1 Introduction

Passively mode-locked fiber lasers have attracted much attention as an ideal platform for the exploration of new areas of soliton nonlinear dynamics. Many well-known and interesting phenomena have been extensively investigated in an anomalous dispersive cavity because of the interactions between dispersive waves, solitons, and continuous waves (CW). For example, ordered multiple-soliton state, disordered multiple-soliton state [1–3], bunched multiple-soliton state, high-order harmonic mode-locking state [4–6], soliton rains state, [7, 8], and so on. However, the majority of previous experimental studies on the multiple-soliton and harmonic mode-locking trains of fiber lasers were based on the nonlinear polarization rotation (NPR) technique [5] and nonlinear amplifying loop mirror (NALM) [4]. Since the NPR and NALM mode-locked fiber lasers are intrinsically environmental unstable, in order to avoid this drawback, the use of real passive saturable absorber (SA) is usually preferred in the mode-locked fiber laser. Various SAs have been utilized to achieve passively mode-locked fiber lasers. Among them, semiconductor saturable absorber mirror (SESAM) for mode-locking has relatively high environmental stability [9] and has been employed in some commercial laser systems. However, the complex fabrication, packaging, and narrow tuning range of SESAM limit their potential application scope. Another SA is the single-wall carbon nanotube (SWCNT), which has the simpler fabrication, cost-effective, and insensitive to the polarization, but it always leads to non-saturable loss. Graphene, as a new SA, compared with SWCNT, has the properties of higher optical damage threshold, super broad bandwidth, ultrafast recovery time, lower loss, and wavelength independent. Since the first report of graphene-based ultrafast mode-locked fiber laser in 2009 [10], the research on passively mode-locked fiber laser with graphene as SA is booming [11–16]. Interestingly, Liu et al. [17] have achieved the operation of dissipative and conventional solitons in one fiber laser with the mixture of graphene and SWCNT as SA. The nonlinear Kerr effect in graphene may impact the formation of multiple-soliton pulses, which has been demonstrated by several research groups. Most recently, Song et al. [18] have experimentally investigated the vector multi-soliton operation and vector soliton interaction in an erbium-doped fiber laser passively mode-locked by atomic layer graphene, and various vector soliton states are observed. With graphene SA, Meng et al. [19] have obtained disordered multiple-soliton, bunched solitons, and high-order harmonic mode-locking. Furthermore, Feng [20] systematically investigated the different soliton operation states in a passively mode-locked erbium-doped fiber laser with graphene as SA. Apart from these works about multiple-soliton, high-repetition-rate of harmonic mode-locking employed graphene as SA has been achieved equally [21–23]. However, the current available mode-locked fiber laser with multiple-soliton operation states is reported mainly in the 1.5-μm region with anomalous dispersion. In the 1-μm region, the mode-locked Yb-doped fiber (YDF) lasers usually operate with all-normal dispersion and produce dissipative solitons with large chirps for enhancing the output power. In 2013, Bao et al. [24] demonstrations of soliton rains in an all-normal dispersion fiber laser for the first time, both soliton bunches and harmonic mode-locking were observed under strong mode-locking through NPR. According to our knowledge, no previous work reported the multipulse bunches in a graphene oxide (GO) mode-locked ytterbium-doped fiber laser (YDFL), and the corresponding formation behavior of multipulse bunches in such lasers still needs to be explored.

In this paper, we give detailed experimental studies of multipulse bunches in a GOSA passively mode-locked YDFL with all-normal dispersion. The single-pulse mode-locking, harmonic multipulse bunches, harmonic mode-locking, and chaotic multipulse states have also been observed. The multipulse bunches state can be obtained reproducibly by adjusting the pump power and the orientation of the polarization controller. Our experiment reveals that the inserted 2.5-nm narrow bandwidth filter incorporated in laser cavity plays an important role in the formation of multipulse. The effective gain bandwidth of the laser is decided by both the 2.5-nm narrow bandwidth filter and the artificial fiber birefringence filter, so the multipulse operation states are sensitive to polarization. It is the first time to demonstrate multipulse evolution in a GOSA passively mode-locked YDFL with all-normal dispersion.

2 Sample preparation and experimental setup

As a graphene derivative, GO not only has all the characteristics of ultrafast recovery time and broadband saturable absorption, but also are much easier and cheaper to be obtained. It has been proved that GO is comparable to graphene as an SA. The fabrication method of GO-based SA is called vertical evaporation, and the fabrication process was similar to our previous works [25–27]. This process can be simply described as follows. Some chemical-oxidized graphite was ultrasonically agitated for obtaining GO sheets. Then, the prepared GO sheets were poured into ~10 ml 0.1 % sodium dodecyl sulfate (SDS) aqueous solution, followed by more than ~10 h of ultrasonic agitation and centrifugation. Next, some polyvinyl alcohol (PVA) power was poured into the GO solution and ultrasonically agitated for ~3 h at ~90 °C. The final procedure was vertically evaporating the GO/PVA solution lasting for more than ~40 h at ~40 °C. The finally prepared samples are shown in the inset of Fig. 1. It clearly shows that both the concentration and the thickness of the samples decrease from bottom to top, which provides different modulation depths in the laser cavity. The corresponding Raman spectrum and wavelength-independent transmission spectrum can be found in Ref. [25].

