Statistics of Non-Rayleigh Speckles Generated from Nonlinear Media

TL;DR

This paper analytically investigates how nonlinear media, specifically focusing and defocusing Kerr nonlinearities, alter the intensity distribution and statistics of speckle patterns, revealing significant modifications in local intensity behavior.

Contribution

It provides an analytical expression for speckle intensity PDF in nonlinear media and compares it with numerical results, highlighting the impact of nonlinearity on speckle statistics.

Findings

Intensity PDF tail lengthens in focusing nonlinear media

Intensity PDF tail shortens in defocusing nonlinear media

Field correlation remains unchanged by nonlinearity

Abstract

We analytically derive an expression for a speckle field's intensity probability density function (PDF) in a nonlinear medium. The analytically driven results are in good agreement with the numerical outcomes. In a focusing nonlinear medium, the local intensity of the speckle is enhanced as manifested through the longer tail of the PDF. In contrast, the local intensity of speckle is reduced in the presence of a defocusing nonlinearity, and the tail of the probability density function also reduces. This change in local intensity of the speckles arises due to the cubic Kerr nonlinearity, which eventually modifies the second-order statistics. Hence, the intensity correlation is altered as per the nature of the associated nonlinearity while the field correlation remains invariant of both types of the nonlinear conditions.