Two-dimensional photonic crystal with ring degeneracy and its topological protected edge states

We propose a two-dimensional photonic crystal that possesses a degenerate ring in the momentum space. The photonic crystal is composed of the parallel-plate metal filled with a periodically arranged square array of metallic cylinders. Opening an air gap breaks the z-inversion symmetry, leading to the modes coupling (bi-anisotropy response) of TE and TM waves. This induced electric-magneto coupling, a similar role of the spin-orbit interaction in the condensed matters, results in a complete topological band gap around the degenerate frequency. The bulk bands below the band gap take non-zero Z₂ topological invariant characterized by the evolution of the Berry phase. As a consequence, the interface of two photonic crystals with opposite bi-anisotropy supports topological protected edge states that exhibit one-way propagation and are highly resistant to disorders. Our work might be very useful for the design of topological photonic crystals and may serve as a platform for studying pseudo-spin photonics.