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

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.