Coupled waveguide model for computing phase and transmission through nanopillar-based metasurfaces

Dielectric metasurfaces are important in modern photonics due to their unique beam shaping capabilities. However, the standard tools for the computation of the phase and transmission through a nanopillar-based metasurface are either simple, approximating the properties of the surface by that of a single cylinder, or use full 3D numerical simulations. Here we introduce a new analytical model for computing metasurface properties which explicitly takes into account the effect of the lattice geometry. As an example we investigate silicon nanopillar-based metasurfaces, examining how the transmission properties depend on the presence of different modes in the unit cell of the metasurface array. We find that the new model outperforms the isolated cylinder model in predicting the phase, and gives excellent agreement with full numerical simulations when the fill fraction is moderate. Our model offers a waveguide perspective for comprehending metasurface properties, linking it to fiber optics and serving as a practical tool for future metasurface design.