Analysis and design of periodic multi-element mmWave metasurfaces by a fast extended method-of-lines formulation

We introduce a method of lines (MoL) formulation for analyzing and designing periodic multi-element millimeter-wave (mmWave) metasurfaces (MS) in a computationally tractable manner. As the complexity of MSs increases, their analysis and especially their design using full-wave methods becomes challenging. The MoL offers a considerably faster alternative, as it is a semi-analytical method where the electromagnetic equations are solved analytically along the direction perpendicular to the MS layers and numerically on the MS plane; hence the required degrees of freedom (DoFs) are substantially decreased. We employ an extended MoL formulation, where a first-order differential equation involving both the total tangential electric and magnetic field components is solved and the transfer matrix of each layer is obtained. As a proof of concept, we analyze various MS filter supercells, varying the polarization of the incident wave and the resonator parameters. Very good agreement with finite element method (FEM) simulations is observed in all cases. By comparing the extended MoL to the FEM in terms of computational requirements, we verify that the MoL presents a considerably faster alternative for MS design. The presented analysis paves the way for the fast synthesis of optimized MSs by changing only the boundary conditions on the layer interfaces. The advantages of our method will be even more pronounced in the design of even more complex devices.