Revealing of long-range soliton interaction induced time and phase dynamics in a mode-locked fiber laser

By means of the dispersive temporal interferometry technique, we carried out a real-time observation of the time separation and relative phase evolutions of two pulses toward harmonic mode-locking. During the separation stage of the buildup process, the time separation increases, while the relative phase decreases synchronously, and the largest change rates are 0.247 fs/r and -0.017 rad/r, respectively. Meanwhile, the two rates show a linear relation with the former 17.4 times larger than the latter. Moreover, a residual phase change rate of -3.89 × 10^-4rad/r is observed in a steady non-uniform dual-soliton state, while such phase change is absent in a uniform four-soliton state. This study unveils the soliton interaction dynamics in lasers, which not only help to reduce timing jitter in multi-soliton mode-locking, but also bring insight to a temporal tweezing of femtosecond pulse.