Sensitivity and Figure-of-Merit Analysis of Terahertz Metamaterial Sensors With the Normalized Mode Volume

The sensitivity and figure of merit (FOM) of optical sensors based on metamaterial (MM) cavities are intricately influenced by both inherent cavity properties (resonance frequency, Q-factor, and mode volume) and the characteristics of the analyte, including its volume and spatial distribution. Notably, a direct correlation between a physical parameter and sensor performance, as well as a quantitative comparison across diverse optical sensors, is currently lacking. This study proposes a novel approach to evaluating the sensitivity and FOM by introducing a normalized (dimensionless) mode volume, denoted as $V_{N}$ . This normalization enables a direct and comprehensive comparison among various sensor structures, with MM sensors employing split resonators featuring interdigitated fingers in the terahertz (THz) frequency range serving as a prime example. The normalized sensitivity and FOM demonstrate a proportional relationship to 1/ $V_{N}$ and $Q/V_{N}$ , respectively. Through systematic analyses involving the variation of geometric parameters, the full-wave simulation results consistently validate the proposed analytical formula. These overarching findings not only lay a robust foundation for the design and optimization of optical sensors utilizing MMs but also provide a framework for a comprehensive performance comparison among different sensor types. This was experimentally verified with a proposed nested U-shaped sensor in comparison with the traditional sensor based on asymmetrical double split ring resonators. This advancement holds significant promise for applications in nanoscale thin-film detection and biosensing.