Time-stretch dispersive Fourier transform (TS-DFT) technique opens a fascinating pathway to explore the ultrafast non-repetitive events, which has been widely employed to study the build-up dynamics of mode-locked lasers  and the evolution of femtosecond soliton molecules . However, the self-starting process of mode-locked lasers is quite sensitive to the environmental perturbation, which causes the transient behaviors of lasers to deviate from the true build-up process of solitons. Recently, we have optimized the laser system to suppress the Q-switched lasing and experimentally demonstrated the entire build-up dynamics of soliton molecules . We have discovered the that the evolution of pulses in the raised relaxation oscillation (RO) stage follows a law that only the strongest one can ultimately survive and, meanwhile, the pulses periodically appear at the same temporal positions for all lasing spikes during the same RO stage (named as memory ability) but they lose such ability between different RO stages.
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