Dispersion Curve Calculation Using the Method of Moments: The Impact of Macro Basis Functions

The Method of Moments (MoM) is a powerful tool for computing the dispersion curves of open and possibly lossy structures. However, the brute-force computation of the dispersion curves associated to a 2D periodic structure using the MoM can be computationally intensive. One way to accelerate the computation is to reduce the number of unknowns used to model the periodic structure using Macro Basis Functions (MBFs). However, using MBFs to compute dispersion curves may seem counter-intuitive, since MBFs are usually obtained from the response of the structure to various excitations, while the dispersion curves are the excitation-free homogeneous solution to Maxwell's equations. In this paper, we investigate the error introduced by the use of MBFs when computing the dispersion curves of printed periodic structure on a layered substrate. We study both the impact of the selected set of excitations used to build the MBFs and, for a given set of excitations, the impact of the number of MBFs used to model the printed patches. From the obtained results, practical rules are proposed for metasurface-type periodic array of printed patches.