A contribution to the efficient computation of multilayered periodic Green´s functions

In this paper we compare two techniques for the efficient computation of the infinite series that lead to the off-diagonal elements of the vector potential dyadic periodic Green´s function in multilayered media. It is shown that the technique based on the combined use of the generalized pencil of functions (GPoF) and Ewald´s method is the fastest technique, but is not accurate when the distance between the field point and the sources approaches zero. To avoid this problem, we present a novel technique based on the combined use of the GPoF and the spectral Kummer-Poisson´s method, which is only slightly slower than the former technique and turns out to be accurate in the whole range of distances between the field point and the sources.