Interaction and motion of solitons in passively-mode-locked fiber lasers
Physical Review A. Atomic, Molecular, and Optical Physics
Interaction and motion of multiple solitons in passively mode-locked (PML) fiber lasers are investigated numerically. Three types of relative motions of two solitons are found in PML fiber lasers. The numerical results show that the relative motion of solitons attributes to the phase shift, which corresponds to the instantaneous frequency of soliton to be nonzero. Different from the classical dynamics of billiard balls, the interaction of solitons is similar to Feynman diagram that is a
... m that is a pictoral way to represent the interaction of particles. After solitons interact with one another, their shapes do not change, but their phases shift and relative motions change. The theoretical results demonstrate that the separation of neighboring solitons in laser cavity is about several hundreds of picosecond to several nanosecond. The theoretical predictions are in good agreement with the experimental results. PACS number(s): 42.65.Tg, 42.81.Dp, 42.55.Wd, 42.65.Re I. INTRODUCTION Passively mode-locked (PML) fiber lasers can provide the simple and economic ultrashort-pulse sources -. They constitute an ideal platform for exploring new areas of nonlinear dynamics . Multiple soliton operation in PML fiber lasers, which has been investigated extensively -, is the typical result of the conjunction of a relatively strong pumping power. Solitons observed in fiber lasers exhibit special features such as the soliton bounding, the soliton bunching, and the quasi-harmonic and harmonic mode locking. Bound solitary pulses, so-called soliton molecules , have attracted a great deal of interest due to their important potential applications. Bound states of solitons can be predicted in the coupled nonlinear Schrödinger equations (NLSEs)  and the quintic complex Ginzburg-Landau equation . Investigations on the interaction between the bound solitons show that the bound pulses always behave as a unit. Usually, the peak-to-peak (P2P) separation of bound solitons is less than several pulse-duration -. Different from the bound states of solitons, the P2P separation of soliton bunching can be over tens of times larger than the pulse width. Pulse bunching is a special behavior that corresponds to the ability of several identical soliton pulses to cluster themselves in a packet. The formation and evolution of multiple solitons are studied numerically and experimentally by many authors . Various features such as the pump power hysteresis, multi-soliton generation, and various modes of multi-soliton operation were observed experimentally and investigated theoretically. Tang et al. proved that the soliton shaping of the dispersive waves or the continuous-wave (cw) components plays a key role on the generation of additional solitons . In our previous reports, it is proved that the mechanism of pulse splitting determines the dual-and multi-soliton generation in the net-anomalous-dispersion fiber lasers , whereas two pulses are gradually formed at the cost of dropping off a pulse in the net-normal-dispersion fiber lasers . Theoretical and experimental results show that the PML fiber lasers alternately evolve on the stable and unstable mode-locking states as a function of the pump strength . An important characteristic of the multi-soliton operation of the laser is that solitons always have erratic motions. A typically experimental result is demonstrated in Fig. 1 . The experimental setup and parameters are shown in our previous report  . The experimental observations show that solitons in the cavity have erratic relative motions. It is import to have a clear understanding of the physical mechanism responsible for the relative motion of solitons in the PML fiber lasers.