New Series Expansions for the 3-D Green´s Function of Multilayered Media With 1-D Periodicity Based on Perfectly Matched Layers

A new formalism based on perfectly matched layers (PMLs) is presented to derive new series expansions for the Green´s function of an infinite set of point sources with a 1-D periodicity embedded in a layered medium. Several PML-based series expansions, both in the spatial and spectral domains, combined with suitable convergence acceleration techniques such as the Shanks transform and Ewald transform, are proposed and their efficiency is evaluated. For each pair of excitation and observation locations, an optimal series expansion in terms of accuracy and CPU time is proposed, resulting in a significant speed-up compared to existing approaches.