Electromagnetic scattering from two-dimensional thick material junctions.

Abstract

Because material junctions are commonplace on structures whose radar cross section is of interest, it is essential that their scattering properties be adequately characterized. The standard impedance boundary condition (SIBC) has been employed in the past along with function theoretic techniques to develop simple scattering models of material junctions with thin and/or high loss slabs. To extend these models to more general slabs, generalized impedance boundary conditions (GIBC) and generalized sheet transition conditions (GSTC) have been proposed. Unfortunately, the solutions obtained with these are usually non-unique in the form of unknown constants, and although the constants have been resolved for a few special cases, previous efforts were unable to determine them in the general case. This dissertation examines the problem of the plane wave diffraction by arbitrary symmetric two-dimensional junctions, where Generalized Impedance Boundary Conditions and Generalized Sheet Transition Conditions are employed to simulate the slabs. Initially, GIBC and GSTC are constructed for multilayer planar slabs of arbitrary thickness and the resulting GIBC/GSTC reflection coefficients are compared with exact counterparts to evaluate the GIBC/GSTC. These are used to treat the plane wave diffraction by a multilayer material slab recessed in a perfectly conducting ground plane, which is formulated and solved via the Generalized Scattering Matrix Formulation (GSMF) in conjunction with the dual integral equation approach. Various scattering patterns are computed and validated with exact results where possible. Next, the problem of plane wave diffraction by a material discontinuity in a thick dielectric/ferrite slab is considered by modelling the constituent slabs with GSTC. A non-unique solution in terms of unknown constants is obtained, and these constants are evaluated for the recessed slab geometry by comparison with the earlier GSMF solution. Several other simplified cases are also presented and discussed. Finally, an eigenfunction expansion method is introduced to determine the unknown solution constants in the general case. Scattering patterns are presented for various slab junctions and compared with alternative results where possible. A short summary of this dissertation is then presented and some recommendations for future work are made.