Fast hybrid multiple scattering theory for full-wave simulation of metasurface with substrate

It is important to characterize accurately the metasurface device for the desired performance using solutions of Maxwell equations for 3D problems. In this paper, we perform a full-wave simulation of metasurfaces with thousands of scatterers above a dielectric substrate, which has not been done previously. To account for the substrate, we developed a new version of the Fast Hybrid Multiple Scattering Theory Method (FHMSTM) by combining Vector Plane Waves (VPW) and Vector Spherical waves (VSW). Transformations between VPW and VSW are used in Foldy–Lax multiple scattering equations. The results are illustrated for two examples: (i) Orbital Angular Momentum (OAM) metasurfaces and (ii) metamirror metasurfaces. We illustrate the case of 5024 silicon elliptical nanopillar scatterers above a dielectric substrate. The CPU and memory requirements are, respectively 1023.2 s and 100 Mb on a standard personal computer. This simulation was previously very difficult for commercial software.