Z topological edge state in honeycomb lattice of coupled resonant optical waveguides with a flat band.

Two-dimensional (2D) coupled resonant optical waveguide (CROW), exhibiting topological edge states, provides an efficient platform for designing integrated topological photonic devices. In this paper, we propose an experimentally feasible design of 2D honeycomb CROW photonic structure. The characteristic optical system possesses two-fold and three-fold Dirac points at different positions in the Brillouin zone. The effective gauge fields implemented by the intrinsic pseudo-spin-orbit interaction open up topologically nontrivial bandgaps through the Dirac points. Spatial lattice geometries allow destructive wave interference, leading to a dispersionless, near-flat energy band in the vicinity of the three-fold Dirac point in the telecommunication frequency regime. This nontrivial structure with a near-flat band yields topologically protected edge states. These characteristics underpin the fundamental importance as well as the potential applications in various optical devices. Based on the honeycomb CROW lattice, we design the shape-independent topological cavity and the beam splitter, which demonstrate the relevance for a wide range of photonic applications.