Second-Order Volumetric-Perturbative Reciprocal Scattering Theory

The aim of this paper is to show how effective analytical treatment of electromagnetic scattering in random 3-D structures becomes viable passing through a complete reconsideration of the perturbative methodology. We propose a general formulation of the volumetric-perturbative reciprocal theory (VPRT), including up to second-order effects. This approach for scattering in random structures along with its derivation holds some remarkable properties: it is methodologically based on volumetric perturbations of the scattering medium structural dielectric properties, so encompassing both interfacial and volume inhomogeneities; its derivation is systematic, by using the reciprocity theorem, so providing meaningful reaction-based general expression for the scattering field; its results are rigorously and easily derived under the purview of distribution theory for discontinuous test functions; its physical counterpart is clear also showing the concepts and role of local and non local scattering. To elucidate the practical power of the VPRT construct, we apply it to the canonical gently rough surface case: the specific solution, which is here derived in a conceptually neat way, is fully consistent with classical second-order SPM one. Finally, the proposed VPRT construct provides a direct attitude to analytically approach a wide class of complex scattering problems that can be arranged in a perturbation framework.