Passively synchronized lasers have attracted significant attention in obtaining tunable multi-wavelength output for their cost-effectiveness and ease of construction [1], which find extensive applications in coherent pulse synthesis and precise timing distribution, time-resolved spectroscopy and imaging, and high-capacity optical communication [2–4]. Within the resonator, the interplay between dispersion and cross-phase modulation (XPM) allows cavity length drifts to be automatically compensated for through adaptive spectral changes, maintaining optical length stability passively [5,6]. This passive self-adaptive mechanism enables instantaneous nonlinear responses to provide high-bandwidth feedback without the need for high-speed electronic devices or complex feedback systems required in active configurations. Passively synchronized fiber lasers operating at closely spaced wavelengths not only inherit the numerous advantages of fiber lasers but also output synchronously mode-locked pulse trains with narrower wavelength separations, which addresses the limitations of traditional synchronous laser systems (operating at different gain regions) and dual-wavelength laser systems [7–10], thereby broadening the wavelength window of synchronized pulse trains. The synchronized output from two relatively independent lasers, with closely spaced center wavelengths and stable repetition rates, is more favorable for applications such as subsequent laser amplification and difference-frequency generation of terahertz waves [11]. Moreover, it brings a synchronized, broadband, phase-coherent light source increasingly desirable in various metrological applications [12].

Previous efforts in passively synchronized fiber lasers have concentrated on optimizing the structure and performance of synchronized lasers [13,14], but the synchronization process still remains an ambiguity. Due to the limitations of conventional measurement instruments, researchers have been unable to investigate the transient phenomena occurring in the initial stages of the synchronization, which is crucial for elucidating the dynamics of synchronization. Furthermore, the energy transfer mechanism within the gain medium during synchronization at adjacent wavelengths remains insufficiently understood. Addressing these fundamental issues helps deepen the understanding of the synchronization process and inspires new approaches to improve the stability and precision of synchronized laser systems. Time-stretch dispersive Fourier transform (TS-DFT) provides an effective method for investigating such dynamic processes [15–17]. A recent study reported the initiation and disappearance of the synchronization process by observing the amplitude fluctuation on the oscilloscope [18]. However, the formation mechanisms cannot be fully analyzed due to a lack of spectral dispersion stretching over long fiber distances. As a result, the transient dynamics underlying the buildup and breakdown of passive synchronization processes remain experimentally unexplored to date. These processes, involving the interaction of two independent nonlinear optical systems, exhibit novel dynamic evolution distinct from that of single optical systems.

In this work, we utilized DFT technology to observe the passive synchronization process, demonstrating the entire evolution of the light-light interaction between the two pulses from the initial state to the final state in both the time and frequency domains. Two distinct synchronization phenomena were observed. In the first case, the slave laser achieved mode locking independently, which we define as the normal synchronization state (NSS). In the second case, the slave laser attained mode locking due to the injection from the master laser rather than independently, and this state is referred to as the induced synchronization state (ISS). Both phenomena exhibited new features compared to traditional mode-locked lasers. Notably, in the regime of ISS, mode locking is influenced by the seed pulse from the master laser, leading to the absence of intensity patterns indicative of modulation instability [19]—an unobserved phenomenon in the past.

The experimental setup is shown in Fig. 1, which consists of a passively synchronized fiber laser system followed by a DFT measurement system. Both lasers are pumped by highly stable laser diodes (pump1 and pump2) with an output power up to 650 mW emitted at 976 nm. The gain fibers are two pieces of 30-cm Yb-doped fibers (YB-1200, Liekki) and all other fibers are single-mode fibers (HI1060, Corning). WP1 and WP2 are λ/2, λ/4 waveplates, respectively. BF1 and BF2 are narrowband interference filters at 1064nm±10nm and 1030nm±10nm, respectively. OC1, OC3 are 1:9 fiber couplers and OC2 is a 5:5 fiber coupler. The net intra-cavity dispersions are estimated to be 0.1707ps2 for laser1 and 0.1414ps2 for laser2, evaluated at their respective design wavelengths.

