Abstract
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.
Highlights
The Ginzburg-Landau paradigm[1] gained wide success in describing phase transitions before the discovery of the quantum Hall effect[2,3]
Unlike previous studies on trapping light with photonic band gaps, in this work we focus on the nodal points in photonic bands in two-dimensional (2D) triangle photonic crystals (PhCs)
The topological phase transition between normal photonic band gap materials and a photonic Z2 topological insulator was proposed in 2D PhCs using normal dielectric materials with isotropic permittivity[16]
Summary
The Ginzburg-Landau paradigm[1] gained wide success in describing phase transitions before the discovery of the quantum Hall effect[2,3]. The topological phase transition between normal photonic band gap materials and a photonic Z2 topological insulator was proposed in 2D PhCs using normal dielectric materials with isotropic permittivity[16]. The 2D PhCs that realize such a transition is a triangle lattice where there are six cylinders in each unit cell forming a pattern with C6 symmetry. We systematically calculate the accidental degeneracy’s at the Brillouin zone center and the topological phase transitions in the 2D core-shell dielectric PhCs. The core-shell triangle photonic crystal structure is simple and mechanically stable and it is compatible with colloidal[19] self-assembled structure as well as biological systems[20]. The photonic bands can be viewed as derived from transfer (hopping) of local Mie resonances of the core-shell structures between adjacent unit cells.
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