Presently, the investigation of solitons has involved many fields such as hydromechanics^[1], Bose–Einstein condensates^[2], and nonlinear optics^[3]. The rapid development of ultrafast fiber lasers also provides conditions for studying optical solitons in nonlinear dissipative systems. Since the first theoretical prediction of the existence of solitons in optical fibers^[4], an abundance of soliton phenomena such as the conventional soliton (CS), dissipative soliton (DS), noise-like pulse (NLP), and soliton explosion has been discovered in ultrafast fiber lasers^[5-8]. Unlike the CS, the DS maintains balance without relying on the positive and negative chirps generated by nonlinear and anomalous dispersion effects. Instead, bandpass filters are introduced to achieve an equilibrium among gain, loss, dispersion, and nonlinearity^[9]. CS or DS is reported to be converted to NLP by the peak-power-clamping effect when the pump power is increased or the polarization controller (PC) is adjusted^[10-13]. However, the dynamic switching process between the DS and NLP and whether it is reversible is still an open question.

Ultrafast fiber lasers also enable mode-locking of multiple wavelengths, resulting in coexisting multicolor pulses^[14,15]. This method can produce highly coherent dual-comb sources with low system complexity, making it a promising single-cavity dual-comb technique^[16]. However, owing to the different group velocities, the dual-color pulses undergo periodic collisions in the cavity. Pulse interactions in the cavity both affect the performance of the dual-comb sources and contain interesting dynamical mechanisms. The same type of dual-color pulse dynamics based on wavelength multiplexing^[17-19] has been reported by exploiting a time-stretch dispersive Fourier transform (TS-DFT) detection technique^[20], although dual wavelengths with different pulse types have been found in wavelength multiplexing^[21]. The dynamics of such dual-color pulse collisions requires still further exploration.

In this Letter, we construct an all-normal dispersion ytterbium-doped fiber laser based on a mode-locked nonlinear amplifying loop mirror (NALM). Real-time spectra of DS and NLP inter-switching are obtained for the first time by adjusting the pump power, and the reversibility of the process is demonstrated. In addition, the dynamics of dual-color pulse collisions for different pulse types are investigated. The results indicate that the pulse duration and pulse period of different types of pulses lead to different collision durations of dual-color pulses. During the post-collision spectral reconstruction process, the dual-color pulses exchange energy twice for their respective accumulation dynamics. Afterward, some energy is released to complete the spectral reconstruction. And the collision process has randomness. These research findings deepen the understanding of soliton dynamics.

The experimental setup of the single-/dual-wavelength mode-locked fiber laser based on NALM is shown in Fig. 1(a). A $\sim 20\mathrm{cm}$ long polarization-maintaining ytterbium-doped fiber (PM-YDF) as a gain medium is pumped by a laser diode with a maximum power of 600 mW through a 980/1064 nm wavelength-division multiplexer (WDM). Among them, PM-YDF also offers sufficient birefringence and filter spacing of $\sim 19\mathrm{nm}$, which is affected by the length of PM-YDF^[6]. In addition, PM-YDF is spliced as close as possible to WDM to increase geometric asymmetry and facilitate self-starting. The NALM ring and unidirectional ring (UR) of a figure-eight cavity are connected by a 50:50 optical coupler 1 (OC1). A polarization-independent optical isolator (PI-ISO) ensures that the unidirectional transmission of the UR and the polarization state are jointly regulated by the PC1 and PC2 in the cavity. The remaining fibers are single-mode fibers with a total cavity length of $\sim 12.80\mathrm{m}$.

