Numerical solutions for the fourth moment of a plane wave propagating in a random medium

Numerical solutions of the plane-wave fourth-moment differential equation are obtained for a two-dimensional homogeneous and isotropic random medium that is characterized by a Gaussian correlation function. Results show that the range dependence of the variance of the intensity fluctuations exhibits both saturation and focusing. In addition to the correlations of the intensity fluctuations, the full spatial dependence of the fourth moment of the propagating field is also described and compared with the the Born and Rytov approximations (weak scattering) and with recent asymptotic results (strong scattering).