Topological phases and the bulk-edge correspondence in 2D photonic microring resonator lattices

We show that 2D photonic lattices consisting of coupled microring resonators can emulate quantum systems driven by periodic Hamiltonians and can thus be used to realize photonic Floquet topological insulators. By transforming a 2D microring lattice into an equivalent array of coupled waveguides with periodic boundary conditions, we explicitly derive the Floquet-Bloch Hamiltonian of the system and determine the winding numbers characterizing the band topology and bulk-edge correspondence of the lattice. By varying the coupling strengths between adjacent resonators, we show that a 2D microring lattice can support both anomalous Floquet insulator edge modes and Chern insulator edge modes over a wide range of coupling parameters.