Diffraction of electromagnetic waves by a right-angled dielectric wedge

Abstract

The diffraction of electromagnetic waves by a dielectric wedge is important in the geometrical theory of diffraction as a canonical problem of edge diffraction, and in various application fields such as radar reflections from dielectric bodies, tapered dielectric antennas, dielectric waveguide matching and dielectric resonators. Rigorous asymptotic diffracted waves from a right-angled dielectric wedge with an arbitrary dielectric constant are obtained for the case of plane wave incidence when the incident electric field vector is polarized parallel with the edge of the wedge. The scattered field is approximated by the physical optics approximation, and its correction term may be derived to satisfy a dual series equation. The physical optics approximation of the scattered field is calculated by approximating the electric field on the interface by those of half space dielectric problem in the absence of the other interface, which gives reflected and refracted waves from the interface, and an edge diffracted cylindrical wave. It is found that the correction field may be interpreted as a cylindrical wave emanating from an unknown line source located at the edge of the wedge. The correction field is then expressed asymptotically in terms of the multipole expansion series and its expansion coefficients are derived to satisfy the dual series equation in which source terms are obtained from the edge diffracted field in the physical optics approximation. Multipole expansion coefficients may then be calculated numerically. Corrected rigorous asymptotic edge diffracted fields are expressed by the Sommerfeld integrals with well defined integrand function, calculated from the numerically derived expansion coefficients, and its asymptotic expressions are shown. It is shown for this solution that the boundary conditions are satisfied exactly for the geometrically reflected and refracted waves by the dielectric interfaces and asymptotically for the edge diffracted cylindrical ...