On the efficient computation of the Green’s function for doubly periodic structures by using the Kunmer’s method of higher orders

Abstract

An auxiliary function in the form of standing spherical waves with attenuation is proposed in the Kummerpsilas method for accelerating the convergence of the spectral series representing the Greenpsilas function of doubly periodic structures in free space. Expressions for the amplitude and phase constants of the auxiliary waves versus their attenuation constant are derived, at which the spectral difference series converges in the worst case as the Floquet mode propagation constant in the power of minus 5, 9, and 13 for the cases of using one, two, and three auxiliary waves, respectively.