International Symposium on Antennas and Propagation
Diffraction by Composite Wedge Composed of Perfect Conductor and Lossy Dielectric: Physical Optics Solution
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One of canonical structures in high-frequency electromagnetic scattering problems is penetrable wedge. In this paper, we present the physical optics (PO) solution to the E-polarized diffraction by a composite wedge consisting of perfect conductor and lossy dielectric. This diffraction problem is formulated into the dual integral equations . Using the modified propagation constants for non-uniform plane wave transmission through conducting media , one may obtain an analytic expression on the geometrical optics (GO) field including multiple reflections inside the lossy dielectric part. Replacing the exact field by the GO field on the boundaries of the composite wedge generates the PO field, which is expressed by an asymptotic integral of the PO diffraction coefficients. And the corresponding PO diffraction coefficients are expressed by a finite series of cotangent functions. Deforming the integral path into the SDP (steepest decent path) , one may express the PO field by sum of the GO and the edge-diffracted fields. One may find the one-to-one correspondence  between the ordinary rays of the GO field and the cotangent functions of the PO diffraction coefficients. Hence the PO diffraction coefficients of the composite wedges can also be constructed in the same analytic form by employing only the ray-tracing data. But it is well recognized that the PO diffraction coefficients cannot satisfy the boundary condition at wedge interfaces and the edge condition at wedge tip. According to the formulation of the dual integral equations, the error posed in the PO solution can be checked by showing how closely the PO solution satisfies the null-field condition in the complementary region . For a typical case, the PO diffraction coefficients and field patterns are plotted here.