  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).
