Gap-engineered four-spiral terahertz metamaterial absorber for ratio-based self-referenced refractive-index sensing

Abstract

A gap-engineered four-spiral terahertz (THz) metamaterial absorber is proposed for multi-mode, self-referenced refractive-index sensing using a normalized ratio-based readout. The unit cell consists of four square-spiral Au resonators arranged in a 2 × 2 configuration on a low-loss PTFE substrate backed by a continuous Au ground plane. By assigning different inner and outer capacitive gaps to otherwise identical resonators, four well-separated absorption modes are obtained at 1.150, 1.720, 2.360, and 3.080 THz, with absorption amplitudes of 91%, 98%, 95%, and 88%, respectively. These modes are functionally assigned as reference, primary sensing, secondary sensing, and auxiliary monitoring resonances. For analyte refractive indices from n = 1.0 to n = 1.8, Mode 2 provides the strongest sensing response, with a sensitivity of 180 GHz/RIU, a quality factor of 33.1, a figure of merit of 3.46 RIU −1 , an estimated limit of detection of 0.0056 RIU for a 1 GHz frequency-extraction uncertainty, and a dynamic range of 0.8 RIU. To improve reliability, the differential response ∆ f sr = f 2 − f 1 and the normalized ratio response R sr = f 2/ f 1 are introduced using Mode 2 as the sensing resonance and Mode 1 as the internal reference. The corresponding differential and ratio sensitivities are 150 GHz/RIU and 0.120 RIU −1 , respectively. Quantitative error and robustness analyses show that R sr suppresses common multiplicative frequency-axis drift and improves stability under correlated perturbations, including TE/TM oblique incidence, gap deviation, substrate-thickness variation, material-permittivity variation, and lateral misalignment. An equivalent RLC model reproduces the full-wave resonance frequencies with errors below 0.5%, supporting the LC-type interpretation of the gap-engineered modes. Although the study is simulation-based, fabrication feasibility and a reflection-mode THz-TDS validation route are discussed. These results indicate that gap-induced modal separation combined with ratio-based normalization provides a compact and robustness-oriented platform for THz refractive-index sensing.