A new approach to the electromagnetic diffraction problem of a perfectly conducting half-plane screen

It is well known that the magnetic vector potential of an electromagnetic (EM) field incident upon a perfectly conducting thin plate satisfies, on the plate, an inhomogeneous Helmholtz equation. Rahmat-Samii, Mittra et al., and also Wilton and Dunaway applied this fact to the numerical solution of the thin-plate EM diffraction problem, using a modified version of the electric field integral equation. They pointed out that the Helmholtz equation alone determines the vector potential on the plate only up to an unknown term which expresses the coupling of the current-density components, which is due to the influence of the edge of the plate. It is demonstrated that their method is applicable in the theoretical analysis of some EM plate diffraction problems as well. The method will be applied, in combination with the Wiener-Hopf method, to reproduce the well-known solution of the classical problem of diffraction of plane electromagnetic waves by perfectly conducting half-plane screens. This approach can be done directly in vector form for general, three-dimensional incident waves. The result is applied to the discussion of grazing incidence.