Diffraction from a small square aperture:approximate aperture fields

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Abstract
An approximate solution is presented that represents the first three terms in a more general expansion for the aperture electric field in a single, small square aperture (2a × 2a, ka « 1) in a thin, perfectly conducting plane screen illuminated by a normally incident, linear polarized plane wave. The solution is motivated by physical intuition and the solutions for circular apertures and slits. Copson’s integrodifferential equation formulation [Proc. R. Soc. London Ser. A 202, 277 (1950)] of the boundary-value problem applied to small apertures is used to investigate the validity of the solution. Numerical calculations show that the solution for the dominant component of the electric field is valid over most of the aperture; its validity is in doubt in the close vicinity of the corners of the aperture. Higher-order terms are needed to describe the field accurately in this region.