Floquet-Bloch Theory for Dispersive Time-varying Metasurfaces

Abstract

Light-matter interaction in time-varying metasurfaces brings about phenomena that transcend the limits of static systems. Temporal modulation enables energy exchange between light and matter, and electromagnetic fields are coupled in both momentum and frequency, with implications across a broad range of photonic applications. Nevertheless, a precise description of such systems necessitates a theory that captures the intertwined effects of spatiotemporal variations while accounting for dispersion in a causal manner, as realistic optical materials exhibit frequency-dependent response and finite temporal memory. Here, a self-contained Floquet-Bloch theory is developed to capture the response of dispersive, time-varying metasurfaces, respecting causality through physically consistent constitutive relations. The theory treats spatial periodicity, nonadiabatic temporal modulation, and material dispersion within a unified formalism, providing access not only to the metasurface's scattering response but also to its inherent modal structure. The formulation is validated against full-wave simulations. As illustrative examples, it is first applied to asymmetric Floquet harmonic generation in an excitonic time-varying metasurface, where excitonic dispersion enables selective harmonic enhancement. It is then used to investigate metasurface-based photonic time crystals, revealing how modal dispersion governs momentum-bandgap formation and dynamics. This work establishes a comprehensive platform for understanding dispersive, time-varying metasurfaces and their underlying physical mechanisms.