Quasi 3-D Mixed Potential Integral Equation Formulation for Periodic Structures

This paper introduces the use of the quasi 3-D mixed potential integral equation formulation for structures with a periodicity in two dimensions. The quasi 3-D formulation allows to use both horizontal and vertical conductors, and dielectric inclusions. The key innovation is the use of an effective algorithm to calculate Periodic Green´s Functions (PGFs) for vertical currents in the planar multilayered background medium. This algorithm retains the same scheme as for a single source Green´s Function (GF). In both cases, the GFs are calculated via an inverse Fourier transform of the GFs in the spectral domain, which are known in closed form. In order to remedy the poor convergence for small source-observation distances, an asymptotic extraction is used, yielding a very compact algorithm, and acceleration techniques are applied. Simple guidelines are proposed to construct asymptotes having the required leading terms and a good convergence. It is shown that many acceleration algorithms widely used in literature are actually able to perform well only in specific circumstances. As far as the authors can see, there is still no general and robust technique, yielding highly accurate results under all circumstances. Several examples illustrate the efficiency of the technique.