Polarization-Multiplexed Spatial Differentiation and Filtering Driven by van der Waals Birefringence

Abstract

We report that the biaxial birefringence of $\hat{I}\pm$-MoO${}_3$ can activate two spectrally distinct quasi-bound states in the continuum (quasi-BICs) within a single symmetric TiO${}_2$ nanobar-pair metasurface, with each resonance governed by a different crystallographic axis pair of the van der Waals crystal. With a full 60\,nm $\hat{I}\pm$-MoO${}_3$ gap fill, a TE resonance at 883.9\,nm ($Q=92$, Fano $q=0.090$) and a TM resonance at 923.2\,nm ($Q=31$, Fano $q=0.393$) are obtained. The Q ratio follows the inverse-square permittivity contrast, $Q\propto (\hat{I}”\epsilon {)}^{-2}$, calibrated across both polarization channels. Oblique-incidence sweeps show that the TE channel acts as a dual-null spatial highpass filter with a broadband stopband ($|H|<0.13$ for $|k_x|\le 0.63\hat{I}¼$m${}^{-1}$, $T_{\mathrm{bg}}=0.962$), while the TM channel transfers as $|H|\propto |k_x|$ ($R^2=0.94$), consistent with first-order spatial differentiation. Both operations are verified on a USAF~1951 resolution chart processed in a simulated 4$f$ framework. Channel selection is purely by input polarization angle with no structural modification.