Tunable topological edge and corner states in an all-dielectric photonic crystal.

Topological photonics has become a new and fascinating area in recent years, which enables electromagnetic waves to propagate with negligible backscattering and excellent robustness even when encountering sharp corners or defects. But the flexible tunability of edge and corner states is challenging once the topological photonic crystals (PhCs) have been fabricated. In this paper, we propose a new all-dielectric PhC with C symmetry constructed by hexagonal array of petal-like aperture embedded in silicon background. The proposed configuration has much wider energy gap than its triangular counterpart, and hence is suitable for wideband and high-capacity applications. When the apertures are filled with liquid crystals (LCs), the topologically-protected edge and corner states can be regulated through changing the refractive index of the LCs under different bias voltages. Moreover, the robustness of topological protection of edge and corner states is further demonstrated. This is the first demonstration of LC based tunable valley higher-order photonic topological insulator. The tunability of the proposed topological PhCs may be beneficial for development of tunable optical waveguides, reconfigurable topological microcavities, and other intelligent topological optical/terahertz devices.