A phase-space Gaussian beam summation representation of rough surface scattering

A Gaussian beam (GB) summation representation for rough surface scattering is introduced. In this scheme, the coherent and incoherent scattered fields are described by a phase-space summation of GBs that emanate from the rough surface at discrete set of points and directions. It thus involves stochastic GB2GB scattering matrices for the coherent and incoherent fields, and deterministic GB propagators. It benefits from the simplicity and accuracy of the latter, and can be used in applications involving propagation in complex scenarios comprising inhomogeneous media with rough surface boundaries. The GB2GB matrices are calculated from the statistical moments of the scattering amplitude, which are given either analytically or empirically. An analytical and numerical example for weakly rough surface is presented and discussed. Applications to the more complicated propagation scenario of doubly rough surface waveguide with multiple reflection phenomena will be presented in a follow-up publication.