van der Waals Crystal Anisotropy Controls Dual-Channel Refractive Index Sensing in a TiO$_{2}$/$\alpha$-MoO$_{3}$ Nanobar Metasurface

Filling the gap of a TiO$_2$ nanobar-pair metasurface with $\alpha$-MoO$_3$, a biaxial orthorhombic crystal, produces two high-$Q$ Fano resonances with asymmetric quality factors: $Q_{\mathrm{TE}}=87$ at 863.3 nm and $Q_{\mathrm{TM}}=31$ at 960.1 nm, separated by 97 nm.

The same device with amorphous or crystalline Sb$_2$S$_3$, both isotropic, yields comparable quality factors in both channels, confirming that the $Q$-ratio asymmetry originates in the biaxial crystal symmetry of $\alpha$-MoO$_3$ rather than the index magnitude of the fill.

The two inequivalent permittivity contrasts of the orthorhombic lattice ($\Delta\varepsilon_{\beta\gamma}=0.983$ for TE, $\Delta\varepsilon_{\alpha\gamma}=2.420$ for TM) place each channel at a different point on the $Q\propto(\Delta\varepsilon)^{-2}$ scaling curve, consistent with quasi-BIC mode character.

The TE channel delivers sensitivity $S=155.3$ nm RIU$^{-1}$, figure of merit 15.71 RIU$^{-1}$, and limit of detection $6.44\times10^{-5}$ RIU.

TM delivers $S=139.1$ nm RIU$^{-1}$, figure of merit 4.44 RIU$^{-1}$, and limit of detection $7.19\times10^{-5}$ RIU.

Simultaneous readout produces a polarization fingerprint with isotropic slope 0.896, deviations from which encode analyte optical anisotropy.