Boundary Perturbation Theory for Scattering in Layered Rough Structures

The electromagnetic wave interaction with layered structures constitutes a crucial topic of current interest in theoretical and experimental research. Generally speaking, several modelling and design problems, encountered, for instance, in SAR (Synthetic Aperture Radar) application, GPR (Ground Penetrating Radar) sensing, radar altimeter for planetary exploration, microstrip antennas and MMICs (Monolithic Microwave Integrated Circuits), radio-propagation in urban environment for wireless communications, through-the-wall detection technologies, optics, biomedical diagnostic of layered biological tissues, geophysical and seismic exploration, lead to the analysis of the electromagnetic wave interaction with multilayered structure, whose boundaries can exhibit some amount of roughness. This chapter is aimed primarily at providing a comprehensive analytical treatment of electromagnetic wave propagation and scattering in three-dimensional multilayered structures with rough interfaces. The emphasis is placed on the general formulation of the scattering problem in the analytic framework of the Boundary Perturbation Theory (BPT) developed by Imperatore et al. A systematic perturbative expansion of the fields in the layered structure, based on the gently rough interfaces assumption, enables the transferring of the geometry randomness into a non-uniform boundary conditions formulation. Subsequently, the fields’ expansion can be analytically evaluated by using a recursive matrix formalism approach encompassing a proper scattered field representation in each layer and a matrix reformulation of non-uniform boundary conditions. A key-point in the development resides in the appropriate exploitation of the generalized reflection/transmission notion, which has strong implications in order to make the mathematical treatment manageable and to effectively capture the physics of the problem. Two relevant compact closed-form solutions, derived in the first-order limit of the perturbative development, are presented. They refer to two complementary bi-static configurations for the scattering, respectively, from and through layered structures with arbitrary number of rough interfaces. The employed formalism is fully-polarimetric and suitable for applications. In addition, it is demonstrated how the symmetrical character of the BPT formalism reflects the inherent conformity with the reciprocity theorem of the electromagnetic theory. 1