An integral-equation method of solving plane diffraction problems

Abstract

When monochromatic electromagnetic waves with electric and magnetic vectors* Ei, Hiare incident on a perfectly reflecting screenS, the waves are scattered at the surface of the screen. The problem of reflexion and diffraction consists in determining the scattered field Es, Hs, which satisfies the following conditions: (i) it is a solution of Maxwell’s equationsikE = curl H,ikH = — curl E, div E = 0, div H = 0; (ii) onS, (Ei+ Es) x N = 0, (Hi+ Hs). N = 0, where N is the outward normal unit vector toS; (iii) it satisfies Sommerfeld's radiation condition at infinity. There is only one field Es, Hswhich satisfies these conditions. The simplest form of the radiation condition is to assume thatk=p—iq, wherepandqare positive andqis 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 ofkcan 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.