Directional emission of the edge states from the photonic topological structure composed of two-dimensional honeycomb photonic crystals

In this work, we investigate a two-dimensional honeycomb photonic crystal (2D HPC) with $${C}_{6}$$ symmetry point group, which is known to demonstrate a double Dirac cone at high symmetry point of the Brillion zone. We also designed two deformed PCs, by modifying the radius of the cylinders from the unit cell center reducing the symmetry from $${C}_{6}$$ to the $${C}_{3\upsilon }$$ group. We find that this new structure exhibits the photonic topological edge states. Consequently, the topologically protected propagation of the edge states with the back scattering-immune feature is observed along the interfaces of the two deformed PCs without any defects or including cavities or bending. Furthermore, the directional surface modes exiting from the photonic topological insulators (PTIs) including various defects are investigated. As well, we explore the propagation and coupling of light through the coupled photonic topological insulators (CPTIs).