Two-scale solution for the intensity fluctuations of two-frequency wave propagation in a random medium

We have solved the equation for the two-frequency fourth-order moment of two parallel monochromatic plane waves having different frequencies and propagating through a randomly inhomogeneous medium. The solution procedure uses a two-scale expansion based on the smallness of a new parameter whose magnitude does not depend on the scattering strength. The results are shown to be valid for all values of the scattering parameter. The multidimensional integral expression for the bichromatic correlation was evaluated for a two-dimensional random medium characterized by a Gaussian correlation function. Further simplification was carried out in the strongscattering regime, using asymptotic techniques. It is shown that the bichromatic correlation decreases with the wavelength separation. Its dependence on range is more complicated: Initially it increases with increasing range, only to level off to zero for large enough scattering strength, wavelength separation, and range.