Topological frequency combs and nested temporal solitons

Recent advances in realizing optical frequency combs using nonlinear parametric processes in integrated photonic resonators have revolutionized on-chip optical clocks, spectroscopy and multichannel optical communications. At the same time, the introduction of topological physics in photonic systems has allowed the design of photonic devices with novel functionalities and inherent robustness against fabrication disorders. Here we use topological design principles to theoretically propose the generation of optical frequency combs and temporal dissipative Kerr solitons in a two-dimensional array of coupled ring resonators that creates a synthetic magnetic field for photons and exhibits topological edge states. We show that these topological edge states constitute a travelling-wave super-ring resonator that leads to the generation of coherent nested optical frequency combs, as well as the self-formation of nested temporal solitons and Turing rolls that are remarkably phase-locked over more than 40 rings. Moreover, we show that the topological nested solitons are robust against defects in the lattice, and a single nested soliton achieves a mode efficiency of over 50%, an order of magnitude higher than single-ring frequency combs. Our topological frequency comb works in a parameter regime that can be readily accessed using existing low-loss integrated photonic platforms like silicon nitride. Optical frequency combs are a key technology in precision time keeping, spectroscopy and metrology. A theoretical proposal shows that introducing topological principles into their design makes on-chip combs more efficient and robust against fabrication defects.