  Simultaneous Kerr comb formation and second-harmonic generation with on-chip
microresonators can greatly facilitate comb self-referencing for optical clocks
and frequency metrology. Moreover, the presence of both second- and third-order
nonlinearities results in complex cavity dynamics that is of high scientific
interest but is still far from well understood. Here, we demonstrate that the
interaction between the fundamental and the second-harmonic waves can provide
an entirely new way of phase-matching for four-wave mixing in optical
microresonators, enabling the generation of optical frequency combs in the
normal dispersion regime, under conditions where comb creation is ordinarily
prohibited. We derive new coupled time-domain mean-field equations and obtain
simulation results showing good qualitative agreement with our experimental
observations. Our findings provide a novel way of overcoming the dispersion
limit for simultaneous Kerr comb formation and second-harmonic generation,
which might prove especially important in the near-visible to visible range
where several atomic transitions commonly used for stabilization of optical
clocks are located and where the large normal material dispersion is likely to
dominate.
