Accidental degeneracy in photonic bands and topological phase transitions in two-dimensional core-shell dielectric photonic crystals.

A simple core-shell two-dimensional photonic crystal is studied where the triangular lattice symmetry and the C₆ point group symmetry give rich physics in accidental touching points of photonic bands. We systematically evaluate different types of accidental nodal points at the Brillouin zone center for transverse-magnetic harmonic modes when the geometry and permittivity of the core-shell material are continuously tuned. The accidental nodal points can have different dispersions and topological properties (i.e., Berry phases). These accidental nodal points can be the critical states lying between a topological phase and a normal phase of the photonic crystal. They are thus very important for the study of topological photonic states. We show that, without breaking time-reversal symmetry, by tuning the geometry of the core-shell material, a phase transition into the photonic quantum spin Hall insulator can be achieved. Here the "spin" is defined as the orbital angular momentum of a photon. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics.