Dual series solution to the scattering of plane waves from a binary conducting grating

The problem of scattering of electromagnetic waves from a perfectly conducting grating with a periodic groove structure is considered. A system of dual series equations is derived by enforcing the electromagnetic boundary conditions; this leads to a boundary-value problem that is 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 makes it possible to obtain analytical results, even where other numerical methods, such as the mode-matching method and spectral iteration methods, are numerically unstable. Consideration is also given to 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 results from the mode-matching method and the spectral-iteration method are also presented