Abstract
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.
Highlights
Recent discoveries in the field of topological non-trivial phases have led to a growing research in topological insulators and semimetals, and these concepts have been introduced to their electromagnetic counterpart communities
The present photonic crystal with toroidal degeneracy is composed of two parallel-plate metal waveguides filled with a periodically arranged square lattice array of metallic cylinders
By judiciously choosing h and the cylinders’ radius r under the condition of the given lattice constant, the second (TE) and third (TM) bands can touch with each other
Summary
Recent discoveries in the field of topological non-trivial phases have led to a growing research in topological insulators and semimetals, and these concepts have been introduced to their electromagnetic counterpart communities. When breaking the z-inversion symmetry, the former bands interact with each other[22] through magneto-electric coupling, resulting in a topological photonic crystal (TPC) with a complete band gap.
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