PERTURBATION THEORY FOR ELECTROMAGNETIC WAVE SCATTERING IN RANDOM LAYERED STRUCTURES

Abstract

The problem of electromagnetic wave scattering in 3-D random layered structures, is analytical treated by relying on original results of the Boundary Perturbation Theory (BPT) and Volumetric-Perturbative Reciprocal Theory (VPRT), whose structured presentation of the pertinent theoretical body of innovative results is proposed and developed in this thesis. The systematic formulation of Boundary Perturbation Theory (BPT) is here introduced to deal with the analysis of a layered structure with an arbitrary number of gently rough interfaces: in this case the proposed theoretical construct is based on a suitable perturbation pertinent to the geometry of the problem and the scattering problem is treated by adopting a proper perturbation of boundary conditions. Specifically, it is demonstrated that, in the first-order approximation, BPT leads to fully polarimetric, formally symmetric and physical revealing closed form solution: the relevant innovative scattering models obtained in this perturbation framework permit to deal with bistatic scattering, from and through three-dimensional layered structures with an arbitrary number of gently rough interfaces. Furthermore, Volumetric-Perturbative Reciprocal Theory (VPRT) is also formulated in this thesis. VPRT methodologically adopts a different approach, which is based on two key elements: the use of the Reciprocity Theorem and an appropriate description of the scattering structure in terms of space-variant volumetric perturbation of the dielectric constant distribution. The VPRT construct also provides meaningful reaction-based expressions for the scattering field, which are straightforward and rich in descriptive power. It is important to emphasize that VPRT, which is methodologically conceived to consistently treat both interfacial and volumetric random inhomogeneities (so providing a unified mathematical formulation and conceptual understanding of two inherent scattering mechanisms), is also fully consistent with the results of BPT. Accordingly, within VPRT framework, both rough-interface and volume scattering are take into account methodologically. Furthermore, within this new theoretical framework, a new look at the classical SPM solution for rough surface is also offered: even such a specific solution (whose derivation hitherto obtained via unnecessary, involved and obscure algebraic manipulations) is derived a surprisingly simple way, clarifying all the same the lacking inherent physical meaning. Beyond a certain compactness of the pertinent closed-form solutions, the fundamental scattering interactions can be revealed, gaining a coherent explanation and a neat picture of the physical meaning of the proposed theoretical constructs. In fact, it is important to note that a deep comprehension of the physical phenomena involved in the electromagnetic wave scattering interaction with such kind of complex structures would have been a rather hopeless task before the introduction of these theories. Finally, it is noteworthy that this theoretical body of results enables a new way to systematically construct meaningful and general expressions for the scattering field pertinent to wide class of scattering configurations, involving complex structures that can be arranged in a perturbation framework, and it is successful in that it exhibit: conceptual clearness, descriptive power and general applicability to random layered structures.