The propagation of stochastic waves in uniform media

Abstract

A solution is presented for the correlation function (mutual coherence) and time average power of a stochastic wave in the uniform half-space <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z \geq 0</tex> , given as a boundary value the correlation function on the plane <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z = 0</tex> . 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.