Topology classification in bi-anisotropic topological photonic crystals via the Wilson loop approach [Invited

Abstract

Topological photonic crystals have attracted tremendous attention due to their promise of robust optical properties and great potential for applications in on-chip devices. Numerous successful experimental demonstrations have shown or proved their topological properties, however, many of them turn out to have a nature of fragile topological phases. Here, using theoretical methods of fragile topology, we analyze two cases of topological photonic crystals with preserved time reversal symmetry, which utilize (1), the intrinsic duality and bi-anisotropy, and (2), accidental duality and structural bi-anisotropy respectively to induce their topological order. Our results show that the former case belongs to a Wannier-obstructed type of topological phase, indicating strong topological protection in their edge states. However, the latter meta-waveguide designs with structural bi-anisotropy widely implemented in experiments are Wannierizable, implying the fragile properties of their topology and gapped edge spectra. Our results provide new insights into the topological properties of photonic crystals as well as other bosonic systems with time-reversal symmetry.