Numerical Solutions of the Fourth Moment Equation

Numerical solutions of the fourth moment differential equation are obtained for a two-dimensional homogeneous and isotropic random medium which is characterized by a Gaussian correlation function. In addition to the covariance of the intensity fluctuations, the full spatial dependence of the fourth moment of the propagating field is described for both plane waves as well as for finite beams. Results are also presented for the interesting geometry in which the four observation points do not form a parallelogram. In the case of an initially Gaussian beam, the dependence of the structure of the fourth moment on the beam diameter is investigated for several propagation distances. The results for the intensity fluctuations index σ²₁, are compared with various formulations of the extended Huygens-Fresnel principle.