On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen

The diffraction of electromagnetic and light waves by an aperture in a plane conducting screen is a classical boundary value problem. As is well known, theoretical analysis aims at a solution of the vector Maxwell equations, which incorporates a prescribed form of excitation and satisfies appropriate boundary conditions on the screen and in the aperture. A small measure of progress towards this objective results from the Kirchhoff diffraction theory, which identifies aperture and incident fields and arbitrarily assigns null values to the field components on the shadow face of the screen. The Kirchhoff formulation suitable for an electromagnetic field (assuming harmonic time variation) is given by Stratton and Chu [l]; this includes charge distributions on the rim of the screen to ensure that the free space fields obey the Maxwell equations. A defect in the Kirchhoff procedure is revealed by its failure to duplicate the assumed boundary values at the conducting screen. The lack of self-consistency has a further consequence that Kirchhoff predictions are qualitatively correct only if the wave length of the electromagnetic field is small in comparison with all aperture dimensions, for then the field on the shadow face of the screen is relatively small. Another method of analysis, which provides information at long wave lengths, is due to Lord Rayleigh [2]. The basic idea is that, in the vicinity of the aperture, the electromagnetic field distributions can be calculated as though the wave length were infinite, making available the results of potential theory. As an example, Rayleigh treats t,he case of a circular aperture, with normally incident harmonic plane waves [3]. After identifying the local field with that of a Hertzian oscillator, the known radiation characteristics of the latter are used to find the diffracted field a t large distances from the aperture. The tangential