Relationship Between High-Frequency Diffraction and Low-Frequency Scattering From a Sharp Wedge

Abstract

ABSTRACT This article describes a new relationship between the two-dimensional high-frequency and low-frequency waves scattered by an obstacle with a sharp wedge. It is shown that these two extremal waves have a unique correspondence in the underlying description of electromagnetic fields. The low-frequency field, which is given as a quasi-static field, is represented in terms of a function of complex variable z = x + iy. The high-frequency field can also be represented in terms of this complex function. The time-harmonic electromagnetic scattered or diffracted fields varying with exp(jωt) are thus bicomplex, which contains two imaginary units i and j. Basic concepts for this bicomplex calculations were discussed in the early paper. To illustrate the new solution in comparison with the exact one, the result is extended here to a half-plane diffraction known as a canonical problem. The same idea is tested to obtain a uniform solution that has no geometric-optical singularity in the far zone.