Diffraction of Electromagnetic Waves by Ribbon and Slit. I

Abstract

Rigorous solutions are presented of the problem of diffraction of plane electromagnetic waves by an infinitely thin, perfectly conducting infinitely long ribbon and by an infinitely long slit in a plane conducting screen, where the plane of incidence is perpendicular to the edge of the ribbon or slit but arbitrary angle of incidence and polarization. The unique solution satisfying the edge condition is obtained from the electric and magnetic type Hertz vectors, each of which has one scalar component, by the method of expansion in the hypergeometric polynomial. The expressions of the scattering coefficient, transmission coefficient, electric current on the ribbon, electric field in the slit, electric field at the distant place are obtained as a function of ka=2πa⁄λ.