Accurate and Efficient Computation of Layered Medium Doubly Periodic Green´s Function in Matrix-Friendly Formulation

This communication proposes a novel approach to evaluate the doubly periodic Green´s function for layered medium in matrix-friendly formulation. Several techniques, including factorization of the Green´s function, generalized pencil of function method and high order Taylor expansion, are employed in a delicate manner to derive the high order asymptotic expressions, which are then evaluated by new fast convergent series derived from Ewald transformation. This approach delivers fast and highly accurate results as well as high order convergence, and also allows fast frequency sweep for calculating Brillouin diagram in eigenvalue problem and for normal incidence in scattering problem.