This system realizes synchronization through the master-slave interaction. Seed light from master laser (laser1) is emitted at fiber coupler OC1 and then injected into the resonator of the slave laser (laser2) at OC2, enabling the optical pulses to overlap in the spatiotemporal domain. Through the combined effects of cavity dispersion and cross-phase modulation (XPM), the spectrum undergoes adaptive changes to compensate for cavity length drift. The mechanism ensuring the stable repetition frequency of the two lasers is based on optical injection synchronization.

To facilitate the DFT measurement, a pair of fiber collimators (Col.3, Col.4) is inserted in the injection path, with a chopper placed between them to interrupt the injected pulse without affecting the mode-locking progress of the master laser. A polarization-independent optical isolator is also included to prevent back-reflection from interfering with the master laser’s mode locking. The DFT system consists of two bundles of 10.05-km single-mode fiber (SMF-28e), two photodetectors (Newport 818-BB-35F, 15 GHz), and an oscilloscope (Tektronix DPO70604C, 6 GHz). This setup allows for simultaneous observation of the dynamic evolution of both lasers when a chopper is placed in the optical path. A spectrometer (Yokogawa AQ6370C) is used to record the spectral evolution, while a radio-frequency analyzer (Agilent E447A) monitors changes in the repetition frequency and records the modulation depth of the mode-locked pulse signals. This configuration enables comprehensive monitoring of both the spectral and temporal dynamics of the synchronization process, offering detailed insights into the interaction and transient behavior of both lasers.

Figure 2 shows the mode-locking characteristics of the two lasers when they are not synchronized (with a light-blocking plate inserted between Col.3 and Col.4). The output characteristics of the master and slave lasers are shown in Figs. 2(a)–2(c) and 2(d)–2(f), respectively.

The mode locking of the master laser (laser1) is achieved through the nonlinear polarization rotation (NPR) effect acting as an effective saturable absorber. The transmission characteristics of the laser in the cavity are controlled by three waveplates, a 1064-nm interference filter (±10nm), and a polarizing beam splitter, which also serves as the laser output port. Figures 2(a)–2(c) show the spectrum, autocorrelation trace, and RF spectrum of the master laser. Figure 2(a) shows the master laser’s spectrum centered at 1057.5 nm with a spectral width of 21.0 nm. As can be seen, the M-shaped spectrum, combined with the normal intra-cavity dispersion, indicates that the mode locking operates in the dissipative soliton regime. From the measured autocorrelation trace shown in Fig. 2(b), the corresponding pulse duration is derived to be 4.14 ps from a Gaussian fit. Figure 2(c) gives the RF spectrum, where the repetition frequency of the master laser is determined to be about 28.966 MHz with a signal-to-noise ratio (SNR) of 93.5 dB. The inset figure demonstrates the long-term pulse train with a span of 5 GHz, which indicates the mode locking is very stable combined with the SNR.

To facilitate the master-slave interaction, a 1:9 optical fiber coupler is used to separate a portion of the seed light and inject it into the slave laser. The mode locking of the slave laser is also achieved through NPR, with three polarization controllers (PC1–PC3) used to control the polarization state of light in the cavity. In the all-fiber cavity, a pair of fiber collimators (Col.5, Col.6) is added, with Col.6 mounted on a movable stage to match the cavity length and observe the synchronization characteristics. A 1030-nm birefringent filter is inserted into the spatial optical path to ensure that the center wavelength of the slave laser is distinct from that of the master laser, thereby avoiding excessive gain competition and crosstalk, which would be changed by a 1030-nm interference filter (±10nm) for subsequent experimental use. This configuration allows for a detailed exploration of the synchronization mechanism between the master and slave lasers, including the impact of cavity dispersion and polarization control on the overall synchronization dynamics. The output of the slave laser is monitored through a 1:9 optical fiber coupler. Figures 2(d)–2(f) show the spectrum, autocorrelation trace, and RF spectrum of the slave laser. The spectrum shown in Fig. 2(d) reveals the center wavelength of the slave laser is 1028.1 nm with a spectral width of 12.3 nm. It is noteworthy that there is no spectral overlap between the output spectra of the master laser and slave laser due to the different center wavelengths of the bandpass filters (BF1 and BF2), which minimizes the effects of gain competition and crosstalk. Figure 2(e) displays the autocorrelation trace of slave laser, and a pulse width of 8.56 ps could be derived from a Gaussian fit. Figure 2(f) plots the RF spectrum of the slave laser; an SNR of 84.7 dB is obtained. And the inset figure shows the long-term pulse train with a span of 5 GHz. The repetition frequency of the slave laser is also near 28.966 MHz due to the cavity length matching by finely tuning the position of Col.6. Both the SNR and long-term pulse train prove the stability of the slave laser.

