International Symposium on Antennas and Propagation
An approximate UTD ray solution of an oblique EM wave diffraction at a junction between two different thin planar material slabs on ground plane
Titipong Lertwiriyaprapa, Prabhakar H. Pathak, John L. Volakis,
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In this paper, it is of interest to extend the normal incidence solution as discussed in  in order to treat the more general case of skew (or oblique) incidence (three-dimensional 3-D). Plane wave (for oblique or skew incidence) and spherical wave illumination are considered here. The geometry of the problem is shown in Fig. 1(a). Previous works dealing with the analytical solutions via the Wiener-Hopf (W-H) solution to diffraction by a junction between two different thin planar material slabs on a perfect electric conductor (PEC) ground plane [2, 3] generally replace the original coated metallic surfaces or material slabs by approximate impedance boundary condition. The latter approximation allows one to arrive at a rigorous analytical solution to the resulting approximate problem configuration. These previous works primarily address the scattering problem in which the illumination is a uniform plane wave that is incident on the thin material discontinuity. In contrast, the present work is expected to be very useful not only to the analysis of scattering situations but also to antenna problems which are equally importance from a practical standpoint. Unlike W-H solution, the solutions developed in this work recover the proper, local plane wave Fresnel reflection and transmission coefficients (FRTCs), and surface wave constants, respectively, for the actual material, and they also allow the material to be both double positive (DPS) or double negative (DNG). DPS materials are those which exhibit positive values of electrical permittivity and permeability while DNG materials are supposed to exhibit negative values for these quantities. The present works provides solutions for finite sources on or near such structures. In addition, it is important to note that the expressions present in this paper are appropriately approximated via physical reasoning so that they can be made free of the complicated integral forms of the W-H split (or factorization) functions.