Dynamic instability of speckle patterns in nonlinear random media

TL;DR

This paper analyzes the stability of speckle patterns in nonlinear random media, revealing conditions under which they become dynamically unstable and potentially chaotic, influenced by the nonlinearity and response time.

Contribution

It provides a linear stability analysis of speckle patterns in nonlinear media, highlighting the conditions for instability and chaos, and clarifying the role of nonlinearity response time.

Findings

Speckle patterns become unstable within a certain frequency band when nonlinearity exceeds a threshold.

The absolute instability threshold is independent of the nonlinearity response time.

Speckle dynamics become chaotic immediately beyond the instability threshold.

Abstract

Linear stability analysis of speckle pattern resulting from multiple, diffuse scattering of coherent light waves in random media with intensity-dependent refractive index (noninstantaneous Kerr nonlinearity) is performed. The speckle pattern is shown to become unstable with respect to dynamic perturbations within a certain frequency band, provided that nonlinearity exceeds some frequency-dependent threshold. Although the absolute instability threshold is independent of the response time of nonlinearity, the latter significantly affects speckle dynamics (in particular, its spectral content) beyond the threshold. Our results suggest that speckle dynamics becomes chaotic immediately beyond the threshold.