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Topological photonics and its topological edge state which can suppressscattering and immune defects set off a research boom. Recently, the quantumvalley Hall effect (QVHE) with large valley Chern number and its multimodetopological transmission have been realized, which greatly improve the modedensity of the topological waveguide and its coupling efficiency with otherphotonic devices. The multifrequency QVHE and its topological transmission havebeen realized to increase the transmission capacity of topological waveguide,but multifrequency and multimode QVHE have not been realized simultaneously. Inthis Letter, the valley photonic crystal (VPC) is constructed with theStampfli-triangle photonic crystal (STPC), and its degeneracies in thelow-frequency and high-frequency bands are broken simultaneously to realize themultifrequency and multimode QVHE. The multifrequency and multimode topologicaltransmission is realized through the U-shaped waveguide constructed with twoVPCs with opposite valley Chern numbers. According to the bulk-edgecorrespondence principle, the Chern number is equal to the number oftopological edge states or topological waveguide modes. Therefore, we candetermine the valley Chern number of the VPC by the number of topological edgestates or topological waveguide modes, further determine the realization oflarge valley Chern number. These results provide new ideas for high-efficiencyand high-capacity optical transmission and communication devices and theirintegration, and broaden the application range of topological edge states.

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