Landau rainbow based on Floquet helical waveguide systems

A topological rainbow can separate topological photonic states with different frequencies to different spatial localizations. The Landau levels offer significant insights for the study of topological bulk states and inspire the discovery of novel topological states and phenomena. The Landau rainbow, as a typical topological rainbow, in which different frequencies of Landau modes can be separated into different positions, exhibits potential applications for designing broadband photonic devices. In this Letter, we propose a Landau rainbow based on the zero-order Landau level of Floquet helical waveguide systems for the first time to our knowledge. The photonic Landau levels are induced by a pseudo-magnetic field by engineering the gradient effective coupling strength, and the helical configuration of the waveguides breaks the degeneracy of the zero-order Landau levels resulting in band tilting. Therefore, the states in the zero-order Landau level exhibit distinct quasienergies and are located at different spatial positions, which show a Landau rainbow effect. The Landau rainbow based on Floquet helical waveguide systems provides new avenues for the realization of robust photonic devices, such as rainbow trapping device, multifrequency divider, and optical information storage.