Scalar Diffraction by Rectangular Apertures in a Thick Screen

Abstract

The problem of diffraction by apertures in a thin screen lends itself to a relatively simple theoretical treatment and for this reason thick screens have not been given the same attention. This paper presents a rigorous study of the case with two rectangular apertures in a thick screen. The method is based on integral relations and could be applied directly to a geometry with any number of apertures. A full vectorial treatment of such a geometry can be constructed along the same lines. In view of the need for rapidly converging methods for three-dimensional problems, considerable effort has been devoted to the study of basis functions that reproduce the singular behaviour of the field at the aperture edges. The technique presented in this article is useful for the calculation of transmission coefficients and could be refined so as to be effective for a wide range of frequencies.