Fourth-moment Analysis for Wave Propagation in the White-Noise Paraxial Regime

TL;DR

This paper analyzes the fourth-order moments of wave fields in a random medium using the Ito-Schrodinger model, providing insights into beam scintillation, intensity covariance, and Wigner transform stability in the paraxial regime.

Contribution

It introduces a fourth-moment analysis for wave propagation in random media, deriving explicit formulas for moments, covariance, and stability measures in the paraxial regime.

Findings

Centered fourth-order moments follow Gaussian summation rule

Derived covariance function of transmitted beam intensity

Quantified scintillation and stability of the Wigner transform

Abstract

In this paper we consider the Ito-Schrodinger model for wave propagation in random media in the paraxial regime. We solve the equation for the fourth-order moment of the field in the regime where the correlation length of the medium is smaller than the initial beam width. As applications we prove that the centered fourth-order moments of the field satisfy the Gaussian summation rule, we derive the covariance function of the intensity of the transmitted beam, and the variance of the smoothed Wigner transform of the transmitted field. The second application is used to explicitly quantify the scintillation of the transmitted beam and the third application to quantify the statistical stability of the Wigner transform.