Guided waves in bounded media with random gross inhomogeneities

Abstract

A formalism to deal with propagation in waveguides containing media with statistically inhomogeneous, random, gross inhomogeneities over a finite axial range is proposed. Statistics of the propagating fields are obtained in terms of those of the medium through an iterative perturbation technique which does not use expansion in a small parameter. A modal expansion, with a nonlinear phase progression term in the exponent of the axial dependence of the incident mode, is utilized and permits the direct calculation of all desired field statistics from the formal perturbation expressions for the modal amplitudes and phase progression. Examples are presented to show that many quantities of interest, involving mode coupling and transmission and reflection parameter., may straightforwardly be determined through this procedure. Some prevalent notions concerning the significance of the mean wave are discussed.