Nonlocal metasurface with angle-robust high-quality-factor flat-band resonances via two-dimensional Brillouin zone folding.

High-quality (Q) factor resonances in nonlocal metasurfaces are highly desired for enhancing light-matter interactions. However, high-Q resonances typically suffer from significant wavelength shifts or Q-factor degradation with varying incident angles. Current strategies to improve angular robustness have been largely confined to one-dimensional cases and work in reflection mode. In this work, we propose a high-Q transmissive metasurface that addresses this limitation by engineering quasi-guided modes to suppress angular dispersion and Q factor degradation in the two-dimensional Brillouin zone. This is achieved through two-dimensional Brillouin zone folding, which replicates geometrically tuned flat bands from the boundary to the center, coupled with asymmetry-engineered far-field excitation. Our approach eliminates the inherent trade-off between maintaining a high Q-factor and ensuring angular stability of nonlocal resonances, demonstrating exceptional robustness: the Q-factor remains above 103 with stable resonant wavelengths and circular-polarization independence over a wide angular range of ±18° in both the x-z and y-z planes. Moreover, our design extends angle-robust high-Q flat-band spectral filtering from reflection to transmission, enabling ultra-narrowband filtering in transmission. This work paves the way for advancements in nonlinear photonics, spectroscopic sensing, and quantum sensing.