Perturbative solution for the scattering from multilayered structure with rough boundaries

The objective of this paper is to investigate analytically the fully polarimetric electromagnetic wave scattering and emission from a three-dimensional layered structure with N-rough interfaces in the framework of SPM method. Assuming that deviations and slopes - with respect to the reference mean plane - exhibited by rough interfaces are small enough, we firstly perform a perturbative expansion of the fields in the rough-interfaces layered structure, following the classical scheme employed to deal with a rough surface. Subsequently, by using effectively the concept of generalized reflection/transmission coefficients, the unknown expansion coefficients of scattered wave propagating upward in the upper half-space are derived via a recursive method. This approach can be also applied to the evaluation of the second-order contribution, opening the way to the accurate calculation of thermal emission from complex layered structure.