▎ 摘　　要

The high quality factor of guided mode resonance (GMR) structures and their sensitivity to the adjacent media's refractive index (RI) make them excellent candidates for sensing applications. In this study, we derive analytical sensitivity equations for the GMR structures for the first time, which can be utilized to better understand and optimize their behavior. The simulated structures (based on the finite element method) show excellent agreement with the analytical sensitivities for both the transverse electric and magnetic (TE and TM) modes. The effects of waveguide height, working wavelength, and material RIs on the obtained sensitivities were surveyed, which helped achieve a design approach based on the analytical equations. The substrate RI should be as low as possible for any application. For analytes, the RI of the waveguide thin film should be low, whereas this trend is different for gas sensors; there is an optimum RI for the waveguide in the TE mode, and in the TM mode, the waveguide should have a higher possible RI. Moreover, the TM-mode gas sensors exhibit optimum sensitivity for a specified waveguide height. The design approach was used for a gas sensor operating at methane resonance wavelength (1653.7 nm), which can be tuned using a double-layer graphene sheet. A linear tunability of up to 5 nm was achieved using 1 eV chemical potential adjustment, whereas the device sensitivity remains between 291.9 to 295.5 nm/RIU. Moreover, higher sensitivities up to 950 nm/RIU can be obtained for analyte sensors at 1550 nm.