Semi-analytical approach for refractive index sensors based on reflective metasurfaces

We present a semi-analytical approach for the analysis and design of refractive index sensors based on metal-insulator-metal (MIM) metasurfaces. While numerical methods require extensive calculations for all values of geometrical parameters, the semi-analytical approach provides straightforward guidelines for a design of optimal metasurfaces with maximized sensitivity. Semi-analytical formulas for refractive index sensitivities are derived from equations of the temporal coupled mode theory and standing-wave resonance model. They require three numerically calculated parameters (resonant frequency and radiative and non-radiative decay rates of the resonant mode), obtained by the fitting of reflectance spectra. Generality of the presented approach allows us to consider the operation of metasurface sensors in three different interrogation methods: spectral (frequency), intensity (reflectance), and phase. Validity of the proposed approach is confirmed by a good agreement with numerical results. Starting from semi-analytical formulas, we derive working frequencies of metasurface based sensors, prove that the critical coupling with equal decay rates of the resonant mode is the optimal working regime, and demonstrate that optimal MIM metasurfaces should have periods as large as possible with the thickness of MIM cavities determined by the critical coupling condition. (C) 2021 Optical Society of America