Topological photonics and topological photonic states have opened up a new frontier
for optical manipulation and robust light trapping. The topological rainbow can separate different
frequencies of topological states into different positions. This work combines a topological
photonic crystal waveguide (topological PCW) with the optical cavity. The dipole and quadrupole
topological rainbows are realized through increasing cavity size along the coupling interface. The
flatted band can be obtained by increasing cavity length due to interaction strength between the
optical feld and defected region material which is extensively promoted. The light propagation
through the coupling interface is built on the evanescent overlapping mode tails of the localized
felds between bordering cavities. Thus, the ultra-low group velocity is realized at a cavity
length more than the lattice constant, which is appropriate for realizing an accurate and precise
topological rainbow. Hence, this is a novel release for strong localization with robust transmission
and owns the possibility to realize high-performance optical storage devices.