Temporal dissipative solitons result from the composite balance between nonlinearity and dispersion, gain and loss [1]. Compared with the case of conventional solitons, the impact of dissipative effects reveals unusual situations in which complex localized structures can be found, such as soliton breathers [2–5], and the coexistence of a large number of solitons (quadruple solitons [6], soliton crystals [7,8], and soliton molecules [9–13]). In general, dissipative solitons are basically generated from coherently seeded and decoherently seeded systems. In typical coherently seeded systems, such as microresonator-based solitons [14–17] or laser cavities with parametric gain [18–21], motion control of solitons can be directly realized by adjusting the seeding conditions.

For example, in a fibre ring resonator that supports the formation of temporal dissipative soliton driven by a localized continuous wave laser, deterministic writing and erasing of solitons are allowed via pump modulation [19]. Moreover it has been demonstrated that the thermal-optic effect in microresonators could cause non-degenerate states of different soliton number, and enable the access to each soliton state by simply backward wavelength tuning the pumping laser [14]. In addition all-optical switching between soliton molecule states with different binding separations could also be controlled by a parametric gain modulation in an optical oscillator [20].

However in contrast to coherently seeded systems, motion control remains challenging in laser systems that are decoherently seeded (e.g., the gain in the laser cavity is via stimulated emission of carriers and therefore has decoherent link to the seeding source). Most researches have focused on instant switching dynamics of soliton states within a short moment, such as soliton formation [22–28], soliton synthesis and dissociation [28–31], solitons internal motion [32–35], solitons collision [36,37], and soliton breathers [4]. Noise-mediated soliton motion [38,39] seems also possible in laser systems, yet it is inherently stochastic. Most necessarily, active motion control in decoherently seeded systems, especially for mode-locked lasers, relies on the introduction of extra parameter-controlled elements [40–45]. Even though build-up and dissociation of dissipative soliton molecules could be theoretically and experimentally observed under different transmission functions of saturable absorbers, the switching took place stochastically [28]. In addition, in hundreds of temporal “reactors,” created in parallel in an opto-acoustically mode-locked fibre laser, one can achieve on-demand synthesis and dissociation of soliton molecules [30,46]. However, at present, a complete set of dynamics of regarding soliton motion and the switching in between different states is still not observed.

Here, we report the observation of a complete set of dynamics of temporal dissipative solitons motion in a mode-locked fibre laser controlled by the spectral filtering effect (SFE). We present a detailed analysis of the observed phenomenon and demonstrate its universal nature. Single switching dynamics of soliton disassembly are observed at one moment when a single soliton is dissociated from a complex soliton molecule. We also observe complex switching dynamics of a soliton pair combined with a single soliton, including complicated soliton assembly and disassembly. Moreover, we investigate the complete soliton switching dynamics of filter scanning and record all dynamics at each switching moment, in which we observe a significant hysteresis between redshift and blueshift. From an application perspective, the presented results provide a new method for temporal dissipative solitons motion control in the decoherently seeded system.

The experimental setup is shown in Fig. 1(a). The focused decoherently seeded system is an erbium-doped mode-locked fibre laser using carbon-nanotube-based saturable absorber (CNT-SA). A 3.1-m length erbium-doped fibre (EDF, LIEKKI 30/4) is used as the gain medium, and the total length of the single-mode fibre (SMF) is ∼8.15m. Thus, the corresponding basic repetition frequency of the cavity is ∼18.167MHz. The net cavity dispersion at the wavelength of 1.56 μm is ∼−0.135ps2. The function of the polarization controller in the laser cavity is to enhance the birefringence on the cavity mode and to enable the self-starting of the laser at a relative low pumping power, which has been widely applied [47,48]. Regarding our lasers, the threshold pumping power for reaching the mode-locking state could be as low as ∼23.71mW, which is much lower compared with nonlinear polarization evolution lasers [33,34]. The output signals are detected by a 33 GHz photodetector (N7004A, Keysight) and recorded by a 59 GHz, 160GSa/s real-time oscilloscope (DSAZ592A, Keysight).

