Complex-Source Beam Diffraction by an Impedance Wedge: Exact and Uniform Asymptotic Solutions, and a Phenomenological Study

We explore the problem of beam-wave scattering by an impedance wave and derive asymptotic solutions that are uniform with respect to both the observation point and the beam-axis displacement from the edge. We, therefore, introduce the new canonical problem of 2-D complex source beam (CSB) scattering by an impenetrable impedance wedge and formulate its exact Sommerfeld-Malyuzhinets (SM) spectral integral solution. We then derive a closed-form Fresnel-based uniform asymptotic solution for cases where the beam hits arbitrarily near the edge, thus exciting strong diffraction, shadow, and reflection boundary (RB) effects and possibly surface waves (SWs). The complex argument of the Fresnel functions accounts uniformly for the beam collimation and its displacement from the edge, as well as the observation points’ location with respect to the shadow and reflection transition zones. Similar expressions are derived for the SW fields. The various edge-related phenomena, the effect of losses in the surface impedance, and the beam properties are explored both analytically and numerically. The numerical examples also demonstrate the excellent accuracy and effectiveness of the asymptotic solution for all observation points compared with the numerical integration of the exact SM solution. These examples also illustrate some applications of the problem.