Floquet topological states in time-varying metasurfaces

Floquet systems offer a nonequilibrium periodic platform to explore previously unknown phases of matter, attracting interest in condensed matter physics, quantum physics, and photonics. Most existing research focuses on linear, closed systems subjected to spatially periodic driving. Here, we present a programmable time-varying metasurface as a platform for investigating Floquet topological states. Our findings indicate that a topological transition occurs in response to modulation frequency increases, producing anomalous edge states with chirality within Floquet harmonic bandgaps. The open nature of the metasurface facilitates harmonic generation via Floquet edge states. Experimentally, we confirm the existence of Floquet harmonic bands and the robust unidirectional propagation of these edge states. In addition, we propose a large-scale coding scheme to dynamically reconfigure propagation paths through programmable binary states of the meta-units. The system not only provides a unique platform to explore interesting physics, it can also offer opportunities for diverse applications.