Anti-aliased metasurfaces beyond the Nyquist limit

Sampling is a pivotal element in the design of metasurfaces, enabling a broad spectrum of applications. Despite its flexibility, sampling can result in reduced efficiency and unintended diffractions, which are more pronounced at high numerical aperture or shorter wavelengths, e.g. ultraviolet spectrum. Prevailing metasurface research has often relied on the conventional Nyquist sampling theorem to assess sampling appropriateness, however, our findings reveal that the Nyquist criterion is insufficient guidance for sampling in metasurface. Specifically, we find that the performance of a metasurface is significantly correlated to the geometric relationship between the spectrum morphology and sampling lattice. Based on lattice-based diffraction analysis, we demonstrate several anti-aliasing strategies from visible to ultraviolet regimes. These approaches significantly reduce aliasing phenomena occurring in high numerical aperture metasurfaces. Our findings not only deepen the understanding in phase gradient metasurface but also pave the way for high numerical aperture operation down to the ultraviolet spectrum. Sampling is a key for metasurface design but causes aliasing at high numerical apertures or short wavelengths. The authors identify appropriateness of the Nyquist criterion and propose anti-aliasing strategies for metasurface design.