TRANSVERSE SPECTRA OF WAVES IN RANDOM-MEDIA

We consider the statistics of the transverse spectra of forward-propag ating waves in a stationary random medium. A short-range perturbation solution is used to derive the difference equations that govern the lo ng-range evolution of the ensemble-averaged transverse wave spectrum a nd coherence. The conditions under which these equations may be approx imated by differential and integro-differential equations are given, a nd it is shown that the approximation is valid for the treatment of be am propagation provided that the transverse dimension of the beam is s ufficiently large, and at ranges where the transverse coherence length of the beam remains larger than a wavelength. The equations that are derived are not limited by the parabolic approximation, and are amenab le to numerical solution by marching techniques. We use the equation t hat governs the spectral density of the total energy flux, and also th e propagation of waves which are statistically homogeneous in transver se planes, to show the conditions under which previously studied appro ximations derive from the present formulation, and to illustrate the n umerical solution of the problem.