Dual Series Solution to the Scattering of Plane Waves from a Binary Conducting Grating

The problem of scattering by electromagnetic waves from a perfectly conducting grating with periodic groove structure is considered. A system of dual series equations has been derived by enforcing the electromagnetic boundary conditions; this leads to a boundary value problem that is successfully solved. The mathematics leading to the solution of the dual series system is derived from the equivalent Riemann-Hilbert problem in complex variable theory and its solution. The solution converges absolutely and allows one to obtain analytical results, even where other numerical methods, such as the mode-matching method and the spectral iteration method, are numerically unstable. As most papers consider only diffraction efficiencies in the grating problems, we are also interested in the relative phase values for the diffracted fields. The phase differences between the scattered fields resulting from two orthogonally polarized incident plane waves can be explicitly determined for any incidence angles and for any groove dimensions. Comparisons with the results from the mode-matching method and the spectral-iteration method are also given.