  Harmonic mode-locking, realized actively or passively, is an effective
technique for increasing the repetition rate of lasers, with important
applications in optical sampling, laser micro-machining and frequency
metrology. 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 ~2 GHz to
the acoustic resonance in a photonic crystal fiber (PCF) core. We characterize
the self-driven optomechanical lattice along the PCF using a homodyne set-up,
and reveal that each soliton undergoes damped oscillatory retiming within its
trapping potential after an abrupt perturbation. In addition we show, through
statistical analysis of the intra-cavity pulse spacing, how the trapping
potentials are effective for suppressing timing jitter. The experimental
results are well described using a dynamic model including dissipation, which
provides valuable insight into the stability and noise performance of
optomechanically mode-locked laser systems, and may also be useful for studying
complex inter-soliton interactions.
