Dielectric-Anisotropy-Induced Quasi-BIC Activation for Spatial Differentiation in All-Dielectric Metasurfaces

Quasi-BICs in dielectric metasurfaces are typically obtained through geometric symmetry breaking. Here, a 20\,nm BeS insert is placed in the gap of a symmetric TiO$_2$ nanobar pair. The anisotropy of the BeS layer ($\Delta\varepsilon \approx 0.27$) relaxes the dipole-cancellation condition and gives rise to a quasi-BIC resonance. Second-order perturbation theory predicts $Q \propto (\Delta\varepsilon)^{-2}$, and for $\Delta n \approx 0.11$ we obtain a quality factor of $Q \approx 181$. The quasi-BIC resonance gives a transfer function with a notch at $k_x = 0$ and a $180^\circ$ phase reversal, both characteristic of first-order differentiation. The transfer function is well described by the Fano model ($R^2 = 0.82$), and edge detection is illustrated using a USAF~1951 resolution chart. Unlike conventional quasi-BIC designs, where symmetry breaking is introduced through geometry, the perturbation here comes from the gap material. This enables resonance tuning through material selection while preserving the device geometry. These findings establish optical anisotropy as a practical route to quasi-BIC engineering and analog optical computing in dielectric metasurfaces.