Multiband topological group-velocity control from slow light to light stopping

We introduce next-nearest-neighbor (NNN) couplings into a Harper–Hofstadter photonic lattice to establish a long-range topological photonic platform for group-velocity engineering. We show that the NNN couplings not only open a previously closed band gap but also flatten the dispersion of the edge states, thereby offering a potential route toward topological slow-light control. Theoretical calculations reveal that the band gaps support band-gap Chern numbers with opposite signs. Propagation simulations demonstrate robust, topologically protected slow-light transport of counter-chiral edge states, while the presence of slow-light edge states in all three topological band gaps enables broadband topological slow light. By further tuning the NNN coupling parameter, multiple topological light-stopping states can be realized. These results establish long-range NNN coupling as an effective mechanism for topological group-velocity engineering and provide new design principles for topological slow-light devices, optical delay lines, and integrated multiband photonic systems.