Edge currents in diffraction theory

A comparatively simple method for obtaining an asymptotic approximation to the electromagnetic field diffracted by a large aperture in a perfectly conducting, infinitely thin, plane screen is suggested. The method is based on two assumptions: first, that in some regions the scattered field is nearly the same as the field that would be generated by certain currents located on the edge of the aperture; secondly, that at any point on the edge of the aperture these currents are nearly the same as the corresponding currents for a half-plane lying in the plane of the diffracting screen, the straight edge of which is locally coincident with the edge of the aperture. In the crudest approximation the calculation is made on the basis that the half-planes are excited by the incident field alone; higher order approximations arise from a consideration of the interaction between the different parts of the edge of the aperture. Applications of the method to the cases of a plane wave normally incident on (1) a slit of infinite length with parallel straight edges, and (2) a circular aperture are considered. In the former case several terms of the asymptotic development of the transmission cross section in inverse powers of the slit width are given; in the latter case the aperture and axial fields based on the zero-order approximation which neglects interaction are compared with experimental data published by various authors and with some rigorous calculations of Andrejewski.