Perturbation theory for phase correlations of a light wave propagating in a turbulent medium

TL;DR

This paper develops a perturbation theory for phase correlations of light waves in turbulent media, introducing a diagrammatic approach to compute corrections beyond linear approximation and establishing conditions for its validity.

Contribution

It introduces a diagrammatic perturbation framework for phase correlation functions in turbulent media, including one-loop corrections and asymptotic analysis.

Findings

Perturbation theory applies when Rytov dispersion is small.

One-loop corrections modify phase correlation functions.

Applicability condition holds uniformly over observation distances.

Abstract

We theoretically investigate the correlation functions of the phase of a light wave propagating through a turbulent medium. We use an equation for the logarithm of a wave packet envelope, which includes a second-order nonlinear term. Based on this equation, we develop a diagrammatic technique to calculate corrections to the correlation function obtained in the linear approximation. We calculate the first corrections determined by one-loop diagrams and find its asymptotic behaviors. Some non-perturbative conclusions are made using the symmetry properties of the equation. These results allow us to conclude that the applicability condition for the perturbation theory is the smallness of the Rytov dispersion, $\sigma_R^2$, and this condition holds uniformly over the distances between observation points.