Diffraction of Electromagnetic Waves by Circular Plate and Circular Hole

Rigorous solutions are presented of the problems of diffraction of plane electromagnetic waves by an infinitely thin, perfectly conducting, circular disk and by a circular hole in a plane conducting screen. The unique solution satisfying the edge condition is obtained from the two component Hertz vector, by the method of expansion in the hypergeometric polynomial. Total scattering cross section, the transmission coefficient, electric current on the disk, electric field in the hole, and electric field at the distant place are shown in the figure as a function of k a =2π a /λ.