The propagation of stochastic waves in uniform media

A solution is presented for the correlation function (mutual coherence) and time average power of a stochastic wave in the uniform half-spacez \geq 0, given as a boundary value the correlation function on the planez = 0. Stationary statistics are assumed and solution is effected via a spectral representation of the field. It is found that when loss is present the evanescent spectrum, as defined for the lossless case, contributes to energy propagation; and criterion are developed which determine when the integral of spectral density can be associated with power.