Phase-velocity-reversed topological edge states and rainbows for field enhancement and radiation control

Topological rainbows hold significant promise for robust on-chip frequency-division multiplexing. In this Letter, we report a spectral control mechanism of topological edge states by modulating boundary onsite potentials. Shifting upper-gap modes into the lower bandgap creates engineered edge states (EESs) with phase velocities opposite to conventional lower-gap edge states (LESs), achieving enhanced localization via anomalous main-side lobe matching. Topological rainbows leveraging these states show distinct behaviors. In parallel-plate waveguides, only BZ-boundary-directed LES rainbows yield over fourfold field enhancement. In open waveguide systems, BZ-center-directed rainbows incur radiation loss upon entering the light cone. Significantly, the reversed phase velocities of EESs invert the radiation direction relative to LESs. This research establishes a disorder-immune strategy for directional radiation control and interconnection in integrated photonic devices.