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

Abstract

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

Efficient Computation of 1-D Periodic Layered Mixed Potentials for the Analysis of Leaky-Wave Antennas With Vertical Elements

“…The numerical integration of such an integrand can effectively be performed through the ad-hoc quadrature formula described in [51].…”

“…The asymptotic behaviors of the erfc function and of the exponential grant a Gaussian decay of the integrand in each harmonic, as O e −R 2 n s 2 . The numerical integration of each integral can then be performed through the quadrature formulas described in [51]; the integration path can simply be chosen as the real axis in the complex s plane.…”

“…As in (32), all the s integrals in (33)-(38) have a Gaussian convergence along the integration line (25), as O e −R 2 n s 2 , and can efficiently be evaluated with the quadrature formula discussed in [51].…”

“…• Novel computationally efficient expressions for the 1-D periodic vertical mixed potentials and their derivatives in fully 3-D structures are derived, based on a previously proposed approach for two-dimensional (2-D) structures [51]. • The proposed formulations have been adapted to the study of all the different types of both proper and improper leaky and bound waves supported by periodic layered structures [17].…”

Accurate Equivalent-Circuit Descriptions of Thin Glide-Symmetric Corrugated Metasurfaces

“…As a consequence, conventional homogenized formulas for periodic surfaces [16] have a reduced accuracy. On the other hand, full-wave models become prohibitively time-consuming if a large structure must be simulated [17].…”