A comparative investigation of the surface radiation condition in electromagnetics

Abstract

This paper assesses a vector surface radiation condition (SRC) in electromagnetics by reference to a canonical problem, namely the scattering of waves by a perfectly conducting sphere. The method furnishes two coupled differential equations for the tangential components of the surface field and so the calculation of the scattered field is reduced to a quadrature. The differential equations are first solved exactly and the distant scattered field is determined analytically. Later, to examine the effect of introducing a high frequency asymptotic expansion the solutions are constructed approximately. Comparisons are made between the exact answer of the problem, the SRC solutions, and the physical optics (PO) approximation. It is observed that, although the SRC method is essentially a high frequency method, it produces surprisingly good results for lower frequencies. In the high frequency range the method is superior to PO approximation and also the combination of the SRC and high frequency perturbation expansion yields better results than PO.