Mode-locked laser sources are crucial foundations in various fields, such as ultrafast science [1,2], advanced manufacturing [3,4], and high-precision measurement [5,6]. Optical soliton in mode-locked fiber lasers, emerging from a delicate balance between group-velocity dispersion (GVD) and nonlinear phase accumulation via self-phase modulation (SPM), stands out as an excellent candidate due to its superior spatial mode quality, resilience to thermal effects, compact size, and cost-effectiveness [7,8]. Soliton mode-locked lasers with the net negative cavity dispersion have been the universal solutions to generate the femtosecond laser.

The further flourishing development of the soliton in recent decades owes much to the exploitation of the cavity dispersion map. When managing the cavity GVD to near zero, the dispersion-managed soliton (DMS) can be obtained, leading to a significant increase of pulse energy by decreasing the nonlinear effect via the periodic broadening and compression of pulses [9,10]. Further, the self-similar (SS) soliton [11,12] and dissipative soliton (DS) [13–15] have been proposed to break the pulse energy limitation with the normal dispersion condition. The SS soliton undergoes monotonic chirp evolution within the cavity, converting accumulated nonlinearity into increased spectral width without compromising pulse stability [12]. The latter, existing in dissipative systems, results from the combined effects of GVD, nonlinearity, gain, loss, saturable absorption, and spectral filtering [13].

As the diverse effects are actually introduced via different intracavity devices, they produce an intracavity evolution dynamics to meet the self-consistent formation process. It has been the common method to structure the formation condition of SS soliton, DS, and even Mamyshev lasers by managing the intracavity amplification and filtering effect [16–18]. And the dissipative condition and device positions also would bring the nonnegligible changes to each type of soliton. To investigate intracavity dynamics, a widely adopted approach involves introducing two or three output ports within the laser cavity [16,18–21]. These ports enable the observation of pulse features as they traverse key intracavity components, such as mode-locking devices, gain fibers, and spectral shaping elements. Information extracted from these critical locations facilitates the optimization of dispersion management, enabling the generation of femtosecond dispersion-managed solitons [19] and self-similar pulses [16]. Additionally, the spectral filtering process can be enhanced, leading to an extension of the spectral bandwidth to several hundred nanometers [20]. This approach also offers the potential to realize auto-setting mode-locked fiber lasers. Furthermore, by combining dispersion Fourier transform (DFT) techniques [22], real-time intracavity dynamics, such as spectral bifurcation and oscillatory behavior, can be observed experimentally [21].

However, these reports using a few output ports are insufficient to reconstruct the complete evolutions of the intracavity pulse. Currently, the experimental monitoring of optical pulse dynamics within the cavity has yet to be fully developed. Although numerical simulations can offer insights into this continuous intracavity evolution [11,16,23–25], discrepancies between theoretical predictions and experimental results are inevitable. These deviations arise from factors such as the omission of higher-order dispersion and nonlinearity effects in the fiber, as well as challenges in accurately determining certain parameter values. Experimentally, observing the full evolution of the pulse within the laser cavity, particularly within the gain fiber segment, remains a formidable challenge.

In this work, a vine-structured erbium-doped fiber (EDF) is fabricated, which contains several delicate branches so that pulse propagation in EDF can be recovered. The intracavity spectral evolution of mode-locked fiber lasers is obtained experimentally for the first time with the vine-structured EDF under different net dispersion values. The dispersion distribution conditions for different types of solitons are studied according to the measured intracavity evolutions. This work gives a deeper understanding of soliton evolution and is helpful for laser design with further exploration of dispersion and nonlinear management.