Fig. 1
figure 1

A schematic diagram of the fiber ring laser. WDM wavelength division multiplexer, YDF Yb-doped fiber, ISO isolator, OC optical coupler, SMF-28 single-mode fiber, PC polarization controller, GOSA graphene oxide saturable absorber

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The experimental setup is schematically represented in Fig. 1. A laser diode (LD) pump source with the maximum output power of ~500 mW at center wavelength 974 nm is used to pump the gain fiber through a fused 980/1,060 wavelength division multiplexer (WDM) coupler. A section of 3.5-m YDF with core absorption of 250 dB/m@975 nm and group velocity dispersion (GVD) parameter of 27.5 ps2/km@1,060 nm is used as the gain medium. A polarization-independent isolator (ISO), placed after the YDF, is used to ensure unidirectional operation and eliminate undesired feedback from the output end facet. A 10/90 fused fiber optical coupler (OC) is used to extract ~10 % energy from the cavity for signal detection. A polarization controller (PC), which for matching the polarization states from one round-trip to the next, consists of three spools of standard single-mode fiber (SMF-28) fiber. A narrow bandwidth filter with a central wavelength of 1,064 nm and 3 dB bandwidth of ~2.5 nm is inserted into the cavity for suppressing the mode competition effect. The prepared GOSA sample was cut in ~1 × 1 mm2, sandwiched between two fiber connectors, and is placed between the narrow bandwidth filter and the WDM coupler. The GVD parameter of SMF-28 is ~17.7 ps2/km at 1,064 nm. Apart from these components, ~180 m length of SMF-28 is incorporated in the ring cavity just after the 10/90 OC to supply appropriate dispersion and nonlinear effect in the ring cavity. The total cavity length is about 190 m, including the YDF and all the SMF-28 in cavity, the net dispersion of the laser cavity is estimated as ~3.397 ps2, and the corresponding round cavity period is about 933 ns. Out of cavity, another 20/80 coupler is used to split output power for simultaneously measuring temporal pulse and optical spectrum. The monitoring of the output temporal pulse trains and optical spectrum is performed using a 1-GHz digital phosphor oscilloscope (Tektronix DPO7104C) and an optical spectrum analyzer (OSA, AQ6370B) with a minimum resolution of 0.02 nm. The pump power and output power are measured by a photodiode power meter.

3 Experimental results and discussion

3.1 Single-pulse mode-locking state

In our experiment, stable mode-locking of the laser is obtained at ~137 mW pump power with an average output power 0.19 mW by adjusting the orientation of PC appropriately. As shown in Fig. 2a, the fundamental repetition rate is 1.072 MHz, corresponding to a cavity round-trip time of about 933 ns and a cavity length of 190 m. The pulse train period matching with the cavity round-trip time is the characteristics of the mode-locked operation. The full wavelength half maximum (FWHM) pulse duration is measured as ~2.3 ns, as shown in Fig. 2b. Figure 2c shows the optical spectrum centered at 1,064.1 nm and a 3 dB spectral width of about 0.477 nm. The time-bandwidth product of the chirped pulse is about ~286. The single-pulse mode-locking state can last several hours if no laser operation conditions are changed. Additionally, if the GOSA is removed from the laser cavity, no pulses can be observed in the oscilloscope even we carefully adjust the PC under different pump powers. It is proved that the GOSA is the only SA in the laser cavity.

Fig. 2
figure 2

a Oscilloscope trace, b single-pulse trace, c optical spectrum of single-pulse operation

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3.2 Multipulse bunches state

By increasing the pump power up to ~150 mW, a typical state of multipulse bunches is formed immediately after the single-pulse mode-locking owing to the peak power-limiting effect [28], as shown in Fig. 3b. The corresponding output power is 0.31 mW. In each cavity round-trip time, there are five pulses coexisting in a bunch. The separation between the pulses is not consistent. Another important feature is that all of the pulses in the laser cavity have the similar pulse intensity, which resembles the feature of soliton energy quantization of conventional solitons in the fiber lasers. Every multipulse bunch is still with a stable state in the cavity without merging or annihilation. The corresponding optical spectrum of the laser emission is shown in Fig. 3h. Fixing the orientation of the PC and further increasing the pump power slightly, we found that the number of pulses in every bunch increased one by one. Under the pump power of ~180 mW, there are already 15 pulses emergence in every bunch, but the separation between pulses exists huge difference, the maximum distance is 100 ns, while the minimum one is about 9.5 ns, and this state is illustrated in Fig. 3d. When the pump power reach 260 mW, more pulses appear in each bunch and nearly distribute over the whole cavity length, as shown in Fig. 3e. However, this state is not consistent, and another quivering state is observed at the same pump power without any artificially changing in the laser cavity, as shown in Fig. 3f. Further increasing pump power, the multipulse bunches state disappears, besides the phenomenon of appearance of addition pulse one by one through increasing the pump power. On the other hand, an inverse progress was observed: The pulse number was decreased one by one with decreasing the pump power slightly, and there are only two pulses coexisting in each bunches when the pump power is decreased to 140 mW. Eventually, single-pulse mode-locking state even could be maintained at the pump power of 133 mW, which is below of 137 mW due to hysteresis phenomena [29]. So, we boldly deduced that the multipulse bunches state can be obtained only under relatively low pump power, and the multipulse bunches state will be changed to the disordered multipulse state at higher pump power.

