Diffraction of plane waves incident on a grated dielectric slab: An entire domain integral equation analysis

Diffraction of electromagnetic waves by periodic grating waveguides is investigated by using a rigorous integral equation method, which combines semianalytical techniques and the Method of Moments with entire domain basis functions. The electric field integral equation is employed with unknown function the electric field on the grooves. This equation is subsequently solved by applying an entire domain Galerkin's technique. The proposed analysis provides high numerical stability and controllable accuracy. All the involved computations are analytically carried out, leading to an analytic solution with the sole approximation of the final truncation of the expansion functions sets. The computed results exhibit superior accuracy and numerical efficiency compared with those already derived by applying different methods. The effect of the incident field's and grating's characteristics on the diffraction process as well as the grating structure's efficient operation as a narrow band reflection filter are thoroughly investigated. The numerical results obtained provide design guidelines, which may be exploited appropriately in the development of millimeter and optical waveguide structures.