Our experimental setup is based on a passively mode-locked EDF laser, depicted in Fig. 1. The vine-structured EDF is designed based on the commercial EDF (Nufern EDFC-980-HP). Seven fused fiber optical couplers are dispersedly fabricated in a 7-m-long EDF, which are fused and tapered with SMF. The length of the SMF pigtail is less than 1 m, and it has little impact on the transmission results inside the output EDF. Detailed specifications and parameters of the vine-structured EDF are provided in the lower section of Fig. 1. The spacing between each coupler is deliberately varied to facilitate the observation of pulse characteristics at the junctions of pulse evolution. Taking the intrinsic optical loss and the length of the EDF segments between couplers into account, we carefully tested the coupling ratios of each coupler (in propagation order: 1.00%, 1.44%, 1.41%, 1.20%, 0.80%, 0.57%, and 0.57%). This approach not only minimizes the perturbation to soliton evolution caused by output coupling losses but also prevents the EDF’s intrinsic optical loss from affecting the accuracy of intracavity evolution observations. As the signal is amplified in EDF, the slight added loss due to the couplers’ output can be compensated in the following gain sections, which ensures the minimum effect on the original evolution. The designing of the couplers is described in the subfigure. Considering that soliton propagation in EDF is not linear, the distribution is designed asymmetrically. The coupler output parameters are calculated under the consideration of the absorption and extra-loss of EDF.

A 976 nm laser diode (LD) pumps the EDF through a wavelength division multiplexer (WDM). An isolator and a 1% coupler are integrated into the device to allow monitoring of the intracavity conditions before the light enters the gain fiber. The pump light in the EDF undergoes stimulated emission, contributing to soliton formation, which can be monitored through the coupler ports. A bandpass filter (1530–1580 nm) after the EDF removes residual pump light, with 10% of the power extracted for analysis. The saturable absorber (SA) is homemade using single-walled carbon nanotubes, and a polarization controller (PC) is placed after the SA to optimize the soliton state by applying stress to the fiber, adjusting the birefringence. Several optical couplers with a 1% tap ratio are spliced into the fiber to monitor the effects of the SA and the SMF. This setup allows over 10 measurements to track the intracavity evolution. As the output power is typically only a few tens of μW, pulse characteristics are mainly studied through optical spectra, as the pulse envelope is too weak to be measured with an autocorrelator, except at port 9. To achieve different soliton types, the total length of SMF in the cavity is adjusted to vary the net cavity dispersion from anomalous to normal.

With the SMF length of approximately 12.0 m, the net dispersion is about −0.103ps2, which indicates the formation of conventional soliton. At pump power of 20 mW, a stable single-pulse soliton operation around 1560 nm is observed. Figure 2(a) depicts the normalized hyperbolic secant spectrum of the conventional soliton with a central wavelength of 1558.5 nm and a full width at half maximum (FWHM) of 7.065 nm. The measured autocorrelation trace corresponding to the spectrum is shown in Fig. 2(b) with an FWHM of 1.332 ps. For the stable state, pulses circulate in the oscillator with the self-consistent evolution process so that the spectral feature for each port can be measured by the optical spectrum analyzer (OSA). Then, they are depicted along the cavity position to show the intracavity spectral evolution after the splitting ratios of each port are calibrated, as shown in Fig. 2(c). The evolutions of the pulse energy and spectral width are also drawn to show the soliton features in Fig. 2(f). The amplification process can be seen clearly in the EDF section where the pulse energy gradually increases and then tends to saturate. The spectra always maintain a similar profile to the typical Kelly sidebands in EDF and other sections, while the bandwidth changes in the range of 6–7.3 nm. In the first 4 m of EDF, the spectral width is decreased due to the SPM effect under negative chirp and the spectral narrowing effect induced by EDF [7]. In the following section of EDF, the spectrum is broadened by SPM under normal dispersion and is further increased by the subsequent SMF and SA, while it is slightly narrowed during propagation in the last SMF. The results illustrate experimentally that the gain and dispersion distributions drive the soliton to evolve periodically in a fiber laser, although the net dispersion is negative, which seems similar with the reported theoretical results [23,26,27].

The Kelly sideband is the typical feature of the conventional soliton, and the sideband positions depend on the phase-matching interference between the soliton and dispersive wave [28,29]. Here, it is found that the sidebands also vary along with soliton propagation in the cavity in Figs. 2(d) and 2(e) demonstrating the action of each component to induce the emission of the dispersive wave. The wavelength difference between two main sidebands in Fig. 2(g) displays a similar changing process to the spectral width in Fig. 2(f), while at the position of ∼4.5m in EDF, the evolution is abnormal indicating the complex action to the dispersive wave [30]. Additionally, the proportions of energy for two sidebands are also calculated. It can be seen in Fig. 2(g) that the sidebands do not follow the energy evolution of the soliton, and they are suppressed in the first 4 m EDF and enhanced in the following sections.

