  Recent advances in realizing optical frequency combs using nonlinear
parametric processes in integrated photonic resonators have revolutionized
on-chip optical clocks, spectroscopy, and multi-channel optical communications.
At the same time, the introduction of topological physics in photonic systems
has provided a new paradigm to engineer the flow of photons, and thereby,
design 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
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 traveling-wave
super-ring resonator that leads to the generation of coherent nested optical
frequency combs, and self-formation of nested temporal solitons and Turing
rolls that are remarkably phase-locked over >40 rings. In the nested soliton
regime, our system operates as a pulsed optical frequency comb and achieves a
mode efficiency of >50%, an order of magnitude higher than single ring
frequency combs that are theoretically limited to only ~5%. Furthermore, we
show that the topological nested solitons are robust against defects in the
lattice. This topological frequency comb works in a parameter regime that can
be readily accessed using existing low loss integrated photonic platforms like
silicon-nitride. Our results could pave the way for efficient on-chip optical
frequency combs, and investigations of various other soliton solutions in
conjunction with synthetic gauge fields and topological phenomena in large
arrays of coupled resonators.
