Ultrahigh-figure-of-merit refractive-index sensing with grating-coupled magneto-optical hyperbolic metamaterials

Plasmonic refractive-index sensors provide a powerful route for label-free detection, but their performance is often limited by the trade-off between sensitivity and resonance linewidth. Here, we propose a magneto-optical hyperbolic metamaterial platform for high-resolution refractive-index sensing at the telecom wavelength of 1550 nm. The structure consists of an Au diffraction grating, a cerium-substituted yttrium iron garnet (CeYIG) magneto-optical layer, and an Ag/SiO₂ multilayer hyperbolic metamaterial. Finite-element simulations show that the grating enables efficient coupling of incident p-polarized light to bulk plasmon polariton modes supported by the hyperbolic stack. By optimizing the CeYIG layer thickness, a critical-coupling condition is achieved for the fundamental BPP₀ mode, resulting in a strongly enhanced transverse magneto-optical Kerr effect (TMOKE) response. The angular position of the TMOKE resonance exhibits a linear dependence on the refractive index of the surrounding aqueous medium, yielding an angular sensitivity of 78° RIU^-1. Owing to the narrow Fano-like TMOKE resonance, the figure of merit varies from 5720 to 9750 RIU^-1, averaging 7990 RIU^-1 over the investigated refractive-index range, with the maximum occurring at n _an = 1.335. These results indicate that grating-coupled magneto-optical hyperbolic metamaterials offer a promising strategy for compact, label-free, and high-resolution refractive-index sensing.