Retiming dynamics of harmonically mode-locked laser solitons in a self-driven optomechanical lattice.

Harmonic mode-locking, realized actively or passively, is an effective technique for increasing the repetition rate of ultrafast lasers. It is critically important to understand how a harmonically mode-locked pulse train responds to external perturbations and noise, so as to make sure that it is stable and resistant to noise. Here, in a series of carefully designed experiments, we elucidate the retiming dynamics of laser pulses generated in a soliton fiber laser harmonically mode-locked at GHz frequencies to the acoustic resonance in a photonic crystal fiber (PCF) core. We characterize the self-driven optomechanical lattice, which is distributed along the PCF and provides the structure that supports harmonic mode-locking, using a homodyne setup. We reveal that, after an abrupt perturbation, each soliton in the lattice undergoes damped oscillatory retiming within its trapping potential, while the retiming is strongly coupled to soliton dissipation. In addition, we show, through statistical analysis of the intra-cavity pulse spacing, how the trapping potentials are effective for suppressing timing jitter. The measurements and the theory developed in this work lay the groundwork for studies of the general stability and noise performance of harmonically mode-locked lasers as well as providing valuable insight into generic multi-pulse phenomena in mode-locked lasers.