Intensity correlation function for waves of different frequencies propagating through a random medium

Abstract

The fourth-moment equation for plane waves of two different frequencies propagating through a two-dimensional, dispersive random medium, is solved numerically using a split step method. In this numerical scheme, the extended medium is replaced by a series of phase screens interspersed with diffraction layers and thus it provides a test for the validity of using a single effective phase screen to describe an extended random medium in the calculation of the intensity cross-correlation function. The intensity cross spectrum in the multiple scattering regime is calculated for different values of the ratio of the two frequencies under the "frozen flow" assumption, when temporal evolution of the irregularities is absent. Irregularities with either a Gaussian or a power law spectrum are considered. The effect of varying irregularity strength on the normalized cross correlation of intensity fluctuations observed at the same location is also investigated. The two-frequency intensity space-time cross-correlation function is determined for a special case of "nonfrozen" flow where the irregularities have a random drift superimposed on uniform convection.