Scheme for Achieving a Topological Photonic Crystal by Using Dielectric Material

We derive in the present work topological photonic states purely based on conventional dielectric material by deforming a honeycomb lattice of cylinders into a triangular lattice of cylinder hexagons. The photonic topology is associated with a pseudo-time-reversal (TR) symmetry constituted by the TR symmetry supported in general by Maxwell equations and the C_{6} crystal symmetry upon design, which renders the Kramers doubling in the present photonic system. It is shown explicitly for the transverse magnetic mode that the role of pseudospin is played by the angular momentum of the wave function of the out-of-plane electric field. We solve Maxwell equations and demonstrate the new photonic topology by revealing pseudospin-resolved Berry curvatures of photonic bands and helical edge states characterized by Poynting vectors.