Propagation of a finite beam through a random medium

The differential equation for the fourth-order statistical moment of the field of a finite beam propagating in a statistically homogeneous and isotropic two-dimensional random medium is solved numerically. Results are presented for the variance and covariance of irradiance scintillations of a Gaussian beam that propagates in a medium with a Gaussian correlation function. It is shown that the range dependence of the variance is highly dependent on the ratio D/ln (D) is the initial beam width; ln is the correlation length of the medium) and approaches that of a plane wave for large enough D/ln. An increase in the variance toward the edge of the beam is also manifested.