Parametrically driven Kerr temporal soliton crystals

We theoretically investigate the excitation, dynamics of parametrically driven soliton crystals and their resulting frequency combs in doubly resonant cavities with quadratic and cubic nonlinearities. We demonstrate that soliton crystal states act as strong attractors, where pump depletion and pump phase play crucial roles in their stabilization by ensuring equal soliton spacing and coherence. The number of solitons is primarily determined by driving strength. 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 states. Furthermore, due to the phase-selective nature of the optical parametric process, we show how different configurations of soliton phases influence the optical frequency combs, which may enable generating odd harmonic combs.