An integral-equation method of solving plane diffraction problems

Abstract

When monochromatic electromagnetic waves with electric and magnetic vectors* E i , H i are incident on a perfectly reflecting screen S , the waves are scattered at the surface of the screen. The problem of reflexion and diffraction consists in determining the scattered field E s , H s , which satisfies the following conditions: (i) it is a solution of Maxwell’s equations i k E = curl H, i k H = — curl E, div E = 0, div H = 0; (ii) on S , (E i + E s ) x N = 0, (H i + H s ). N = 0, where N is the outward normal unit vector to S ; (iii) it satisfies Sommerfeld's radiation condition at infinity. There is only one field E s , H s which satisfies these conditions. The simplest form of the radiation condition is to assume that k = p — iq , where p and q are positive and q is small, and to require each field component to vanish at infinity. This corresponds physically to assuming that the medium has a small conductivity. The imaginary part of k can be made zero at the end of the analysis. It is important to note that a field which satisfies the radiation condition and which has no singularity anywhere in space is null.