  Topological photonics and its topological edge state which can suppress
scattering and immune defects set off a research boom. Recently, the quantum
valley Hall effect (QVHE) with large valley Chern number and its multimode
topological transmission have been realized, which greatly improve the mode
density of the topological waveguide and its coupling efficiency with other
photonic devices. The multifrequency QVHE and its topological transmission have
been realized to increase the transmission capacity of topological waveguide,
but multifrequency and multimode QVHE have not been realized simultaneously. In
this Letter, the valley photonic crystal (VPC) is constructed with the
Stampfli-triangle photonic crystal (STPC), and its degeneracies in the
low-frequency and high-frequency bands are broken simultaneously to realize the
multifrequency and multimode QVHE. The multifrequency and multimode topological
transmission is realized through the U-shaped waveguide constructed with two
VPCs with opposite valley Chern numbers. According to the bulk-edge
correspondence principle, the Chern number is equal to the number of
topological edge states or topological waveguide modes. Therefore, we can
determine the valley Chern number of the VPC by the number of topological edge
states or topological waveguide modes, further determine the realization of
large valley Chern number. These results provide new ideas for high-efficiency
and high-capacity optical transmission and communication devices and their
integration, and broaden the application range of topological edge states.
