A coupled-mode-theory formulation for periodic multi-element metasurfaces in the presence of radiation losses

We derive a coupled-mode theory (CMT) formulation for the fast analysis of periodic multi-element metasurfaces in the presence of radiation losses. Full-wave simulations of periodic multi-element metasurfaces are very time- and memory-consuming, especially as the size and complexity of the metasurface increase. The CMT formulation provides a considerably faster and efficient alternative. It results in a small system of equations with size equal to the number of supported resonator modes in the frequency range of interest, allowing to calculate the resonator mode amplitudes and, consequently, the metasurface response. Subsequently, we systematically derive analytical closed-form expressions for the coupling coefficients between two weakly coupled resonators in the presence of radiation losses and incorporate them into the CMT model, which is found important for the accurate description of the metasurface, while also providing insight into the underlying physics of complex metasurfaces. We validate the proposed formulation on benchmark examples of both metal- and dielectric-based metasurface absorbers (MSAs) by comparing the CMT results to spectral FEM simulations of the composing supercell. To further demonstrate the potential of the proposed formulation, as a proof of concept, we use the CMT to synthesize a larger optimized periodic multi-element MSA. A comprehensive comparison to full-wave FEM simulations of the composing supercell is included in terms of time and computational requirements, which shows that our method provides a valuable and efficient alternative solver for synthesizing complex metasurfaces.