Coupled mode theory for metasurface design

Efficient theoretical modeling of metasurface is highly desired for designing metasurfaces. However, most of current modeling of metasurfaces relies on full-wave numerical simulation methods that solve the Maxwell's equations. As a metasurface typically consists of many meta-units, solving Maxwell's equations is computationally expensive and thus inefficient for designing metasurface. Here, we develop a general theoretical framework for modeling metasurface based on the coupled mode theory (CMT), which fully describes the interaction between the meta-units and light by a simple set of coupled-mode equations. Consequently, the CMT formulism is far less computationally demanding than the Maxwell's equations. We show that our CMT approach allows us to quickly and efficiently optimize the design of a beam-steering metagrating. The optimal design obtained from our CMT model is further validated by numerical simulation. The proposed CMT model provides an efficient tool to model and design optical devices based on multiple optical resonators.