1 Introduction

The formation of multiple solitons is a well-known phenomenon in the domain of mode-locked fiber lasers and has attracted considerable attention in the past [1,2,3,4,5]. Various mechanisms have been proved to be the formation of multiple solitons, including the spectral filtering effect [6], the soliton peak clamping effect [7, 8], the wave-breaking effect [9], energy quantization [10], and over-saturation of the nonlinear polarization evolution (NPE) [11, 12], as well as the soliton shaping of dispersive waves [13] and so forth. Pulse energy for a single soliton is limited to \(\sim \) 0.1 nJ, due to the effect of soliton energy quantization [14]. In 2007, Chong et al. reported an all-normal dispersion (ANDi) fiber laser which generated dissipative solitons (DSs) with a pulse energy output of approximately 20 nJ [15]. After that, ANDi systems attracted considerable attention due to the high pulse energy and the simple cavity [16,17,18,19,20,21,22].

The dynamics of the DSs are managed by the balance among the normal cavity dispersion, nonlinearity of the cavity fiber, cavity gain, and cavity loss, i.e., the dissipative process, as shown in soliton pulse laser [23], stretched-pulse laser [24], and self-similar pulse laser [25], and so on. The multiple DSs operations in the ANDi lasers were also observed experimentally. Depending on the selection of ANDi cavity parameter, a variety of multiple DS nonlinear dynamics have been observed, such as soliton rain [18], soliton molecules [19], breathing DS explosions [20], twin-pulses [21], and harmonic mode-locking [22]. Abdelalim et al. numerically studied multiple DSs in the normal-cavity-dispersion Yb-doped fiber laser [17]. Bao et al. reported an experimental observation of soliton rains in an ANDi Yb-fiber laser, in which the soliton rain was obtained in the weak mode-locking regime [18]. In the ANDi systems, the spectral filter is a significant factor in the multiple DSs generations [6, 26]. The selection of spectrum filters affects not only the characteristics of output pulse, such as pulse shaping, pulse quality, and pulse energy, but also the features of output wavelengths, such as tuning wavelength [15, 27]. Özgören et al. proposed the use of a short section of polarization-maintaining fiber (PMF) as a birefringent medium to construct an all-fiber Lyot filter inside the cavity to obtain an all-fiber-format ANDi mode-locked femtosecond laser system [28]. The mode-locked operation was guaranteed by NPE mechanism and Lyot filtering effect. However, long-term stability of the NPE based lasers was unsatisfactory, especially when a segment of PMF was introduced to assist the NPE [29]. Real saturable absorbers (SAs), including semiconductor SAs, carbon-nanotube, two-dimensional materials and nanoparticles have all been applied to improve the environmental stability in mode-locked lasers with all-PMF [30,31,32,33,34]. Luo et al. proposed multi-wavelength dissipative soliton (DS) generation in an all-normal-dispersion ytterbium-doped fiber laser based on a graphene-deposited tapered fiber [35]. However, the required spectral filter in the laser cavity further increases the complexity of the laser system. In addition, the filter insertion results in laser operation with limited bandwidth, which constrains the short pulse width and high pulse energy that can be achieved. Zhang et al. reported on the generation of DSs from an all-fiber Yb-doped fiber laser without dispersion compensation or an additional filter [36]. Pan et al. demonstrated an ANDi Yb-doped fiber laser through a carbon nanotube saturable absorber (CNT-SA) with higher modulation depth without dispersion compensation and an additional spectral filter [37]. The higher modulation depth of the CNT-SA could contribute to stabilization of the mode-locking operation. Li et al. reported an L-band wavelength tunable Er-doped mode-locked laser with a hybrid structure of no-core fiber and graded index multimode fiber (NCF-GIMF), which can be used as both the SA and the wavelength selective element. The proposed device is simple and compact [38].

In this paper, multiple DSs with tunable wavelength Yb-doped fiber laser is reported and demonstrated for the first time. Depending on the NPE effect, triple DSs are obtained without dispersion compensation and an additional spectral filter. The spectral filtering is introduced by the NPE, which acts as an artificial spectral filter and shapes the pulses to obtain the mode-locked pulses. By gradually increasing the pump power, the triple DSs can be reached finally, and the temporal distances between adjacent pulses are all equal to 33.9 ns. With the pump power of 560 mW, the highest output energy of the triple DSs is 48.8 nJ at a repetition rate of 2.541 MHz. The spectral range of laser output can be adjusted from 1036.24 to 1043.44 nm by adjusting the polarization states of the laser cavity via the wave plates. We observe the hysteresis phenomena with the pump power changing, which is also caused by the NPE effect.

