Plane Wave Diffraction by Arbitrary-Angled Lossless Wedges: High-Frequency and Time-Domain Solutions

This paper concerns the diffraction phenomenon originated by a uniform plane wave impacting an arbitrary-angled lossless dielectric wedge with planar surfaces. The high-frequency diffraction coefficients are obtained by performing uniform asymptotic evaluations of the radiation integrals resulting from the physical optics approximation of the electric and magnetic equivalent surface currents located on the inner and outer faces of the wedge. The final expressions are in closed form and contain the standard transition function of the uniform theory of diffraction and the Fresnel reflection and transmission coefficients related to the geometrical optics propagation mechanisms. Moreover, they allow a simple physical interpretation of each contribution and they are easy to use and to implement in a computer code. The knowledge of such diffraction coefficients in the frequency domain permits to apply the inverse Laplace transform to obtain the time-domain counterparts, which enable the evaluation of the transient diffracted field originated by an arbitrary function plane wave.

I. Introduction

Asymptotic methods based on ray tracing are more attractive and efficient than numerical techniques when solving high-frequency scattering problems. This statement is well known to researchers and electromagnetic (EM) engineers working on radio planning, analysis and design of antennas, through-wall building imaging, and so forth. Their activities usually benefit from the use of the geometrical theory of diffraction [1] and its uniform theory of diffraction (UTD) version [2], which describe the EM wave propagation in terms of incident, reflected, transmitted, and diffracted rays. Such ray-based methods allow one to solve a large number of real scattering problems by using the solutions of a reduced number of simple canonical problems. Moreover, they provide physical insight into the radiation and scattering mechanisms arising from the various parts of the structure. Unfortunately, the applicability of ray-based methods to penetrable structures suffers from the absence of a closed-form exact solution to the canonical diffraction problem involving a dielectric wedge. This is a challenging problem and the boundary conditions matching at the wedge interfaces represent an obstacle to solve it. Several analytical and heuristic approximate solutions have been proposed in the past few decades, as well as procedures combining analytical and numerical techniques for solving the diffraction problem in an exact sense. Although of great interest from theoretical viewpoint, some of them have limited applicability owing their low computation efficiency. Representative studies on diffraction by dielectric wedges are reported in [3]–[18].