The results clearly indicate that the master laser, due to its higher pump power and the stronger filtering effect of its NPR-based structure employing a free-space optical path, achieves a shorter pulse duration and higher modulation depth compared to the slave laser. This corresponds to a higher peak pulse power, making the master laser an ideal seed source to drive the synchronization process with the slave laser.

Typically, two lasers would work in the asynchronous regime. In this regime, if pulse trains of two lasers were simultaneously displayed on the oscilloscope, one of the pulse trains would slide left and right rapidly for the difference of repetition rate. However, if the cavity length matching (by moving Col.6) is good to some extent, the interaction occurring in the shared cavity between laser1 and laser2 would enable the repetition rate of both lasers to keep consistent. Under this condition, the real-time pulse trains shown on the oscilloscope are stable, which manifests that the synchronization is realized. Figure 3 illustrates the synchronized pulse sequences of two lasers in the synchronous regime, which is simultaneously obtained by the oscilloscope (Tektronix DPO70604C) under the following conditions: the pump power of the master laser is set to 540 mW, and the pump power of the slave laser is set to 347 mW. Both lasers work in continuous-wave (CW) mode locking with a pulse interval time of 34.5 ns. The synchronization could sustain for 6 h, demonstrating its long-term stability and robustness under these conditions.

The synchronization performance of the system is further investigated. Figure 4(a) illustrates the repetition frequency drift of the slave laser with respect to the cavity length mismatch, which is adjusted by finely tuning position of Col.5 with a precision translation stage. In Fig. 4(a), the triangular and circular lines represent shifts of repetition rates with respect to cavity length mismatch in the synchronized or non-synchronized regimes, respectively, while the dashed line corresponds to a simulation result in non-synchronization state with the formula f=c/Lopt, where f denotes the repetition rate, c is light speed in vacuum, and Lopt represents the optical path of the fiber laser. It is determined that the tolerance for cavity length mismatch is 210 μm, corresponding to a variation of 556 Hz in the free spectral range at a central repetition rate of 28.966 MHz. Figure 4(b) gives the tolerance of cavity length mismatch with respect to the pump power of the slave laser when the pump power of the master laser is fixed at 540 mW or 340 mW, which shows the tolerance has a maximum value instead of increasing continuously with pump power. Typically, with the increase of pump power, the intra-cavity power of the slave laser would be higher and the interaction is enhanced. However, a too strong slave laser pulse within the cavity would reduce the influence of the injected pulse, resulting in a deterioration in the master-slave synchronization; thus the tolerance having a maximum value can be understood.

Figure 4(c) illustrates the spectral evolution of the slave laser under synchronized conditions as its cavity length varies, which indicates the offset in cavity length corresponding to each real-time spectrum. Although in previous reports on synchronized laser systems operating at 1 μm/1.5 μm [20] or 1.5 μm/2 μm [21] spectral shifts in center wavelength were observed, such significant spectral reshaping besides center wavelength has not been reported. We consider this phenomenon is primarily due to the gain competition and crosstalk within the gain band of Yb-doped fibers, which dominate the spectral reshaping process. The contributions of cross-phase modulation (XPM) and higher-order dispersion are not obvious in comparison. Furthermore, with the cavity length increasing, the center wavelength of the spectrum sees a redshift, which indicates that the net intra-cavity dispersion is positive, consistent with the theoretical analysis.

Favoring the advantage in detecting transient phenomena [22], DFT technology is particularly suitable to be used in ultrafast diagnosis. So, we built a DFT device to detect the transient synchronization process (shown in Fig. 1). During the DFT measurements of the synchronized mode-locked pulses, we identified two distinct synchronization states: normal synchronization state (NSS) and induced synchronization state (ISS). In NSS, the slave laser can achieve independent mode locking without the pulse seed from the master laser. In contrast, in ISS, the slave laser cannot be independently mode locked in the absence of the master laser’s pulse seed. The dynamic processes exhibited by these two synchronization states show significant differences, highlighting the contrasting mechanisms underlying their formation.

