Floquet engineering Dirac bands in synthetic frequency lattices

A waveguide coupler under periodically cascaded dielectric modulation is proposed to generate a Floquet lattice in synthetic frequency dimension. The Floquet bands may hold linear in the entire Brillouin zone, referred to as Floquet Dirac bands and giving rise to nondiffracting frequency shifts. The direction of frequency shift depends on the component of incident transverse modes, analogous to the spin-momentum locking realized in driven ultracold atoms recently. Furthermore, the shape of Floquet bands can be flexibly adjusted by applying external modulation voltage, resulting in a tunable group velocity and diffraction coefficient. The discrete diffraction and dynamic localization are also demonstrated in the Floquet frequency lattice. The study provides a versatile platform to explore multiband Floquet lattice physics in synthetic dimensions, and may find applications in spectral manipulation, mode conversion, and mode-division demultiplexing.