Correlations of the phase gradients of the light wave propagating in a turbulent medium in the regime of strong scintillations

TL;DR

This paper analyzes the correlation functions of light wave phases in turbulent media under strong scintillation conditions, combining analytical and numerical methods to understand phase gradient behaviors.

Contribution

It provides a theoretical and numerical study of phase gradient correlations in strong scintillation regimes, relating them to envelope correlations assuming Gaussianity.

Findings

Correlation functions approach theoretical predictions as scintillation strength increases.

Phase gradient correlations differ from theory at larger distances due to non-Gaussian effects.

Numerical simulations confirm the theoretical relationship for small separations.

Abstract

We investigate analytically and numerically correlation functions of the phase of light waves that propagate through turbulent media. We examine the case of strong scintillations that occur at large values of the Rytov dispersion, $\sigma^2_R$. Then, it is possible to relate the pair correlation function of phase gradients to the known pair correlation function of the envelope dependent on the distance $r$ assuming Gaussianity of the envelope of the beam. Our direct numerical simulations show that the profile of the pair correlation function for phase gradients gradually approaches the theoretical expression as the value of $\sigma_R^2$ increases, if $r<r_0$ where $r_0$ is the Fried length. For larger $r$ the behavior of the computed correlation function is quite different because of destroying the Gaussianity.