Complex-mode-volume perturbation theory for frequency-agile terahertz sensors

We derive a first-order perturbation formula that links the complex eigenfrequency shift of terahertz resonator-based sensors directly to its complex mode volume V~c. This closed-form expression simultaneously captures the resonance shift, the linewidth change, sensitivity, and figure of merit, and remains valid across a wide range of resonator types by accounting for both the real (confinement) and imaginary (leakage) components of 1/V~c. Full-wave eigenfrequency simulations of a high-Q photonic-crystal cavity and a low-Q split-ring resonator confirm that the model accurately predicts the complex-frequency shift and sensing performance. In contrast, the conventional real-volume approximation ignores linewidth variation and, therefore, fails in low-Q or strongly radiative systems, significantly underestimating sensitivity. The complex-mode-volume framework, thus, offers a unified and quantitative basis for designing and optimizing open terahertz sensors, revealing the trade-offs between field confinement and radiative loss that ultimately limit detection performance.