Electromagnetic scattering by discrete random media. II: The coherent field

The computation of the coherent field in the case of a plane electromagnetic wave obliquely incident on a discrete random layer with non-scattering boundaries is addressed. For dense media, the analysis is based on a special-form solution for the conditional configuration-averaged exciting field coefficients, and is restricted to the computation of the so-called zeroth-order fields without a special treatment of the boundary regions. In this setting, we calculate the coherent fields reflected and transmitted by the layer, and the coherent field inside the layer. We found that these fields are analytically equivalent to plane electromagnetic waves, and investigated the fulfillment of the boundary conditions for the electric fields at the layer interfaces. The results are then particularized to the cases of normal incidence and a semi-infinite discrete random medium. For sparsely distributed particles, we present a self-consistent derivation of the coherent field and discuss the Twersky and Foldy approximations.