Methods for the accelerated computation of Green´s functions with 2-D periodicity in layered media

A review of some recent methods for the efficient computation of two-dimensional (2-D) periodic Green´s functions in layered dielectric media is presented in this contribution. 2-D periodic vector and scalar mixed-potential Green´s functions for a multilayered environment are derived in the spectral domain first, and then the corresponding spatial-domain quantities are obtained through an efficient sum of spatial harmonics. Numerical acceleration techniques are performed by extracting slowly-converging and singular terms. Kummer-Poisson´s formula and Ewald¿s transformations are applied when the sum of the extracted terms is added back and a comparison is performed, which shows the efficiency of the proposed methods for this kind of problems.