Dual-band large-area topological edge states and higher-order corner states in a valley Hall photonic crystal

Topological photonics has been an emerging research field in optics and a promising area within the broader realm of topological physics. One recent focus has been on the exploration of large-area topological edge states with tunable widths. At the same time, there has been considerable interest in higher-order topological corner states that can manipulate wave localization. Challenges remain in achieving multiband large-area topological edge states and higher-order corner states to flexibly manipulate the localization and transmission of electromagnetic waves. In this paper, we propose a valley Hall photonic crystal (VPC) with two types of interfaces capable of achieving both large-area topological edge states and large-area higher-order corner states in the dual-band frequency ranges. We demonstrate numerically and experimentally that large-area edge states enable width-tunable waveguide transmission and topological cavities in two frequency ranges. In addition, we also construct corner structures based on the two interfaces and achieve large-area higher-order corner states at dual-band frequency ranges. Therefore, our proposed VPC possesses both large-area topological edge states and large-area corner states at dual-band frequency ranges. It is expected that this VPC can serve as a multifunctional device for manipulating electromagnetic waves.