As shown in Fig. 1(d), the bandwidth of a tuneable bandpass filter (TBPF) is ∼40nm, and its centre wavelength is tuneable in the range of 1520–1600 nm. For the dispersion Fourier transform (DFT) based real-time spectrum system, a 5-km length dispersion compensation fibre (DCF) is used as the dispersion medium to provide a total cumulative dispersion of ∼−679ps/nm at 1545 nm. The duration of stretched pulse Δτ can be calculated by [34,49]Δτ=|DL|Δλ,(1)in which Δλ is the wavelength range of the input signal, and DL is total cumulative dispersion of dispersive medium. Therefore, the scale of wavelength to time mapping is ∼1.47nm/ns. Meanwhile, the maximum time resolution of the detecting system is ∼0.1ns; the corresponding maximum electronic spectral resolution is ∼0.147nm. In addition, the maximum 3-dB bandwidth of soliton spectrum is ∼3.1nm; the 30-dB bandwidth of that is ∼12.5nm. Therefore, calculated temporal separation is 8.5 ns, meaning that pulses with a separation greater than 8.5 ns are recognized as two separate pulses in the time domain, while pulses that are closer would be transformed to reveal the spectral profile, cf. Figs. 5(e)–5(h) as an example.

While the centre wavelength of the TBPF is set at the centre wavelength of the laser output, all effective spectra are included in the pass band of TBPF. By carefully adjusting the TBPF, the red and blue boundaries of the filtered gain spectrum can be determined. Beyond the boundaries, the intracavity gain fibre cannot provide enough gain to form temporal solitons. During long-term filtering scanning, the temporal dynamic evolution of intracavity solitons is shown in an oscilloscope (OSC), such as the evolution of two-soliton molecules (TSMs) into complex soliton molecules (CSMs), as shown in Figs. 1(c) and 1(f). Due to the limitation of oscilloscope resolution, the directly recorded pulse trains cannot distinguish the fine structure of soliton molecules. Therefore, a power stage of pulse trains is clearly shown in OSC. Figure 1(e) shows a typical spectrum of solitons that are affected by the edge of the bandpass filter, which reveals a similar edge on the spectral profile.

In order to directly observe the switching dynamics of solitons, the soliton spectra of each roundtrip are mapped to the pulse train in time domain via DFT, and the switching moment of solitons could be recorded by an oscilloscope. In our work, two methods were used to assist quickly and accurately the collection of the split-second switching moments. On the one hand, the original signal is set as a trigger signal, and some switching moments with distinct power stage can be precisely collected by setting an appropriate trigger level. On the other hand, the external burst signal is alternative as the trigger; further, all switching moments can be recorded by setting an appropriate time delay, as shown in Fig. 1(c).

The gain spectrum of the fibre cavity is jointly determined by the gain fibre and TBPF. The gain fibre is uniquely determined, and the intracavity gain changes accordingly when the TBPF is tuned. The composite balance between gain and loss, nonlinearity and dispersion is re-established and expresses different soliton states. The real-time responses to this effect are the relative motion of solitons and change of soliton characteristics, such as intensity, phase, and separation.

The experiments reveal a relationship between SFE and the soliton switching. When the centre wavelength of TBPF is ∼1568nm and the centre wavelength is continuously tuned, one moment of deterministic switching is recorded via DFT. Figure 2 shows the switching dynamics between CSM and TSM, specifically, solitons disassembly. The complete transition from a CSM state to a TSM state is illustrated in Fig. 2(c), while Fig. 2(e) shows significant details at the beginning of the transition. From Figs. 2(e) and 2(f), one could conclude that the transition is via the dissembling of one pulse from the CSM, where the temporal separation between the pulse and the molecule is increased, accompanied with an accumulative change in the phase. Moreover, limited by the resolution of the retrieved spectrum, the evaluated autocorrelation trace is within a time range of ∼55.4ps. Hence, there may have a folding effect [Fig. 2(d)] when the free pulse is separate far away outside the effective range. In practice, we unfolded the evolution of the autocorrelation trace and retrieve a complete dissembling dynamic during the CSM to TSM transition.

