Real-time spectroscopy based on an emerging time-stretch technique can map the spectral information of optical waves into the time domain, opening several fascinating explorations of nonlinear dynamics in mode-locked lasers. However, the self-starting process of mode-locked lasers is quite sensitive to the environmental perturbation, which causes the transient behavior of laser to deviate from the true build-up process of solitons. Here, we optimize the laser system to improve its stability that suppresses the Q-switched lasing induced by the environmental perturbation. We therefore demonstrate the first observation of the entire build-up process of solitons in a mode-locked laser, revealing two possible ways to generate the temporal solitons. One way includes the dynamics of raised relaxation oscillation, quasi mode-locking stage, spectral beating behavior, and finally the stable single-soliton mode-locking. The other way contains, however, an extra transient bound-state stage before the final single-pulse mode-locking operation.
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