Evaluating double-angular power spectrum of waves in stochastic media by random walk

A propagation model was recently developed to characterize the waves between two communicating volumes in the presence of multipath stochastic media [1]. A double-angular power spectrum (DAPS) is a crucial part of this model. It relates the directional propagation of waves on the transmitting side to that on the receiving side. To obtain the DAPS of a system, one may conduct direct measurement or fullwave solutions to the Maxwell´s equations. But both of them become resourcefully demanding when the system is random. In the study of [1], it was suggested to use the reduced incident intensity in the classic transport theory [2] to approximately estimate the spectrum. The reduced incident intensity leads to very convenient application of the model, but it also seriously compromises the physics by neglecting the effects of diffusive transport of waves. In this paper, an attempt is made to evaluate the DAPS of some general systems by using a random walk approach. It is based on the tight connection between wave transport and particle transport, and takes the multiple scattering and diffusive nature of the waves into account.