  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,
nearly-flat energy band in the vicinity of the three-fold Dirac point in the
telecommunication frequency regime. This nontrivial nearly-flat band yields
topologically protected edge states. The pertinent physical effects brought
about due to non-Hermitian gain/loss medium into the honeycomb CROW device are
discussed. The generalized gain-loss lattice with parity-time symmetry
decouples the gain and the loss at opposite zigzag edges, leading to purely
gain or loss edge channels. Meanwhile, the gain and loss effects on the
armchair boundary cancel each other, giving rise to dissipationless edge states
in non-Hermitian optical systems. These characteristics underpin the
fundamental importance as well as the potential applications in various optical
devices such as polarizers, optical couplers, beam splitters and slow light
delay lines.
