Momentum-resolved Floquet spectroscopy on curved-time metasurfaces

Periodic temporal modulation and geometric curvature represent powerful but largely independent mechanisms for reshaping optical dispersion. No previous platform has engineered Floquet quasi-energy surfaces using a spatially structured temporal curvature field. This work demonstrates a metasurface/SAW platform where polarization and temporal modulation reshape Floquet bands and Berry curvature in k-space, enabling momentum-resolved control of quasi-energy gaps. In this regard, a polarization-encoded holographic metasurface that unifies Floquet light dressing, non-Hermitian mode coupling, and curvature-driven temporal potentials within a single platform has been introduced in this study, to the best of our knowledge, for the first time. Spatially structured polarization fields imprint momentum-dependent holographic phases that sculpt the Floquet interaction landscape, enabling valley-selective hybridization and anisotropic quasi-energy gaps. Simultaneously, surface-acoustic-wave-induced Gaussian acceleration fields generate a tunable lapse function Λ(x) that renormalizes the local clock rate, opening geometric Floquet gaps and producing Berry curvature originating purely from engineered temporal geometry. Using momentum-resolved temporal interferometry and Fourier-plane spectroscopy, curvature-modified Floquet splittings are directly visualized across k-space, and experimentally accessible gaps of 0.1-1 THz are predicted on graphene and ZnO metasurfaces. These results establish holographically encoded curved-time metasurfaces as a reconfigurable platform for shaping photonic quasi-energy bands, enabling momentum-selective optical logic, topological steering, and geometry-driven Floquet photonics.