Multifrequency and multimode topological waveguides in a Stampfli-triangle photonic crystal with large valley Chern numbers

The multifrequency quantum valley Hall effect (QVHE) with a large valley Chern number has been realized to significantly improve the transmission capacity of topological waveguides and increase the mode density of topological waveguides. However, multifrequency and multimode QVHEs have not been realized simultaneously. In this work, using tight-binding model calculations and numerical simulations, a valley photonic crystal (VPC) consisting of a Stampfli-triangle photonic crystal is constructed, and its multiple degeneracies in the low-frequency and high-frequency bands split simultaneously to realize the QVHE with multiple topological edge states (TESs). The multifrequency and multimode topological transmission with two low-frequency modes and four high-frequency modes is realized by means of simulations and experiments through a Z-shaped waveguide constructed using two VPCs with opposite valley Chern numbers to prove the realization of a large valley Chern number in the two frequency bands. The two low-frequency modes are successfully distinguished with position-dependent selective excitations, which experimentally demonstrates the occurrence of a large valley Chern number. A frequency-dependent multimode beam splitter is theoretically proposed for high-performance integrated photonic device applications. These results provide new ideas for high-efficiency and high-capacity optical transmission and communication devices and their integration; furthermore, they broaden the application range of TESs.