Multiple scattering by a collection of randomly located obstacles distributed in a dielectric slab

Scattering of electromagnetic waves by discrete, randomly distributed objects inside a (finite or semi-infinite) slab is addressed. In general, the non-intersecting scattering objects can be of arbitrary form, material and shape with number density n0 (number of scatterers per volume). The main aim of this paper is to calculate the coherent reflection and transmission characteristics for this configuration. Typical applications of the results are found at a wide range of frequencies (radar up to optics), such as attenuation of electromagnetic propagation in rain, fog, and clouds etc. The integral representation constitutes the underlying framework of the solution of the deterministic problem, which then serves as the starting point for the solution of the stochastic problem. Conditional averaging and the employment of the Quasi Crystalline Approximation lead to a system of integral equations in the unknown expansion coefficients. The slab geometry implies a system of integral equations in the depth variable. Explicit solutions for tenuous media and low frequency approximations can be obtained for spherical obstacles.