Propagation in one-dimensionally stratified time-independent scattering media

We calculate the probability density distributions of the power reflection coefficient, and of the various fluxes of the components of an erstwhile plane wave that propagates in a one-dimensionally stratified slab of a time-independent scattering medium. We determine the second- and fourth-order statistics of the power-fluxes, discuss the relevance of this problem to the localization phenomenon, examine the distribution of the emerging power-flux and the limitations on the assumption that it possesses a lognormal distribution, and finally discuss and rationalize the differences between the above and the corresponding characteristics of the radiation propagating in a time-dependent variant of this problem.