Broadband frequency generation by four-wave mixing in an all-bands-flat Floquet-Lieb topological insulator.

All-bands-flat topological photonic insulators are photonic lattices with all dispersionless bulk bands separated by nontrivial bandgaps. A distinct feature of these systems is that the edge modes can be excited across the flatband frequencies without scattering into the localized bulk modes, thus allowing the edge mode spectrum to extend beyond the gap size. Here we exploit the wide edge mode spectrum of a Floquet-Lieb topological insulator with all flatbands to achieve broadband frequency generation by four-wave mixing on a topological silicon photonic platform. Our all-bands-flat Floquet insulator is based on a Lieb lattice of microring resonators with perfect couplings, which provides a wide frequency generation bandwidth spanning more than six microring's free spectral ranges. The all-bands-flat microring lattice can also serve as a robust topological platform for other broadband nonlinear processes such as stimulated Raman scattering, frequency comb generation, supercontinuum generation, and soliton propagation based on topologically protected edge modes.