Topological photonic states and directional emission of the light exiting from the photonic topological structure composed of two dimensional honeycomb photonic crystals with different point group symmetries

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 k=0 of the Brillion zone. Then we design two deformed PCs from the original one, by modifying the radius of the cylinders from the unit cell center in which the symmetry C_6 is reduced to the C_3\u{psion} group and new structure exhibits the photonic topological edge states. Consequently, the topologically protected propagation of the edge states with back scattering-immune feature is observed along the interfaces of the two deformed PCs without any defects or including cavities or bend. Furthermore, the directional surface modes exit from the photonic topological insulators (PTIs) including various defects, is investigated. As well as, we explore the propagation and coupling of light through the coupled photonic topological insulators (CPTIs).