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In this work, we investigate a two dimensional honeycomb photonic crystal (2DHPC) with C_6 symmetry point group, which is known to demonstrate a doubleDirac cone at k=0 of the Brillion zone. Then we design two deformed PCs fromthe original one, by modifying the radius of the cylinders from the unit cellcenter in which the symmetry C_6 is reduced to the C_3\u{psion} group and newstructure exhibits the photonic topological edge states. Consequently, thetopologically protected propagation of the edge states with backscattering-immune feature is observed along the interfaces of the two deformedPCs without any defects or including cavities or bend. Furthermore, thedirectional surface modes exit from the photonic topological insulators (PTIs)including various defects, is investigated. As well as, we explore thepropagation and coupling of light through the coupled photonic topologicalinsulators (CPTIs).

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