On Two Alternative Uniformly Asymptotic Procedures for Analyzing the High-Frequency Diffraction of a Complex Source Beam by a Straight Wedge

Abstract

When spectral wave integrals, representing the radiation and diffraction of electromagnetic waves, are characterized by a first-order saddle point and poles in the integrand, they can usually be evaluated, in essentially closed form, at high frequencies by the leading terms of any of the two well-known alternative uniformly asymptotic procedures, namely, the Pauli–Clemmow method (PCM) and the Van der Waerden method (VWM), respectively. The PCM has the advantage that its leading terms directly yield a solution in the simple ray format of the uniform geometrical theory of diffraction (UTD). On the other hand, it is commonly noted that it is not the leading term of the PCM but that of the VWM which remains valid for the case of complex waves. Nevertheless, it is shown here that the PCM can surprisingly work even for some special complex wave cases, only if certain conditions are met. Indeed, it is demonstrated here that the PCM meets these conditions for the special case of the diffraction of a complex source beam (CSB) by a wedge. Also, the PCM directly yields a UTD like solution for this case. The latter result is significant as it provides a strong justification for obtaining a simple UTD type solution for the more general problem of the diffraction of a CSB incident from an arbitrary direction on a wedge with arbitrary curvature, directly via analytic continuation of the corresponding UTD result available for a curved wedge illuminated by a point source in real space. It is also shown that the VWM solution can be trivially cast in the UTD format, by expressing it as a sum of the PCM solution plus a UTD slopelike correction term; a similar result was obtained previously using a higher order term from a generalization of the PCM procedure given elsewhere.