A total of 90% of the optical signal oscillates inside the cavity, and the remaining 10% is output by OC2 to monitor output characteristics. Figure 1(b) displays the monitoring device, where the output signal is divided by the OC (70:30) into two parts for separate detection. A total of 70% of the output pulse signal is stretched by 2 km of dispersion compensating fiber (DCF, G652C/250, $|D|=39.87\mathrm{ps}{\mathrm{nm}}^{-1}{\mathrm{km}}^{-1}$), and then real-time spectra are measured by the TS-DFT detection technique with a spectral resolution of 0.57 nm. The technique relies on photodetector 1 (PD1, ET-3600 F/APC, 22G) and a high-speed real-time oscilloscope (MSO73304DX, 33G). The output characteristics of the other pulse signals are directly monitored by PD2 (DET08CFC/M, 5G), a radio frequency (RF) spectrum analyzer (N9000B, Keysight), an oscilloscope (DSO9104A, Agilent Technologies), and an autocorrelator (PulseCheck-50, APE).

Experimentally, the saturation absorption effect of NALM causes the laser to operate in a passively mode-locked state. As shown in Fig. 2, by carefully manipulating the PCs, the DS and NLP are obtained at pump powers of 107 mW and 117 mW, respectively, with 3 dB bandwidths of 6.32 nm and 5.48 nm. Setting the rising edge trigger of the oscilloscope to the amplitude height of the NLP increases the pump power from 107 mW to 117 mW, thereby capturing the dynamic spectrum of the DS to NLP evolution. We intercepted the time series of 140 µs and segmented it with a period of 62.30 ns for spectral dynamic evolution analysis, and the result is shown in Fig. 3(a). It is worth mentioning that the DCF used in the experiment operates at 1.5 µm, and the UPC jumper has a large return loss at 1 µm. This led to the creation of weak reflected pulses with the same evolution next to the main pulse, which did not affect the analysis of the evolution of the main pulse. The shot-to-shot spectra in dashed box 1 are shown in the inset of Fig. 3(a), where the conversion of DS to NLP can be observed at the $\sim 890$^th round-trip, due to the instantaneous increased pump power. The spectral profile is observed to remain constant and without substructure for the 700^th to $\sim 889$^th round-trips, indicating that the pulse is a DS. NLP properties are observed in the $\sim 891$^st to 1200^th round-trips, including long ($\sim \mathrm{ns}$) packets constituted of a large number of ultrashort ($<\mathrm{fs}$) spikes, as well as the complex chaotic evolution of these peaks^[22]. Moreover, in order to present the evolution more clearly, Fig. 4(a) shows several typical single-shot spectra. As exhibited in Fig. 3(b), the repetition frequency of the DS is 16.05 MHz, corresponding to the cavity length. In addition, the signal-to-noise ratio (SNR) is $\sim 71\mathrm{dB}$, and the pulse duration is slightly greater than $\sim 19.52\mathrm{ps}$ (due to the limitations of the autocorrelation measurement range). The SNR of the NLP in Fig. 3(c) is $\sim 55\mathrm{dB}$, which is lower than that of the mode-locked DS. A significant noise pedestal of the spectrum caused by amplitude noise can be observed due to variations in the NLP amplitude. The double-scale autocorrelation trace of the NLP is presented in Fig. 3(d) with $\sim \mathrm{fs}$ scale spike and $\sim \mathrm{ps}$ scale pedestal. The typical properties of the DS and NLP mentioned above evidence that they are in a stable mode-locked state.

Simultaneously, the switching process between the DS and NLP is reversible. With the pump power reduced from 117 mW to 107 mW, we capture the dynamic process of NLP to DS evolution as shown in Figs. 3(e)–3(h). The NLP contains high energy and requires multiple relaxation oscillations to release the energy with the aim of transitioning to stable mode-locked DS. However, the number and duration of relaxation oscillations depend on the equilibrium state in the cavity having some randomness. In Fig. 3(e), the NLP undergoes two relaxation oscillations and then obtains mode-locked DS. On closer inspection, the shot-to-shot spectra mode-locked from the 700^th to the 1100^th round-trips in dashed box 2 are the NLP state shown in Fig. 3(f). Figure 3(g) shows the 4000^th to 5000^th round-trips in dashed box 3, which is experiencing small relaxation oscillations, but the spectrum is still characterized by significant NLPs. Figure 3(h) shows the shot-to-shot spectrum from the 9500^th to 12,000^th round-trips in dashed box 4. During the relaxation oscillations, the NLP characteristic is gradually weakened (the 9500^th to ∼10,200^th round-trips) and evolves into DS relaxation oscillations (the ∼10,201^st to ∼11,060^th round-trips), and the amplitude of the oscillations gradually decays until stable DS output is formed (the ∼11,061^st to 12,000^th round-trips). Further, typical single-shot spectra during NLP to DS evolution are shown in Fig. 4(b). Interestingly, switching between the DS and NLP is also possible by adjusting the PCs, but capturing the dynamic evolution is relatively difficult.

