Aperture fields of an array of rectangular apertures

This paper presents a rigorous formulation of the boundary value problem posed by an electromagnetic wave incident upon a plane screen containing a doubly periodic array of rectangular apertures. The differential-integral equation method of Copson is employed to derive integral equations in the components of the aperture field. These are then solved approximately for normally incident plane-wave excitation. A numerical solution is obtained for square apertures which is valid over the aperture resonance region,
kd \approx 1.5
. Values of scattering cross section and plots of the aperture field are presented for aperture sizes larger, smaller, and near resonant dimensions. The effect of singularities of the aperture field near the edges is discussed.