With a chopper placed between Col.3 and Col.4, the seed light would pass or be blocked into the cavity of the slave laser periodically, and the buildup or breakdown process of the synchronization could be detected by the DFT device. Figure 5 presents the DFT image of the output light from the slave laser in NSS and Fig. 5(a) gives the spectral evolution during the buildup of synchronization, where an obvious switching between two different states is observed, with an apparent shift in the center wavelength and spectral reshaping due to the seed light injection from the master laser. The spectral evolution during the breakdown process is shown in Fig. 5(b), where a phenomenon similar to soliton explosions occurs, causing the light pulse to deviate from the dissipative soliton state and stabilize in a distinctly different state. Figures 5(c) and 5(d) show the corresponding field autocorrelations yielded from the Fourier transform of each single-shot spectrum, where changes in the soliton state can be clearly observed.

To better understand the synchronization buildup and breakdown processes, we extracted spectral evolution images of the transition stage from Fig. 5 and present them in Figs. 6(a) and 6(b), respectively. Seen in Fig. 6(a), the pulse undergoes a process from soliton explosion to noise-like pulse [23], and then stabilizes back to the soliton state during the buildup of NSS. That buildup of synchronization takes about 110 roundtrips corresponding to 3.8 μs in time. It is noteworthy that although the formulae of the synchronization process have been proposed in theory [5,6], this is the first time that the synchronization time is obtained experimentally. In the process marked with α1, the suddenly injected external mode-locked pulse causes the light soliton to break into noise-like pulses, with the center wavelength remaining unchanged and the overall intensity increasing (220th–247th roundtrips, 0.93 μs), as shown in the 240th roundtrip spectrum in Fig. 6(c). Afterward, the center wavelength and spectral width undergo several changes, with the center wavelength shifting towards shorter wavelengths, the spectrum narrowing, and the overall intensity weakening (248th–270th roundtrips, 0.79 μs). In the process marked with α2, the noise-like pulse stabilizes back into a soliton pulse with a smaller energy. The center wavelength shifts close to the center wavelength of the final state, and the spectral profile starts to stabilize, as shown in the 280th roundtrip spectrum in Fig. 6(c). After self-phase modulation (SPM), the spectrum symmetrically broadens and simultaneously reshapes, with the intensity at 1026 nm significantly increasing while the intensity at the spectral edges remains almost constant, causing the center wavelength to shift again towards shorter wavelengths.

Figure 6(b) shows the breakdown process of the NSS, which lasts 10.36 μs, obviously longer than the buildup. We speculate this difference may be related to the observation method, as the synchronized state during the disappearance phase is not exactly the same as during the establishment phase. This discrepancy could arise from the transient dynamics and the inherent complexities of the synchronization process, which may be influenced by varying experimental conditions or measurement techniques. In the β1 process, the loss of the injected seed light leads to a lack of gain competition within the cavity, causing the original light pulse energy in the slave laser to increase (400th–410th roundtrips, 0.35 μs). However, the accompanying nonlinear environmental changes—caused by the emergence and disappearance of the injected light within the slave laser cavity—render the pulse unstable, leading to a periodic decrease in both soliton energy and spectral width (411th–480th roundtrips, 2.42 μs). Eventually, the soliton enters the common spectral breathing state, reaching a stable balance between gain and loss within the cavity (481st–600th roundtrips, 7.59 μs), with the center wavelength slightly shifting toward longer wavelengths.

As mentioned above, the slave laser cannot be independently mode locked in the absence of the master laser’s pulse seed in ISS. We replaced the birefringent filter in the slave laser cavity with an interference filter (1030nm±10nm) to achieve the ISS state more easily. To accurately measure the ISS, both the master laser and slave laser are injected into two bundles of 10-km single-mode fibers (SMF-28e, Corning), converted into electrical signals followed by two photodetectors, and finally input into two separate channels of one oscilloscope for simultaneous observation and recording. By varying the lengths of the fiber jumper cables, we ensure the relative time delay between the two signals is less than 1 ns, which is much smaller than a single period (∼34.5ns in our experiment). As a result, the time delay between two lasers’ dynamic phenomena in the simultaneously measured DFT images is considerably reliable.

