Efficient interpolation of mixed-potential periodic green’s functions in layered media

In the study of infinite periodic printed structures through the Method of Moments (MoM), the computational domain can effectively be reduced to a single unit cell by applying the Floquet-Bloch theorem. As a main drawback of this approach, several quantities of interest, such as the impedance-matrix elements or the Periodic Green’s Functions (PGFs) are expressed through extremely slow converging series. In a stratified medium a Mixed-Potential Integral Equation (MPIE) formulation in the spatial domain is very convenient to analyze planar structures (whose metalization is orthogonal to the direction of stratification). In order to be very efficient, however, the accelerated numerical computation of spatial-domain PGFs for the scalar and vector potentials in multilayered media is required. A solution to this problem consists in the pre-calculation of PGFs for a finite number of points within a unit cell and then in the use of interpolation algorithms. The interpolation procedure can be optimized by carrying out an appropriate regularization of the involved Green’s functions. This leads to a minimal number of pre-calculated points provided that the interpolation basis functions are correctly chosen. The Source Point (SP) is expected to be the most critical point that mines the regularity of the PGFs in the unit cell. Hence, the PGFs regularity in the SP will limit the degree of regularity of the basis functions. This paper aims to present a new regularization of PGFs in layered periodic planar problems, leading to an efficient interpolation procedure.