  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.
