Self-organization in Kerr-cavity-soliton formation in parametric frequency combs

We show that self-organization and synchronization underlie Kerr-cavity-soliton formation in parametric frequency combs. By reducing the Lugiato-Lefever equation to a set of phase equations, we find that self-organization arises from a two-stage process via pump-degenerate and pump-nondegenerate four-wave mixing. The reduced phase equations are akin to the Kuramoto model of coupled oscillators and intuitively explain the origin of the pump phase offset, predict antisymmetrization of the intracavity field before phase synchronization, and clarify the role of chaos in Kerr-cavity-soliton formation in parametric combs.