We next observe the complex switching dynamics of solitons assembly at a second moment. When the centre wavelength of TBPF is ∼1555nm and continuously tuned, we first have stable TSMs circulating in the cavity and subsequently switch to CSMs, as shown in Figs. 3(a) and 3(b). The transition also features self-adjustment on the interval in between solitons, once the CSM state is formed (corresponding to the roundtrips 107,000–120,000).

Figure 3(c) shows nine slices within the whole transition, revealing detailed soliton motions. Solitons do not simply approach each other directly but go through a complex intermediate process. This is largely similar to the formation of intermediate products in chemical reactions of substance molecules. The CSMs with a mutative interval between single soliton and soliton pair are intermediate products of this complex switching. The bonds between solitons undergo complex processes such as multiple breaks and recombination; subsequently, solitons recombine into new soliton molecules.

We recorded the full switching dynamics of temporal dissipative solitons via filter scanning. The TBPF is controlled by a programable motor to scan in the redshift and blueshift directions. At the moment, the tuning of the bandpass filter is at a speed of ∼4.89nm/s. In the meantime, the spectral resolution of the DFT system is ∼0.147nm. In this way, tuning the filter to have a resolvable change in the wavelength may take ∼30ms, which is more than 100 times longer compared with the build-up time (∼100μs) of the mode-locked laser [23]. Therefore, the scan of the filter is relatively in the static mode. The filter scanning is operated starting from different states, such as two-soliton molecules and complex soliton molecules (see Visualization 1 and Visualization 2). The whole tuning process starting from complex soliton molecules includes complete soliton states, such as Q-switched instability, unstable soliton, complex soliton molecule, two-soliton molecule, and single soliton, as shown in Fig. 4(a). More obviously, the blueshift process shows significant hysteresis in contrast with the redshift process, which is a typical characteristic of the mode-locked fibre laser, a nonlinear optical system.

As shown in Fig. 4(b), combined with two data acquisition methods, we collected all switching dynamics at each moment. When the TBPF is near the boundary, the net gain of the cavity is greatly limited and cannot accumulate enough energy to form solitons. Thus, the laser is under the Q-switched instability state of kHz repetition rate. With the redshift of TBPF, the net gain window gradually becomes larger, and the laser begins to form unstable solitons, cf. the state 1 in Fig. 4(b), and state 8 during the blueshift scan of the filter. When the net gain window is fully open, solitons undergo a complex intermediate process to form CSMs composed of the largest number of solitons (here are three solitons), as shown in Fig. 4(b) panel 2, which corresponds to Fig. 4(b) panel 7 during the blueshift. The filtering edge on the other side limits the net gain window as continuous scanning of TBPF, which results in solitons disassembly with single switching dynamics, as shown in Fig. 4(b) panel 3, which corresponds to Fig. 4(b) panel 6 during the blueshift. When approaching the right-hand boundary, two-soliton molecules first transform into a single soliton and then transform into Q-switching instability due to the narrowest net gain window in the red shift process, as shown in Fig. 4(b) panel 4, which corresponds to Fig. 4(b) panel 5 during the blueshift.

Such deterministic events, soliton assembly and disassembly, are not easy to occur in a dissipative system. However, it is still possible that a soliton interaction mechanism mediated by the continuum noise floor can lead to soliton drift in mode-locked fibre lasers [38,39]. Physically, the sharp edge on the soliton spectrum corresponds to an oscillating waveform in the time domain. This is understood as the main cause of soliton splitting and the cause for the formation of soliton molecules, provided that the effective gain in the laser cavity is also reduced by the filter. More importantly, by tuning the bandpass filter, such a responded oscillating wave is also travelling within the cavity, potentially resulting in the assembling and dissembling behaviors of the soliton molecule.

In conclusion, we have demonstrated universal dynamics and deterministic motion control of temporal dissipative solitons in a mode-locked fibre laser via the SFE. By introducing external element, TBPF, we could actively control the solitons motion for assembly and disassembly. This provides a deterministic route toward soliton switching inside decoherently seeded systems. Based on the DFT detecting system, we also investigated the completed dynamics at each moment. We observed specific dynamics of soliton assembly and disassembly and revealed the single and complex relative motion of solitons, which is like a chemical reaction of material molecules. These switches are the result of the SFE breaking the established balance of the laser cavity and rebuilding a new one.