Long-range coupling enabled multiband group-velocity control of topological edge states from slow light to light stopping

Abstract

Topological edge states provide robust optical transport immune to disorder, yet their propagation velocity is usually constrained by the intrinsic band dispersion, limiting dynamic control of topological light transport. We introduce long-range next-nearest-neighbor (NNN) couplings into a Harper--Hofstadter photonic lattice and establish a versatile platform for group-velocity engineering. We demonstrate that the NNN couplings play two distinct roles: the vertical coupling opens a previously closed topological band gap by lifting the degeneracy of bulk bands, while the horizontal coupling reshapes the edge-state dispersion through momentum-dependent corrections, enabling controllable topological slow-light transport. Furthermore, the band-gap Chern numbers associated with different gaps exhibit opposite signs, giving rise to topological edge states with opposite chiralities. Propagation simulations reveal robust unidirectional transport of these counter-chiral edge states with reduced group velocities. By continuously tuning the NNN coupling strength, the group velocity of topological edge modes can be reduced toward zero at specific momenta, resulting in topological light-stopping effects. These results demonstrate that long-range NNN couplings provide an effective mechanism for engineering momentum-dependent topological group velocities and offer new possibilities for robust slow-light devices, optical delay lines, and multiband integrated photonic systems.

12 pages, 6 figures