Polarization-Robust and Electrically Tunable Quasi-Bound States in the Continuum in C4-Symmetric Terahertz Metasurfaces for Refractive-Index Sensing

Polarization sensitivity and limited tunability remain important challenges for high-Q terahertz (THz) metasurfaces based on quasi-bound states in the continuum (q-BICs), particularly when geometric perturbations are introduced to enable radiative coupling. Here, we numerically demonstrate a graphene-integrated all-dielectric THz metasurface that combines high-Q q-BIC resonances, polarization robustness, electrical tunability, and refractive-index sensing through a C4-symmetric supercell design. Each metamolecule consists of two orthogonal amorphous-silicon strips, in which a width perturbation δ introduces local geometric asymmetry and enables the symmetry-protected states to couple to free space, while the four metamolecules related by successive 90° rotations preserve the global C4 rotational symmetry. Two q-BIC modes are supported, with their Q factors exhibiting the characteristic inverse-square dependence on δ. Multipolar analysis reveals that the lower-frequency q-BIC is dominated by magnetic-quadrupole radiation, whereas the higher-frequency mode is primarily governed by toroidal-dipole radiation and exhibits weaker overall radiative leakage. Owing to the C4-symmetric arrangement, the resonance spectra remain nearly invariant for normally incident linearly polarized THz waves over polarization angles from 0° to 90°. Integration of monolayer graphene further enables continuous electrical modulation of the resonance contrast and Q factor by varying the Fermi level from 0 to 0.7 eV, while inducing only minor resonance-frequency shifts. For bulk refractive-index sensing, the two q-BIC modes achieve sensitivities of 345 and 475 GHz/RIU, with maximum figures of merit exceeding 800 and approaching 104, respectively. These results provide a versatile strategy for integrating polarization-robust high-Q resonances, electrical reconfigurability, and high-performance refractive-index sensing in THz metasurfaces.