Multistable Kuramoto Splay States in a Crystal of Mode-Locked Laser Pulses

We demonstrate the existence of coexisting frequency combs in a harmonically mode-locked laser that we link to the splay phases of the Kuramoto model with short range interactions. These splay states are multistable and the laser may wander between them under the influence of stochastic forces. Consequently, the many pulses circulating in the cavity are not necessarily coherent with each other. As these partially disordered states for the phase of the field still feature regular intensity pulses, we term them as incoherent crystals of optical pulses. We provide evidence that the notion of coherence should be interpreted by comparing the duration of the measurement time with the Kramers' escape time of each splay state. Our theoretical results are confirmed experimentally by performing high resolution spectral measurements via a heterodyne technique of a passively mode-locked vertical external-cavity surface-emitting laser.