All-Bands-Flat Floquet Topological Photonic Insulators with Microring Lattices

Coupled microring lattices are versatile photonic systems that can be used to realize various topological phases of matter. In two-dimensional (2D) microring lattices, the periodic and unidirectional circulation of light in each microring gives rise to a time-like dimension, so that the lattice emulates a (2 + 1)D system with much richer topological behaviors than static 2D lattices. Accurate treatment of these systems requires a departure from the static tight-binding model of coupled resonators and take into account the periodic coupling sequence of light in the lattice network. This article provides an overview of the theory and design of (2 + 1)D microring lattices for realizing Floquet topological photonic insulators (TPIs). Particular focus is placed on the microring Lieb lattice with perfect couplings, which emulates an anomalous Floquet insulator with all flat bands. Such a system exhibits some unique properties, including wide edge mode continuum exceeding a Floquet–Brillouin zone, super-robustness to lattice disorder, Aharonov–Bohm (AB) caging and compact localized flat-band states that can be used to realize high-quality factor topological resonators. All-bands-flat Floquet–Lieb microring lattices provide a versatile platform for investigating topological physics as well as potential applications in realizing topologically-protected photonic devices.