  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.
