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 sta-tistically homogeneous and isotropic two-dimensional random medium is solved numerically. Results are present-ed 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/l (D) is the initial beam width; 4, is the correlation length of the medium) and approaches that of a plane wave for large enough D/1_. An increase in the variance toward the edge of the beam is also manifested. The theoretical investigation of finite-beam propaga-tion through random media has been handled, until now, by various approximate methods. Several in-vestigators",2 have used the Rytov approximation to derive results for the variance and covariance of the log-amplitude fluctuations. Their results are valid only for weak turbulence and do not describe saturation ef-fects. An extension of Rayleigh-Sommerfeld scattering theory was employed by Leader3 to obtain results als