Parametrically driven Kerr temporal soliton crystals

Abstract We theoretically investigate the dynamics of parametrically driven soliton crystals (PDSC) and their associated frequency combs in doubly resonant cavities with quadratic and cubic nonlinearities. We show that, with significant pump-signal walk-off, PDSCs emerge as robust attractors in a monostable regime, and the soliton number is set primarily by the driving strength. Pump-signal walk-off extends pump depletion from a local perturbation to a global constraint, enabling long-range soliton interactions; in combination with the pump phase, this mechanism stabilizes the crystal’s equal spacing and preserves comb coherence. Additionally, we identify a novel nonlinear state in parametric soliton crystals in which circulating solitons periodically alternate their intensities and group velocities, a phenomenon we term the soliton-pursuing state. Furthermore, due to the phase-selective nature of the optical parametric process, we show how different configurations of soliton phases determine the optical frequency combs, enabling odd-harmonic and subharmonic-like combs.