In this paper, we present a theory of transport based on the Bethe-Salpeter equation for a three-dimensional disordered medium with randomly rough interfaces illuminated by an electromagnetic wave. The slab is defined by a random medium composed of nanospheres randomly distributed in a layer. We study the electromagnetic coherent effects of the wave scattering inside the random volume bounded by randomly rough interfaces. Coherent effects are related for example to backscattering enhancement due to the interaction of the wave with the randomly rough boundaries or the random volume. The phenomenon manifests itself at the level of configurationally averaged mean intensity. We examine the solution by moments of the Bethe-Salpeter equation and we introduce the ladder and most-crossed contributions of the transport theory including the randomly rough boundaries of the considered structure. In this paper we are concerned with the wave transport behavior beyond the effective medium picture in taking into account the multiply scattered behavior.
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