2 Experimental setup

The experimental tunable wavelength configuration provided with the multi-pulse DSs Yb-doped fiber laser is shown in Fig. 1. All fibers in the laser cavity is composed of pure ANDi fibers. A piece of 28 cm Yb-doped fiber is used for gain fiber (618 dB/m absorption at 976 nm), which is pumped by a laser diode with a maximum pump power of 560 mW and a central wavelength of 976 nm supplemented by a wavelength-division multiplexer (WDM). A single-mode fiber (SMF) of 70 m length is used to increase the nonlinear effect in the laser cavity.  The passively mode-locked mechanism is based on the NPE effect, which can be achieved by a half-wave plate, a polarizing beam splitter (PBS), and two quarter-wave plates. The laser is emitted via the NPE ejection port. The total length of the laser system is \(\sim \) 72 m. There is no dispersion compensation or additional spectral filter in the laser cavity. The output spectral of lasers are measured by an optical spectrum analyzer (Yokogawa AQ6370B). The output pulses are converted into electrical pulses using an 11 GHz photodetector, which can be measured using a 13-GHz digital storage oscilloscope (Agilent E4440A) and a radio-frequency (RF) spectrum analyzer (13.6 GHz bandwidth).

Fig. 1
figure 1

The configuration of an ANDi passive mode-locked Yb-doped fiber system without an additional spectral filter. \(\lambda \)/4, \(\lambda \)/2: quarter and half-wave plates

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3 Results and discussion

In the experiment, by adjusting the wave plate in the cavity, triple DSs are achieved in the ANDi Yb-doped fiber laser. The laser has a threshold power of approximate 50 mW. When the pump power exceeds the threshold, the laser is generated from the NPE ejection port. A self-starting mode-locked with single DS is obtained with a pump power of 202 mW. By increasing the pump power to a maximum of 558 mW, the triple DSs can be reached by altering the polarization state via the wave plates.

Figure 2 shows the characteristics of the output mode-locked laser with triple DSs when the pump power is 560 mW. Figure 2a shows the spectral wavelength of the triple DSs. From Fig. 2a, we can see that the central wavelengths of the laser is 1036.2 nm, and the full width at half maximum (FWHM) of the mode-locked wavelength is only 12.46 nm which shows the falling edges is quite steep. And this phenomenon coincides with the conclusion of Ref. [23] which says the steep spectral edges of the triple DSs outputs is one of the typical characteristics of the ANDi system.

Figure 2b shows the pulse trains of the triple DSs outputs measured by the high-speed photodiode and oscilloscope. It can be seen that the triple DSs look like a pulse bunch distributed in the time domain. The distance between each pulse bunch is \(\sim \)394.10 ns, which corresponds to the fundamental repetition frequency of 2.541 MHz as shown in Fig. 2c. From the inset of Fig. 2b, we can see that the intensity of each of the triple DSs is nearly equal. Besides, the pulse-to-pulse distances in one pulse bunch are all the same as \(\sim \) 33.9 ns. This is similar to the phenomenon of bound-state pulses reported in Ref. [26], where the solitons are oscillating at a fixed positions. However, when comparing with the bound-state pulses, there is no modulation in the spectrum of the triple DSs outputs, because the pulse-to-pulse distance is too large to interact with each other as shown in Fig. 2a, b.

Fig. 2
figure 2

a Spectrum of the triple DSs; b the mode-locked pulses train of the triple DSs; inset: the enlargement of the triple DSs; c radio-frequency spectrum of the triple DSs with 6 KHz bandwidth; d radio-frequency spectrum of the triple DSs with 100 MHz bandwidth

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RF spectra were measured to confirm the stability of the triple DSs mode-locked work. In Fig. 2c, the fundamental repetition frequency of the mode-locked outputs is 2.541 MHz, which corresponds to the laser cavity of \(\sim \) 72 m. The signal-to-noise ratio (SNR) at the fundamental repetition frequency is greater than \(\sim \)72 dB observed in the range of 6 KHz bandwidth with resolution bandwidth (RBW) of 1 Hz. The high SNR can attribute to the following reasons: the pump diode has high temperature control precision (\(\sim \) 0.1 \({^\circ })\); and the current control precision is \(\sim \) 1 mA; besides, the isolator can filter out most reflected light (\(\sim \) 30 dB). Figure 2d shows the RF spectrum with 100 MHz bandwidth and an RBW of 333 KHz. Due to the triple DSs are oscillating simultaneously, there is a modulation envelope in the RF spectrum. The period of modulation envelope is 30.67 MHz, which corresponds to the temporal separation of 33.9 ns between the adjacent pulses in each DSs. The maximum power of the triple DSs output is 124 mW, and deduce the maximum average energy of the triple DSs is 48.8 nJ. It is found that the laser cavity can operate for several hours (at least 7 h) maintaining the same state of the mode-locking without degradation of the power, and variation of the output spectrum.