Proverbially, intracavity birefringence and polarization-dependent loss can jointly generate spectral filtering effects^[23]. Selecting a reasonable free spectral region ensures that the spectral filter has two transmission peaks simultaneously in the higher amplified spontaneous emission band, thereby creating conditions for mode-locked dual-wavelength. In our experiment, by boosting the pump power to 261 mW and rotating the PCs, three modes of mode-locking at 1039 nm and 1059 nm are achieved, including dual-NLP, NLP-DS, and dual-DS, as shown in Fig. 5. The dynamic evolution of dual-wavelength collisions with different pulse types is analyzed using the TS-DFT technique, where the pulses at 1039 nm and 1059 nm are defined as a blue pulse and red pulse, respectively.

Figures 6(a)–6(d) illustrate the output characteristics of dual-color pulses in mode-locked dual-NLP. Different wavelengths have different group velocities, which leads to periodic collisions of dual-color pulses in the cavity. The collision period $\mathrm{\Delta }t=1/\mathrm{\Delta }f$, where $\mathrm{\Delta }f$ represents the difference in fundamental repetition frequency, and the calculated value $\mathrm{\Delta }t=0.4\mathrm{ms}$. The shot-to-shot spectral evolution in the 140 µs range around the collision of dual-color pulses is shown in Fig. 6(a), and a close-up of the collision is included. The horizontal axis is the time rather than the wavelength, as the pulse interval of the dual-color pulses is constantly changing. If pulses collide, it will be reflected in the intensity of the real-time spectrum. Dual-color pulses approach each other and do not interact during the 1^st to $\sim 915$^th round-trips. From the spectral intensity variation curves of dual-color pulses, it can be distinctly observed that the collision occurred at the $\sim 916$^th to $\sim 1030$^th round-trips, at which point their intensities produce explosive peaks (the red and blue curves represent red pulse and blue pulse, separately). Typical single-shot spectra during the collision [the 910^th, 930^th, 968^th, 1010^th, and 1030^th of the black box in Fig. 6(a)] are presented in Fig. 7(a). As shown in Fig. 7(a)-I, the dual-color pulses are exactly next to each other. Then, the dual-color pulses gradually overlap as they move toward each other, and the intensity of the pulses increases until they completely overlap and the intensity reaches a peak, as shown in Figs. 7(a)-II and 7(a)-III. Subsequently, the dual-color pulses gradually separated, at which time their positions were interchanged and the intensity of the pulses gradually weakened, as displayed in Fig. 7(a)-IV. This collision process ends with the complete separation of the dual-color pulses as illustrated in Fig. 7(a)-V. As the collision process ends, the dual-color pulses undergo accumulation dynamics and complete the spectral reconstruction process under the action of self-organization effects, respectively^[24].

