Fourth-order moment of the light field in atmosphere

TL;DR

This paper derives an explicit expression for the fourth-order moment of light in the atmosphere, revealing photon correlations and fluctuations useful for understanding laser beam propagation through turbulence.

Contribution

It provides a novel analytical solution for the fourth-order moment of the light field in atmospheric turbulence, linking photon correlations to measurable fluctuations.

Findings

Explicit formula for fourth-order moment in turbulence

Identification of shot noise dominance range

Photon fluctuations as a diagnostic tool

Abstract

The quasiclassical distribution function for photon density in the phase space is obtained from solution of the kinetic equation. This equation describes propagation of paraxial laser beams in the Earth atmosphere where "collision integral" embodies the influence of turbulence. The anisotropy of photon distribution is shown and explained. For long propagation path, the explicit expression for fourth-order moment of light is obtained as a sum of linear and quadratic forms of the average distribution function. This moment describes a spatial correlation of four light waves, giving the information about the photon distribution in the cross-section of the beam. The fourth moment can be measured using two small detectors outside the central part of the beam. The linear form describes the shot noise (quantum fluctuations) of photons. The range where the shot noise exceeds the classical noise is found analytically. Derived photon fluctuations are the valuable source of information about statistical properties and local structure of the laser radiation that can be used for applications.