Acceleration of Mixed Potentials From Vertical Currents in Layered Media for 2-D Structures With 1-D Periodicity

An original acceleration procedure is proposed for the efficient calculation of the vertical components of the dyadic and scalar mixed-potential layered-media periodic Green's functions. The extraction of suitable asymptotic terms, i.e., quasi-static images, is performed in order to speed up the convergence of the relevant spectral series. This procedure, well known for planar Green's functions, is here generalized to treat the off-diagonal dyadic components and the corrective scalar potential arising from the vertical currents. The extracted terms are homogeneous-medium Green's functions due to a periodic phased array of half-plane currents, computed through a modified Ewald method, leading to a pair of Gaussian-convergent series. The highly improved convergence rate of the relevant series is shown, and the reduction of the computation time is numerically tested and discussed. The algorithm is implemented in EIGER, an open-source code based on the method of moments; several periodic structures are analyzed and fully validated through numerical comparisons. The proposed formulation has been proven very efficient, accurate, and stable.