Coherent light scattering of heterogeneous randomly rough films and effective medium in the theory of electromagnetic wave multiple scattering

We have developed a general formalism based on Green's functions to calculate the coherent electromagnetic field scattered by a random medium with rough boundaries. The approximate expression derived makes it possible to determine the effective permittivity, which is generalised for a layer of an inhomogeneous random medium with different types of particles and bounded with randomly rough interfaces. This effective permittivity describes the coherent propagation of an electromagnetic wave in a random medium with randomly rough boundaries. We have obtained an expression, which contains the Maxwell–Garnett formula at the low-frequency limit, and the Keller formula; the latter has been proved to be in good agreement with experiments for particles whose dimensions are larger than a wavelength.