Second-order statistics of non-Gaussian fluctuations of coherent waves reflected from disordered media

Abstract

We show that the second-order statistics of speckle patterns of scalar waves, multiply scattered on reflection by disordered media, may be non-Gaussian, even though the first-order statistics are Gaussian. This occurs at intermediate sizes of the illuminated samples of the medium that are large enough to produce Gaussian first-order statistics of the scattered field but are small enough to break down the so-called factorization approximation in directions of the incident and scattered wave vectors at which there are enhanced long-range angular-correlation peaks. We propose joint probability distributions of the scattered intensity that are given in terms of modified Bessel functions of the second kind. © 1993 The American Physical Society.