By shortening the length of SMF to 5.76 m, the DMS is produced under the net cavity dispersion of −0.015ps2. The intracavity spectral evolution is depicted in Fig. 3(a), where the smooth Gaussian-shaped spectra can be seen without a clear sideband. The pulse energy follows a similar evolution process in that it is amplified and saturated in EDF and then decreased gradually in the other sections. However, the slight difference exists between these in Figs. 2(f) and 3(a), owing to the change of cavity length and port position. The spectral width changes from 11.5 to 13.5 nm, which is a slightly larger breathing ratio of 1.17 than that in Fig. 2. Noting that the conventional soliton and DMS exhibit similar evolution dynamics; although the spectral profile and width are distinct, it is feasible to clarify the conventional soliton as a DMS in mode-locked fiber lasers. Then, the SMF length is gradually reduced, and the soliton evolution maintains the similar dynamics until 5.56 m, as shown in Fig. 3(b), where the net cavity dispersion is 0.0011ps2. Additionally, the spectral breathing ratio increases obviously to 1.3 from 14.2 to 18.4 nm.

As the length of SMF is further reduced to 4.9 m, the spectral evolution dynamics changes dramatically, as shown in Fig. 3(c). The spectrum is first narrowed to 12.05 nm in the first 3 m EDF and then suddenly broadened to 12.45 nm in the following EDF. In the other sections, the spectrum is narrowed to 12.2 nm by SMF and SA functioning as the filtering effect. However, the bandwidth changes slightly in cavity, and the spectral breathing ratio is much smaller than DMS. The spectral profile of the soliton closely resembles a parabolic shape, rather than a Gaussian or sech2 function, indicating that the operating state can be regarded as an SS soliton.

After adjusting dispersion to 0.052ps2, the rectangular spectra can be observed at a pump power of 30 mW in Fig. 3(d). This is the typical characteristic of the DS under normal dispersion. The steep spectral edges originate from the filtering effect to balance spectral broadening processes in the gain medium [31]. In the mode-locked fiber laser, there is no actual filter device, and the spectral narrowing effect induced by EDF plays an important role in the evolution. The evolution dynamics can be obviously observed in Fig. 3(d).

Spectrum and autocorrelation trace results of four solitons measured from 10% output port are demonstrated in Fig. 4. In the spectrum domain, Gaussian profiles are used to fit with the DMS [Figs. 4(a) and 4(b)]. The spectrum curve in Fig. 4(c) is approximate with the parabolic profile (red dashed curve), indicating that an SS soliton is propagating in the laser. The dissipative soliton spectrum is fitted with a flattop profile whose edge is steep [Fig. 4(d)]. The autocorrelation trace results are well fitted with their predicted pulse shape. Under the effect of dispersion and chirp, the four soliton pulses widen with the dispersion from the anomalous to normal dispersion regime. Pulse durations are calculated as 1.282 ps, 1.832 ps, 2.168 ps, and 3.770 ps, respectively.

To investigate the evolution dynamics of solitons under distinct dispersion maps, we conduct simulations of mode-locked fiber laser with the Ginzburg-Landau equation [32,33] and pulse cycling method [16,25,27,34]. The pulse propagation in SMF and EDF can be described as ∂A∂z+iβ22∂2A∂τ2=iγA|A|2,(1)∂A∂z+iβ22∂2A∂τ2=iγA|A|2+g2A+g2Ωg2∂2A∂τ2,(2)in which A=A(z,τ) represents the pulse function, z represents the propagation distance, τ represents time, β2 represents the second-order dispersion coefficient, γ represents the fiber nonlinear coefficient, g represents the gain coefficient, and Ωg represents the gain bandwidth. The numerical model is solved by the stepwise Fourier method, which divides the continuous domain of time or space into multiple steps and then performs Fourier transforms at each step, thereby converting the continuous problem into a discrete one. By stitching together the results of each step, the complete intracavity evolution process of solitons can be obtained. The saturable absorber, which is the key device of mode-locking, can be modelled by the function as follows: T(τ)=1−T0[1+P(z,τ)/Psat]−1−Ts,(3)where T0 is the modulation depth, P(z,τ)=|A(z,τ)|2 is the pulse power, Psat is the saturation power, and Ts is the unsaturated loss.

