Electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces

Abstract—A closed-form first-order perturbative solution to the problem of electromagnetic scattering from a layered structure with an arbitrary number of rough interfaces is presented in this paper. Following the classical scheme employed to deal with a rough surface, a perturbative expansion of the fields in the rough-interface layered structure is performed, assuming that roughness heights and slopes are small enough. In this manner, in the first-order approximation, the geometric randomness of the corrugated interfaces is translated into random current sheets imposed on the unperturbed (flat) interfaces and radiating in the unperturbed (flat boundaries) layered media. The scattered field is then represented as the sum of up- and down-going waves, and a systematic approach that involves the use of matrix formalism and generalized reflection/transmission coefficients is employed. This approach permits us to avoid the necessity of the cumbersome Green function formalism. The demonstration of the consistency of the presented solution is analytically provided, showing that the proposed solution reduces to the corresponding existing ones when the stratification geometry reduces to the simplified ones considered by the other authors.