Multiple topological phase transitions in Floquet hexagonal photonic lattices

A three-step quenched honeycomb photonic Floquet topological insulator is constructed by simulating quantum system driven by periodic Hamiltonian. The system consists of a two-dimensional microring lattice, which we map to an equivalent waveguide array with periodic boundary conditions. We explicitly derive the Floquet–Bloch Hamiltonian and propose a general approach for generating flat bands in Floquet systems, identifying key topological invariants that satisfy bulk-edge correspondence. By tuning the resonators during quenching, we demonstrate the emergence of Chern insulator, anomalous Floquet topological, and weak Floquet topological phases. The weak Floquet state arises from interactions between Floquet bands of non-adjacent periods, thereby distinguishing this system from its static counterparts.