Helical edge states of topological photonic crystals with line defects.

Topologically protected edge states of honeycomb photonic crystals (PCs) have been extensively studied in recent years. Here we propose several optimized two-dimensional PC configurations with distinct line defects introduced by breaking the C symmetry of each topological lattice along the interfaces between two different topologies. The spin-flipping nature of the defect modes of these PC configurations is measured, which is expected to offer a novel realization mechanism of quantum spin Hall effect. The line defects can be treated as unidirectional air waveguides due to the characteristic topological properties. We manipulate the coupling effect of two helical edge states with tunable waveguide widths. It shows that the air waveguide has possibility for practical applications because of its suppression of backward scattering and considerable transmission efficiency.