A chopper is placed between Col.2 and WP2, operating with a chopping frequency of 10 Hz to modulate the master laser. The resulting ISS buildup process is shown in Fig. 7, where the master laser follows a traditional soliton formation process, starting from modulation instability [illustrated in the intensity patterns in Figs. 7(a) and 7(c)], evolving into solitons during the oscillation phase, experiencing spectral breathing, and ultimately stabilizing. In contrast, the slave laser does not exhibit the common intensity patterns typically seen before soliton formation. Instead, after the master laser evolves into solitons, the slave laser directly generates optical pulses within the cavity, followed by a noise-like phase and asymmetric spectral broadening, which eventually forms solitons.

To better observe the effect exerted by the master laser on the slave laser, we extracted the synchronization buildup process of both lasers, then selected several characteristic spectra, and display them in Fig. 8. During the master laser’s initiation process (1600th–1724th roundtrips, 4.28 μs, process marked with γ1), no oscillations were observed in the slave laser; as a result no pulse signals were captured on the oscilloscope. However, when the master laser formed solitons and entered the breathing state (1725th–2050th roundtrips, 11.22 μs, process marked with γ2), the slave laser immediately generated solitons, as shown in Figs. 8(c) and 8(d). In a short time (within 25 roundtrips), the energy increased, and the pulse fragmented into noise-like pulses (1725th–1889th roundtrips, 5.66 μs, process marked with δ1), as shown in Fig. 8(d). This process is synchronized with the master laser’s soliton formation and spectral broadening. It is speculated that the master laser’s pulse train acts as a timing gate to promote mode-locked pulse formation in the slave laser cavity, while the absence of intensity patterns suggests insufficient modulation for independent soliton formation.

When master laser’s soliton-breathing state weakened and stabilized on soliton mode locking, the slave laser returned to a stable soliton state. Due to the modulation induced by the master laser’s pulse seed, the cross-phase modulation effect caused asymmetric spectral broadening, leading to a shift in the center wavelength towards the shorter wavelength, which resulted in a synchronization. The slave laser then continued to experience spectral jitter due to the influence of the master laser’s breathing state, with further pulse broadening. Finally, after the master laser exited the breathing state and stabilized, the slave laser also stabilized (1890th–2050th roundtrips, 5.52 μs, process marked with δ2).

Thus, in the induced synchronization state, the slave laser is instantaneously modulated by the master laser’s pulse light, with a response delay within one cycle. The stability of the injected seed light from the master laser greatly determines the stability of the slave laser’s mode locking.

The breakdown of synchronization in ISS is also recorded. To facilitate the measurement, the chopper is placed before Col.2 to selectively inject or block part of the master laser into the slave laser cavity and control the state of the master laser. Figure 9 presents the DFT images during the extinction of the mode-locking process, which is also the breakdown of synchronization. Seen in Figs. 9(a) and 9(b), the maser laser and slave laser keep in the synchronization state. When the chopper works, the master laser would experience a soliton breathing process till the light is cut off completely. And the slave laser is also influenced by the master laser. After the master laser has been cut off, the slave laser could not sustain the mode locking and transitioned to a pulse state with an obvious spectral narrowing instead of mode locking. The field autocorrelations shown in Figs. 9(c) and 9(d) confirm this fact.

In DFT measurements for pulse dynamic evolution, sufficient dispersion is required for all the spectral components to be fully stretched and mapped into the time domain. The mapping relation can be written as Δt=|D|·L·Δλ,(1)where Δλ is the spectral width, Δt is the time interval after DFT, and D and L are the dispersion parameter and the length of the single-mode fiber, respectively. Given the values of D and L, the temporally consecutive data extracted from a high-speed oscilloscope can be mapped into corresponding wavelength based on Eq. (1). In our experiment, D is approximately 36.72ps/(nm·km) and L is 10 km. Therefore, we obtain the simplified relation from Eq. (1): Δt=0.3672ns/nm×Δλ.(2)

