NUFFT for the Efficient Spectral Domain MoM Analysis of a Wide Variety of Multilayered Periodic Structures

In this paper the Method of Moments (MoM) in the spectral domain is used for the analysis of multilayered structures containing periodic arrays of either patches or apertures. The patches and apertures may have many different geometries including complex surfaces limited by two parallel lines and two arbitrary curves, circular and elliptic rings, circular and elliptic arcs, and circular and elliptic sectors. Basis functions accounting for edge singularities are used in the approximation of the electric/magnetic current density on the patches/apertures, which enables a fast convergence of MoM with respect to the number of basis functions. Since the 2-D Fourier transforms of the basis functions cannot be obtained in closed-form, these Fourier transforms are efficiently computed by means of the nonuniform fast Fourier transform (NUFFT) algorithm. Results have been obtained for frequency-selective surfaces (FSSs), and for the elements used in the design of both reflectarray and metasurface antennas. The results obtained indicate that the software based on the NUFFT is only 15% slower than the standard spectral domain MoM software used for structures in which the 2-D Fourier transform of the basis functions is analytical, and between 50 and 80 times faster than CST.