The device parameters used in the numerical simulations are the same as in the experiment. The length of the vine-structured EDF, considering the non-visible parts of the coupler, is fixed at 7 m. The second-order dispersion coefficient and nonlinear coefficient are taken from the standard parameters of this commercial EDF, β2=0.018ps2/m and γ=0.004W−1m−1, as the fabrication process only modifies the geometry and optical loss at the fused taper regions, with negligible impact on the overall dispersion and nonlinearity. The length of single mode fiber varies to adjust the net dispersion; here, SMF 28e with β2=−0.0216ps2/m and γ=0.0013W−1m−1 at 1550 nm is used. A 10% output is set to simulate the coupler set at the end of EDF, considering the extra output resulting from more than 10 couplers. Carbon nanotubes (CNTs), used as an SA, possess special optical characteristic that if a soliton pulse intensity arises, the transmission of CNTs also increases. The home-made CNT-SA and its associated research on saturable absorption have been characterized in several previous studies [35,36]. In the simulation, optimized values of T0=0.3, Ts=0.3, and Psat=10W were adopted, ensuring that the numerical simulation results closely matched the experimental observations while remaining consistent with the order of magnitude reported in previous studies.

Soliton evolution is simulated, illustrated by the curve of the spectral bandwidth, pulse duration, and pulse energy as functions of positions in the cavity, corresponding to the experimental results in Figs. 2 and 3 by adjusting the length of the SMF, which is 10.7 m, 6.6 m, 5.85 m, 5.65 m, 5.5 m, and 3.5 m from Figs. 5(a) to Fig. 5(f), respectively. The corresponding intracavity dispersions for the respective cases are −0.103ps2, −0.0124ps2, 0.0000504ps2, 0.00698ps2, 0.0113ps2, and 0.0307ps2. The dip-shaped evolution of spectral bandwidth within the EDF is clearly observed for conventional solitons, DMS (in both net negative and net positive dispersion regimes), and SS solitons with slight net positive dispersion, as shown in Figs. 5(a) to 5(d). This evolution trend can be attributed to the combined effects of the EDF gain, nonlinearity, and group velocity dispersion (GVD) on the compression and stretching of the spectrum. This phenomenon appears more obvious in the experiment result in Fig. 3, and even the SS soliton and DS spectrum undergo a compression propagation. The evolution characteristics of the SS soliton in this case differ from those reported previously [8,11,16,37–39], where strong self-similar amplification and filtering effects cause more dramatic fluctuations of the spectral bandwidth. In contrast to previous EDF-based studies where the spectral bandwidth undergoes gradual expansion within the gain fiber followed by sharp spectral compression after passing through the mode-locking device [16,37–39], our system demonstrates minimal spectral fluctuations throughout the cavity. These deviations may originate from two key factors: first, the modified spectral filtering effects induced by our redesigned filter configuration, and second, the altered balance between nonlinear and dispersive effects in the cavity. While the overall spectral bandwidth remains comparable to typical Er-doped systems, the observed stabilization of spectral dynamics suggests that SS solitons can exist in regimes governed by effective averaged cavity parameters, as supported by both numerical simulations in Fig. 5(d) and experimental measurements in Fig. 3(c).

