Means, variances, and covariances for laser beam propagation through a random medium

Abstract

Wave propagation in a random continuous medium is studied by solving the stochastic wave equation with a random function for the refractive index coefficient. By the application of the Rytov transformation, an equivalent spatial form of the nonlinear Riccati equation is obtained which is then solved by means of an iteration scheme. The statistical properties of the propagated wave are then computed for the case of a coherent focused source with a Gaussian amplitude distribution. These formulas contain, as limiting sub-cases, the results of previous analyses for the spherical and plane wave. More generally, they describe the propagation of a laser beam.