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We derive a time-domain mean-field equation to model the full temporal andspectral dynamics of light in singly resonant cavity-enhanced second-harmonicgeneration systems. We show that the temporal walk-off between the fundamentaland the second-harmonic fields plays a decisive role under realisticconditions, giving rise to rich, previously unidentified nonlinear behaviour.Through linear stability analysis and numerical simulations, we discover a newkind of quadratic modulation instability which leads to the formation ofoptical frequency combs and associated time-domain dissipative structures. Ournumerical simulations show excellent agreement with recent experimentalobservations of frequency combs in quadratic nonlinear media [Phys. Rev. A 91,063839 (2015)]. Thus, in addition to unveiling a new, experimentally accessibleregime of nonlinear dynamics, our work enables predictive modeling of frequencycomb generation in cavity-enhanced second-harmonic generation systems.

Walk-off-induced modulation instability, temporal pattern formation, and frequency comb generation in cavity-enhanced second-harmonic generation