chaotic intensity fluctuations is of the order of $1/\Omega_\mathrm {max}$.