Simulation methods for large-area meta-surfaces: comparison local periodic, overlapping domains, and full wave calculations

Metasurface design is often done in one of two distinct ways: at one hand we have full wave based optimization (e.g. adjoint optimization) resulting in a rigorous solution at the expense of very long simulation times and small active areas of a few 10 μm², on the other hand is a library based approach where full wave simulation of individual meta-atoms is combined with local periodic approximation (LPA) based calculations to combine them into a large area meta-surface. The latter approach results in fast calculation and larger areas become possible (mm² to cm²) but with an approximated result. To tackle the approximation issues coming from LPA, we here analyze under which conditions the LPA is no longer valid. Overlapping domain analysis (ODA) has been proposed to improve the accuracy of simulation by accounting for neighbouring meta-atoms without requiring full wave calculation of the entire area at once. We observe specific locations where there are large discrepancies between neighbouring structure forms. Based on this result we propose a workflow for large metasurfaces: 1) LPA based design of the component, 2) ODA to locate the specific regions where LPA approximations are insufficient and 3) optimization of the specific structure on these location based on extended metaatom simulations. We compare the simulation results and calculation time of the following 3 methods: LPA, overlapping domains and full wave FDTD to determine practical areas where each method is appropriate.