Fast and Accurate MoM Analysis of Periodic Arrays of Multilayered Stacked Rectangular Patches With Application to the Design of Reflectarray Antennas

Abstract

Abstract-The scattering of plane waves by periodic arrays of stacked rectangular patches in multilayered substrates is a problem that has to be solved many times when designing reflectarray antennas made of those patches under the local periodicity assumption. The solution to the periodic multilayered problem has been traditionally carried out by means of the Galerkin's version of the method of moments (MoM) in the spectral domain. This approach involves the computation of double infinite summations, and whereas some of these summations converge very fast, some other converge very slowly. In this paper, the slowly convergent summations are computed by making use of an enhanced mixed potential integral equation (MPIE) formulation of the MoM in the spatial domain. This enhanced formulation is based on the interpolation of the multilayered periodic Green's functions, and on the efficient computation of the four-dimensional (4-D) integrals leading to the MoM matrix entries. Both the novel hybrid spectral-spatial MoM code and the standard spectral domain MoM code have been used for the design of a contoured beam reflectarray antenna. It has been verified that the spectral-spatial MoM code requires CPU times that are typically 30 times smaller than those required by the pure spectral domain MoM code.

Computationally efficient analysis of extraordinary optical transmission through infinite and truncated subwavelength hole arrays

“…A spectral domain approach combined with an analytical regularization of the EFIE is used in [15] for the efficient analysis of a large class of infinite periodic structures both in the resonant regime and in the extraordinary transmission regime. A different strategy is used in [16], where the authors use a hybrid spectral-spatial domain approach for the efficient solution of the EFIE arising in the analysis of multilayered infinite periodic structures with stacked metallic patches in the unit cell. In the current paper, we borrow some of the ideas presented in [16] to solve the EFIE involved in the analysis of an infinite periodic array of rectangular slots in a perfect electric conductor screen of negligible thickness.…”

“…A different strategy is used in [16], where the authors use a hybrid spectral-spatial domain approach for the efficient solution of the EFIE arising in the analysis of multilayered infinite periodic structures with stacked metallic patches in the unit cell. In the current paper, we borrow some of the ideas presented in [16] to solve the EFIE involved in the analysis of an infinite periodic array of rectangular slots in a perfect electric conductor screen of negligible thickness. Since the direct application of the pure spectral domain approach leads to the determination of double infinite summations that are slowly convergent, in this paper a pure spatial domain approach is applied to the solution of the EFIE.…”

“…where u pr and u qv are numbers that can be obtained by means of the recurrent relations (42)-(47) of [16], and where the constant coefficient C G stands for the limit…”

Method of Moments Based on Equivalent Periodic Problem and FFT with NURBS Surfaces for Analysis of Multilayer Periodic Structures

“…The proposed method exhibits a behaviour of CPU time consumption of O(N b Log10N b ) as the number N b of BFs increases. This behaviour provides significant CPU time savings with respect to the expected behaviour of O(N b 2 )provided by the direct computation of the MM matrix entries.Electronics 2020, 9, 234 2 of 18 improvements on the MM [8-10], also for multilayer periodic structures [11][12][13]. The MM is usually used to solve electric field integral equations (EFIEs) where the unknowns are the induced current densities on the metallic layout.…”

Resonantly induced transparency for metals with low angular dependence

“…Included in these are method of moments 5 and mode-matching. 6 However, the complexity of the previously cited methods makes them suitable only for modelling electrically big structures.…”