Non-Gaussian Statistics of Multiple Filamentation

TL;DR

This paper analyzes the statistical behavior of light amplitude fluctuations during multiple filamentation in Kerr media, revealing a transition from Gaussian to non-Gaussian distributions with heavy tails caused by filament dynamics and dissipation effects.

Contribution

It introduces a detailed statistical analysis of filamentation, highlighting the universal form of near singular filaments and their impact on amplitude fluctuation distributions.

Findings

Gaussian behavior at small amplitudes

Power-law tails at large amplitudes

Filament dynamics determine non-Gaussian fluctuations

Abstract

We consider the statistics of light amplitude fluctuations for the propagation of a laser beam subjected to multiple filamentation in an amplified Kerr media, with both linear and nonlinear dissipation. Dissipation arrests the catastrophic collapse of filaments, causing their disintegration into almost linear waves. These waves form a nearly-Gaussian random field which seeds new filaments. For small amplitudes the probability density function (PDF) of light amplitude is close to Gaussian, while for large amplitudes the PDF has a long power-like tail which corresponds to strong non-Gaussian fluctuations, i.e. intermittency of strong optical turbulence. This tail is determined by the universal form of near singular filaments and the PDF for the maximum amplitudes of the filaments.