Fig. 3
figure 3

Tunable spectra of the triple DSs mode-locking operation by changing the polarization state of the cavity

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Figure 3 shows the outputs of the triple DSs at different wavelengths in the ANDi regime by changing the polarization state. During the tuning process, the pump power is maintained, the mode-locking state remains unchanged without re-adjusting the system elements. When adjusting the half-wave plate of the cavity, the mode-locked spectra have a redshift, i.e., from 1036.24 to 1043.44 nm. The maximum tuning range of the wavelength is 7.2 nm. This is the first time that the ANDi system provides continuously tunable triple DSs without additional spectral filters. During the entire tuning process, the output power gradually declines from 124 to 102 mW when the pump power remains at 560 mW. This is because the limited bandwidth of gain medium (Yb-doped fiber) is around 1030 nm during the tuning process. It should be noted that the wavelengths of the mode-locked output are continuously adjusted with only one half-wave plate. This is completely different from what was reported earlier [1], where wavelength tuning was based on the birefringent states in the cavity. When different wavelengths required, the birefringent and wave plates have to be re-adjusted. That was very complicated and impracticable in industrial applications. Here, by solely changing the half-wave plate in the cavity, the laser with a continuously tunable wavelength is realized in a well-controlled and repeatable manner.

Fig. 4
figure 4

The relationship between the DSs number N and the pump power P. The red and black step lines show the decreasing and increasing procedures, respectively

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It should be interesting to investigate the evolution of the mode-locking regime when the pumping parameter is changed. This is available to represent the results in a diagram that describes the number of pulses N changing with the pumping power P. The result of the experiments is given in Fig. 4. Several significant features can be seen in Fig. 4. The number of DSs decreases one by one when the pump power is reducing. This phenomenon occurs until the laser becomes continuous light at \(P\approx 124\) mW. In the opposite process, while increasing pumping power, the laser first outputs a continuous light. When the pump power reaches 300 mW, the laser directly falls into the mode-locking state, and the first pulse emerges. Continuously improving the pump power, the number of DSs can increase one by one, such as the twin-pulse (\(N=2\)) DSs are achieved when the power increases to 406 mW. Finally, the triple DSs will appear when the pump power is up to 498 mW. Clearly, with the further increasing of pump power, the number of pulses should continue increasing. The process of the formation and annihilation of each pulse is called the hysteresis phenomena with the pump power, which is one of the results of the spectral filtering [39]. As we have known that a discrete spectral filter in the ANDi system is used to convert the frequency chirp to the self-amplitude modulation [7,8,9]. As a result, almost all the previously reported DSs operations in Yb-doped fiber laser mode-locked with the NPE were using an intra-cavity band-pass filter. However, there is not any spectral filter in our laser cavity. It is interesting to find what mechanisms are working in the system to cause the multi-pulse with hysteresis phenomena. Ref. [36] reported a DS was achieved in the ANDi system without a spectral filter. The pulse formation is contributed to the NPE, which can serve as an artificial spectral filter in the laser cavity. It is necessary for the fiber lasers to work in NPE mode-locking when the cavity transmits like a sinusoidal function. It can make the light have a linear and nonlinear phase shift in the cavity. As a function of the linear cavity birefringence, the cavity transmission performs variable transmission bandwidths. Adjusting the birefringence of the cavity by changing the polarization controller, the effective bandwidth in the cavity transmission is changed. In our experiments, the wave plates are equivalent to the polarization controller in the NPE. And the NPE plays a role of an artificial bandwidth filter to cause not only the DSs with multi-pulse hysteresis phenomenon but also the laser with tunable wavelength. In a word, while changing the wave plates in the cavity, the tunable wavelength with multiple DSs can be achieved in the ANDi systems.

4 Conclusion

In summary, a tunable triple DSs mode-locked laser without a spectral filter in the ANDi system has been demonstrated. By changing the half-wave plate in the cavity, the triple DSs mode-locked laser was achieved with a tunable spectral range from 1036.24 to 1043.44 nm, and pulse-pulse space is all equal to 33.9 ns in the time domain. During the wavelength tuning process, the mode-locking states were stabilized. Furthermore, with the pump power of 560 mW, the highest output energy of the triple DSs is 48.8 nJ at a repetition rate of 2.541 MHz. The NPE acted as an artificial bandwidth filter for formatting the pulses with multiple DSs hysteresis phenomenon and adjusting the output wavelength with tuning. The approach of steady multi-pulse DSs offers new possibilities for nonlinear fundamental research, multi-comb frequency, and multi-pulse applications in nonlinear detections, and so on.