To check if introduced dispersion is enough, a comparison has been carried out between the spectra directly detected by an optical spectrum analyzer (OSA) and mapped by DFT based on Eq. (2). Figure 10 presents both spectra, where the orange line represents the spectrum of the slave laser without any injected light, measured by OSA, with a spectral width of 12.3 nm and a center wavelength of 1028.1 nm. The blue line represents the dynamic spectrum of a single frame, measured by DFT. As shown in Fig. 10(a), the spectrum obtained from DFT is highly consistent with that obtained from the OSA, confirming the reliability of DFT in probing the pulse evolution of fiber lasers. However, in Fig. 10(b), the dynamic spectrum obtained by DFT during ISS does not perfectly match the spectrum measured by the OSA. Although the profiles are similar, noticeable oscillatory structures are present; we speculate they might be related to stripe solitons [24], which have a similar spectral structure. The replacement of the interference filter enhanced mode coupling and interference inside the cavity. The injected seed light is elliptically polarized, and the cross-phase modulation effect causes nonlinear coupling between the two orthogonal polarization components, while the self-phase modulation effect causes nonlinear coupling between multiple peaks within each component. Both effects change the spectral energy distribution and cause a frequency shift of the two components, eventually resulting in modulations in the spectrum. Another possible reason is that the spectrum from OSA is indeed a time-averaged result; thus the random oscillation is cancelled with the average over a relatively long period. In comparison, the DFT result is only a frame data (on the order of a pulse width, i.e., ps, fs for ultrashort pulse), and the oscillation is difficult to be cancelled compared to a spectrometer. However, the quite close profile and FWHM of both spectra prove the reliability of the DFT device and corresponding experimental results.

In summary, we have presented a stable synchronized fiber laser system composed of two mode-locked Yb-doped fiber lasers in a master-slave configuration. This system could deliver two tightly synchronized ultrafast laser beams with different wavelengths near 1 μm. The synchronization could sustain stably for more than 6 h. The tolerance of cavity length mismatch with respect to the pulse energy is observed in the slave laser, and it is found that the tolerance reaches a maximum of 210 μm at definite pulse energy instead of increasing simply with pulse energy, which is speculated to be related to the synchronization mechanism of the master-slave configuration, where an excessively strong slave laser pulse within the cavity may reduce the influence of the injected pulse.

Based on the synchronized laser, time-stretched dispersive Fourier transform technology is introduced and real-time transition dynamics of the synchronization were obtained successfully. The synchronization has been divided into two different states: normal synchronization state (NSS) and induced synchronization state (ISS). In NSS, spectral shaping is found during synchronization. Furthermore, tuning the cavity length of the slave laser while the synchronization is sustained, the center wavelength shifting is obviously observed, and the wavelength shifts towards long wavelength in the case of positive intra-cavity dispersion, which is very consistent with the theoretical prediction. The spectral evolution and center wavelength shift can be clearly observed. The buildup of synchronization takes about 110 roundtrips, corresponding to 3.8 μs in time. Similarly, the breakdown of synchronization takes about 300 roundtrips, 10.36 μs in time. Entirely different from NSS, the results of DFT in ISS demonstrates there is no “mode-locking memory” process upon chopping, and no initiation process is observed. Instead, pulses are directly generated, and then evolve into a noise-like state and ultimately stabilize into a dissipative-soliton pulse. The slave laser has no signal while the master laser initiates oscillation, and when the seed light is formed as a soliton, the slave laser produced a soliton at the same time (in a single cycle), which demonstrated that the seed light soliton assisted the slave laser in mode locking, acting as a timing gate that periodically modulated the nonlinear effects and losses within the cavity. Thus, the synchronization is instinctive since the mode locking of the slave laser is controlled by the master laser. These results demonstrate that the introduction of DFT provides valuable insights into understanding the synchronization process. To the best of our knowledge, this is the first time that pulse formation, spectral reshaping, central wavelength shift, as well as synchronization time of the synchronization process are precisely revealed in an ultrafast scope experimentally. Since the synchronization is essentially a kind of light-light interaction within materials, this method can be applied in the diagnosis of other synchronized laser sources and ultrafast laser interactions. We believe the use of DFT would help to improve the performances of synchronized laser devices and deepen understanding of the mechanisms of other light-light interactions in diverse kinds of materials.