Soliton molecules in a fiber laser mode-locked by a graphene-based saturable absorber

We have experimentally investigated a novel kind of soliton molecule in a graphene-based mode-locking fiber laser with anomalous dispersion. The soliton molecule exhibits a stable rectangular profile on the oscilloscope, whereas it shows randomly distributed peaks in the autocorrelation trace, which indicates that the temporal separation of pulses in the molecule is varying all the time. The optical spectrum is modulated with a depth of about 7 dB over the whole profile, induced by the interaction of the intra-molecule solitons. The experimental results demonstrate that solitons in the pulse molecule oscillate randomly in temporal domain and the neighboring molecules are temporally separated by a fundamental cavity repetition rate, which is very different from that of the multi-solitons or bound-state solitons.