Efficient calculation of Green´s functions for periodic arrays using a new asymptotic extraction technique

The goal of this paper is to extend the effective approach that is used for the calculation of Green´s functions (GFs) in planar multilayered structures for a single dipole to the case of a periodic array of dipoles. In both cases the GFs in the spatial domain are calculated via a Fourier transform of the GFs in the spectral domain, which is known in closed form. The transform is expressed in terms of double infinite integrals for a single dipole or a double infinite series for a periodic array. The direct calculation of the transform is not always very efficient. A possible solution consists in the introduction of special asymptotes that annihilate the problematic behavior of the spectral GFs. We demonstrate that it is possible to use the same asymptotes very efficiently in both cases (for a single dipole and a periodic array).