Converging and Diverging Beam Diffraction by a Wedge: A Complex-Source Formulation and Alternative Solutions

In a previous publication, the problem of 2-D beam diffraction by a wedge has been solved via the complex-source (CS) approach. However, the straightforward CS formulation may be applied only when the incident beam is diverging as it hits the edge, but not when it is converging as it hits the wedge. In this paper, we generalize the CS setup, so that it can address both problems. The surprising result is that the CS approach can be applied for the converging beam case, but only if the CS coordinates are defined in a specific fashion. We then formulate the angular harmonics and the spectral integral representations for both cases, and also derive uniform asymptotic expressions for beam diffraction by a wedge. The validity of the results is verified by calculating the diffracted field via each one of these formulations, and comparing them with yet another approach, wherein the field of the incident diverging or converging beam is synthesized using a plane-wave integral, and the diffracted field is then calculated via multipole expansion. The overall goal of this paper is the derivation of techniques for the analysis of 3-D beam diffraction by a cone.