Consistency and Validity of Perturbative Formulations for Scattering From Rough Multilayers

Two different perturbative approaches have been recently presented for the evaluation of scattering from layered media characterized by rough interfaces: the Boundary Perturbation Theory (BPT) and the Volumetric-Perturbative Reciprocal Theory (VPRT). These two approaches are conceptually different: They employ different strategies to provide closed-form solutions to the scattering problem, and, at first sight, they rely on different basic assumptions, so that different regimes of validity seem to be expected. In spite of that, both approaches lead to the same expression of the first-order scattered field. To solve this (seeming) incongruence, in this paper a careful theoretical analysis of basic assumptions of VPRT is carried out. This requires also considering the procedure to obtain the VPRT solution that, in this paper, is reformulated relying on a more physically sound way. The performed analysis demonstrates that, actually, basic assumptions of VPRT are equivalent to those of BPT, so that their ranges of validity are, consistently, also the same. Thus, the seeming incongruence is solved: The two theoretical constructs can be now regarded in a conceptually coherent frame.