Efficient evaluation of layered medium doubly periodic Green's function

A novel approach to evaluate the doubly periodic Greens function for layered medium in matrix-friendly formulation is proposed, which takes advantages of factorization of the spectral Green's function, approximates a smooth part of it accurately, and then exploits high order asymptotic extraction techniques. The approach is fast and accurate for all ranges of distances between the source and observation points, and also allows fast frequency sweep for calculating Brillouin diagram in eigenvalue problem and for normal incidence in scattering problem. Numerical examples are presented to show the efficiency of the approach.