Typical single-shot spectra during reconstruction [the 1275^th, 1342^nd, 1492^nd, 1500^th, and 1681^st in Fig. 6(a)] are presented in Fig. 7(d). The process is accompanied by two energy exchanges of dual-color pulses, where the energy of the blue pulse is swallowed by the red pulse, and the energy of the red pulse reaches a peak, as shown in Fig. 7(d)-I. After accumulating enough energy^[25], the red pulse releases some energy while the blue pulse gradually increases in energy until it swallows up the energy of the red pulse, as shown in Figs. 7(d)-II and 7(d)-III. After that, the blue pulse also releases some energy, causing the dual-color pulses to reshape into a stable mode-locked state for the next new collision, as shown in Figs. 7(d)-IV and 7(d)-V. To our knowledge, the process of explosion and collapse caused by collision and then the return to a stable state is a unique soliton explosion phenomenon in dissipative system dynamics^[26]. In the pulse sequence of Fig. 6(b) without DCF, the amplitude instability of dual-color pulses is one of the characteristics of the NLP. In the RF spectrum shown in Fig. 6(c), the repetition rate difference is $\sim 2.5\mathrm{kHz}$, corresponding to the collision period. There is a noise pedestal, and the amplitude of the beat frequency follows the trend of the noise pedestal. Figure 6(d) shows the double-scale autocorrelation trace with a $\sim \mathrm{ps}$ scale pedestal and $\sim \mathrm{fs}$ scale narrow spike, which further confirms the appearance of the NLP.

The shot-to-shot spectra of the blue pulse as the NLP and the red pulse as the DS are shown in Fig. 6(e), which have the same evolution process as dual-NLP. Typical single-shot spectra of the collision [the 910^th, 930^th, 968^th, 1010^th, 1030^th in Fig. 6(e)] and reconstruction processes [the 1320^th, 1637^th, 1656^th, 1680^th, 1760^th in Fig. 6(e)] are presented in Figs. 7(b) and 7(e). The pulse train of the DS with a smooth amplitude and the NLP with large fluctuation is shown in Fig. 6(f), where the pulse energy of the NLP exceeds the DS. The noise pedestal in Fig. 6(g) is due to the presence of the NLP. The pedestal of the autocorrelation trace in Fig. 6(h) is slightly reduced compared to Fig. 6(d).

The shot-to-shot spectra of the dual-color pulses (both DS) are shown in Fig. 6(i). To satisfy the conditions for NLP generation, the DS splits the pulse when the 261 mW power is too high. Because of the same evolutionary features, the spectral intensity variation data in the inset are taken from the set of pulses on the right. The small burst peak from the $\sim 873$^rd round-trip to the $\sim 990$^th round-trip in Fig. 6(i) is the effect produced by the collision of the split pulse. Additionally, typical single-shot spectra of the collision [the 1348^th, 1365^th, 1416^th, 1463^rd, 1483^rd in Fig. 6(i)] and reconstruction processes [the 854^th, 901^st, 954^th, 984^th, 1243^rd in Fig. 6(i)] are presented in Figs. 7(c) and 7(f). Figure 6(j) shows four pulse sequences with stable amplitudes and parallel pairwise generation by the splitting of dual-color pulses, indicating the generation of the dual-DS. The spectrum pedestal and beat frequency signals in Fig. 6(k) are both stabilized. The single-scale autocorrelation trace in Fig. 6(l) further demonstrates the existence of the DS.

The different pulse durations and pulse periods of the dual-color pulses in the three modes lead to slight differences in the interaction length at the time of the collision^[27]. Furthermore, close-ups of the regions of two collisions of dual-color pulses consisting of dual-DS are displayed in Fig. 8. By comparing 40 sets of single-shot spectra of five intervals uniformly distributed in the dashed box, we find that the characteristics of each collision are similar, but with the chaotic nature of soliton explosions^[28], which makes the spectral details of each collision not the same. In addition, during the reconstruction process after the collision of dual-color pulses, the blue pulse at 1039 nm always completes the reconstruction first. The reason is that the gain intensity at 1039 nm is higher than that at 1059 nm, and the blue pulse occupies a competitive gain advantage in the reconstruction process.

In summary, we document and analyze the dynamics of DS and NLP inter-switching by adjusting the pump power of a single-/dual-wavelength mode-locked fiber laser based on NALM. The collision dynamics of dual-color pulses with three different pulse types at wavelengths of 1039 nm and 1059 nm also have been investigated, respectively. The entire process experiences dual-color pulse collisions and completes accumulation dynamics separately, and then releases energy and reconstructs a stable spectrum. Our research enriches the soliton dynamics in terms of collisions with different pulse types.