Real-Time Observation of the Buildup of Soliton Molecules

Real-time spectroscopy access to ultrafast fiber lasers opens new opportunities for exploring complex soliton interaction dynamics. Here, we have reported the first observation, to the best of our knowledge, of the entire buildup process of soliton molecules (SMs) in a mode-locked laser. We have observed that the birth dynamics of a stable SM experiences five different stages, i.e., the raised relaxation oscillation (RO) stage, beating dynamics stage, transient single pulse stage, transient bound state, and finally the stable bound state. We have discovered that the evolution of pulses in the raised 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. Moreover, we have found that the buildup dynamics of SMs is quite sensitive to both the polarization state of intracavity light and the fluctuation of pump power. These results provide new perspectives into the ultrafast transient process in mode-locked lasers and the dynamics of complex nonlinear systems.

Figure 1

Schematic diagram of the experimental setup for the mode-locked laser.

Figure 2

Experimental real-time characterization of the entire buildup process of a SM in a mode-locked laser (a) with and (b) without the TS DFT technique, respectively. The intensity profile evolves along with the round-trip time ($y$ axis) and the round-trip number ($x$ axis). Insets in (a),(b) denote the cross sections at the $-570$ and $-590$ round-trip numbers (red curve) and at the time (blue curve) of 34.5 ns, respectively. Indications for $P_0$ to $P_5$ represent a pulse appearing on six spikes at the time of 34.5 ns. An enlargement of the raised RO stage in (a) is shown in Fig. S1 in the Supplemental Material [28].

Figure 3

Formation and evolution of a SM with beating dynamics. (a) Experimental real-time interferograms during the formation and evolution of SM. A full animation is shown in movie of the Supplemental Material [30]. (b),(c) Close-ups of the data from the $A$ and $B$ regions of (a), revealing the interference pattern for the beating dynamics.

Figure 4

(a) Field autocorrelation of each single-shot spectrum, exhibiting the separation between two solitons during the transient bound-state region. (b) Dynamics of the SM formation mapped into the interaction plane from about 3600 to 6500 round-trips.

Figure 5

(a) Optical spectra of SM measured by OSA. (b) Exemplary single-shot spectrum, corresponding to the last frame in Fig. 2.

Figure 6

RO stage of lasers without the modelocker. The projection on the round-trip intensity plane shows the intensity profile along with the round-trips.

Figure 7

Buildup process of SMs in lasers mode-locked by (a) the nonlinear polarization rotation technique and (b) CNT SA with a fluctuating pump power. The projection shows the temporal evolution along with the round-trips.