Statistical properties of the laser beam propagating in a turbulent medium

TL;DR

This paper analyzes the statistical behavior of laser beams in turbulent media, demonstrating Gaussian intensity fluctuations at large distances and providing criteria based on physical parameters, with explicit correlation function calculations.

Contribution

It introduces new quantitative criteria for Gaussian statistics in laser propagation through turbulence and explicitly computes correlation functions and non-Gaussian corrections.

Findings

Intensity fluctuations are Gaussian at large distances.

Explicit formulas for the laser envelope correlation functions.

Conditions for Gaussian behavior depend on propagation distance, beam waist, frequency, and turbulence strength.

Abstract

We examine statistical properties of a laser beam propagating in a turbulent medium. We prove that the intensity fluctuations at large propagation distances possess Gaussian probability density function and establish quantitative criteria for realizing the Gaussian statistics depending on the laser propagation distance, the laser beam waist, the laser frequency and the turbulence strength. We calculate explicitly the laser envelope pair correlation function and corrections to its higher order correlation functions breaking Gaussianity. We discuss also statistical properties of the brightest spots in the speckle pattern.