Efficient computation of periodic Green’s functions for printed structures with vertical elements

The vertical components of the mixed-potential Green’s functions due to one-dimensional (1-D) or bidimensional (2-D) phased array of dipoles in a layered medium are computed through suitable homogeneous-medium asymptotic extractions from the standard spectral series of Floquet’s harmonics. The extracted terms can be expressed as potentials for a 1-D or 2-D array of half-line sources. Their computation requires a suitable modification of the Ewald method, thus resulting in new modified spectral and spatial series, having Gaussian convergence even in the case of complex modes and improper harmonics. Numerical comparisons have been performed to validate the proposed acceleration technique.