However, some discrepancies between the simulation and experimental results remain. For instance, as shown in Fig. 5(d), the spectral bandwidth of the SS soliton in the simulation is approximately 5 nm larger than the experimental value presented in Fig. 3(c). Additionally, while the experimental results for the dissipative soliton [Fig. 3(d)] exhibit a concave spectral evolution within the EDF, the simulation results [Fig. 5(f)] predict a steady increase. These differences may stem from the complex loss distribution and filtering effects in the laser system, as well as the high-order dispersion and nonlinear effects. The temporal evolution has the obvious difference that the conventional soliton possesses the smaller breathing ratio and can maintain the pulse width in several sections, while the DMS under near-zero dispersion is compressed twice with larger breathing ratio. The experimental pulse widths are 0.945, 1.282, and 1.832 ps for three cases indicating the larger chirp, which is also confirmed in simulation.

For SS soliton and DS, the action of gain competition and loss must be considered in simulation to reproduce the evolution pattern in experiment, demonstrated in Figs. 5(d)–5(f). A big difference between the DMS and SS soliton is a decrease of the spectral breathing ratio. The SS soliton experiment measurement fits better with Fig. 5(d), except that the front part of the cavity exhibits a relatively large spectral width. We assume that this situation is due to the effect of the pump. The later section agrees with the experiment that the spectra change slightly. Figure 5(e) demonstrates the variation process from the SS soliton to completely DS, indicating that the transition process of the two types of solitons is gradual. In the temporal domain, the SS soliton and DS are stretched in EDF and compressed in SMF, but also have the relatively large chirp that can be confirmed by the autocorrelation traces.

To gain a broader understanding of soliton evolution dynamics along the dispersion map, we conduct a series of simulations on soliton formation processes, varying the net group dispersion continuously from the anomalous to the normal regime, as shown in Fig. 6. We adjust the length of the SMF to set the net dispersion between −0.120ps2 and 0.072ps2, and investigate its effects on soliton characteristics by monitoring the spectral breathing ratio, temporal breathing ratio [25], and time bandwidth product (TBP). As illustrated in Fig. 6, along the anomalous and small positive normal dispersion regimes, the soliton pulse’s spectral breathing ratio (represented by blue dots) and the TBP at the maximum bandwidth change smoothly. In contrast, the temporal breathing ratio (represented by orange squares) exhibits a stair-step pattern, which aligns well with the pulse duration evolution shown in Fig. 5. All simulations indicate that the transformation from a conventional soliton to a DMS is a relatively gradual process. In stark contrast, the transition from the DMS to SS soliton is abrupt, occurring at a net dispersion of 0.00396ps2. The intracavity evolution of the spectral bandwidth and pulse duration changes suddenly, as depicted in Fig. 5(d). This leads to a decrease in the spectral breathing ratio, an increase in the temporal breathing ratio, and a variation in TBP. Subsequently, as the net dispersion becomes increasingly normal, the soliton’s spectral bandwidth narrows gradually, resulting in a decrease in TBP. Meanwhile, the intracavity evolution stabilizes, as evidenced by the breathing ratio approaching 1 over time.

The transition from the DMS to SS soliton is discussed in detail due to its particularity. The effect of saturable absorption slims the pulse stretched by normal dispersion [40], so a linear pulse chirp usually appears in normal dispersion regime, which is considered as a characteristic of the SS soliton. Saturable energy is a key parameter of saturable absorption, which affects the pulse saturable gain process, further affecting the formation of the SS soliton. Thus, controlling the laser output by adjusting Es is probably reasonable.

A mode-locked fiber laser that enables the observance of intracavity soliton evolution is presented. Soliton characteristics such as sideband, energy, and bandwidth in the cavity are monitored and analyzed. The net dispersion of the cavity is adjusted from anomalous to normal dispersion by changing the length of SMF, resulting in various types of solitons. Simulation of the cavity is constructed; the numerical results agree well with the experimental observations. Additionally, the dispersion variation has been correspondingly supplemented in the experiment. The transition from the conventional soliton to DMS is gradual at the anomalous dispersion regime. Conversely, the shift from the DMS to SS soliton occurs abruptly in the near-zero normal dispersion regime. Finally, the transformation from the SS soliton to DS reverts to being gradual in the normal dispersion regime. This work contributes a significant structure that facilitates the investigation of the intracavity evolution of optical solitons in the ultrafast lasers.