Fig. 3
figure 3

The evolution of the output pulse trains {(a), (b), (c), (d), (e), (f)} and their corresponding spectra {(g), (h), (i), (j), (k), (l)} with the pump increasing

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All the multipulse bunches states mentioned above were at the same polarization state. In order to explore the relationship between the polarization state and the multipulse bunches state, we compare the multipulse bunches state under different polarization states by changing the PC at the pump power of 196 mW. We find that the pulse number in the bunch also could be changed by just rotating the PC. Two pulses and more than 30 pulses in the bunch are obtained, as shown in Fig. 4. Another interesting phenomenon is that the relative pulse intensity decreases with the increases in the pulse number in the bunch. But the total output power and repetition frequency of bunches remain unchanged. Hence, the total energy of each bunch is regarded as constant in different polarization states under the same pump power. Unlike the reports in references [17, 30], the fiber lasers are insensitive to the polarization. In our experiment, the multipulse bunches operating states are strongly dependent on the orientation of PC.

Fig. 4
figure 4

The evolution of the output pulse trains {(a), (b), (c), (d), (e), (f)} and spectra {(g), (h), (i), (j), (k), (l)} with different polarization at the pump power of 196 mW

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In fact, it is not easy for YDFL to show the gain-limiting effect due to the broader gain bandwidth of ytterbium and the larger gain saturation power than an Er-doped fiber laser. The insertion of the narrow bandwidth filter plays a crucial role in the formation of the multipulse bunches. When the gain bandwidth is limited by a narrow bandwidth filter, the emission single-pulse energy would be restricted, which induces the pulse to break by increasing pump power. Additionally, the effective gain bandwidth of the laser also depends on the artificial fiber birefringence filter [31–37]. Usually, in the weakly birefringent cavity fiber lasers, the cavity birefringence-induced artificial birefringence filtering effect could normally be ignored due to the large filtering bandwidth. In our fiber laser, we introduced strong cavity birefringence into the laser cavities by over-bending the fibers looped in PC. So, the artificial birefringence filter effect of the laser cavity is no longer ignorable. The peak wavelength spacing of a birefringence filter is decided by the cavity birefringence, which is given by ∆λ = λ 2/(LB), where λ is the central wavelength, L is the cavity length, and B is the strength of the birefringence [38]. When rotating the PC, the birefringence magnitude is changed, resulting in changing the effective cavity transmission bandwidth, which can be viewed as variation in the bandwidth of the gain in the laser. Thus, the effective gain bandwidth of the laser is determined by both the 2.5-nm narrow bandwidth filter and the artificial fiber birefringence filter. As a result, the different multipulse operation states are not only determined by the pump power, but also dependent on the orientation of the PC.

3.3 Harmonic multipulse bunches and harmonic mode-locking

Through carefully adjusting the orientation of the PC and changing the pump power, a new bunched state, second-harmonic multipulse bunches can be obtained in our laser as shown in Fig. 5. Its main feature is that two separated multipulse bunches coexist in one round-trip time. Additionally, different amounts of pulses were demonstrated in the bunch state, e.g., as in the case of Fig. 5a and b. There are only four and six pulses appear in the two bunches during one round-trip time, respectively. However, 24 pulses were measured in one round-trip as shown in Fig. 5c. It is noticed that the output spectrum in Fig. 5f at pump power of 220 mW was different from the two examples in Fig. 5d and e.

Fig. 5
figure 5

Second-harmonic multipulse bunches {(a), (b), (c)} and their corresponding spectra {(d), (e), (f)} at different pump powers

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Further changing the PC and the pump power, we observed another new state: harmonic mode-locking. Passive harmonic mode-locking is the result of quantization of the cavity energy by the fundamental pulse energy. As shown in Fig. 6a and b, 4th- and 8th-order harmonic mode-locking was obtained at the pump power of ~170 and 178 mW, and the repetition rate is about ~4.24 and 8.57 MHz, respectively. The corresponding spectra are shown in Fig. 6d and e. The higher-order harmonics also could be obtained by increasing the pump power and adjusting the PC. But the pulses turn into unstable state. As shown in Fig. 6c, the 24th-order quasi-harmonic mode-locking was achieved at the pump power of ~190 mW, and the corresponding spectrum is in Fig. 6f. The 2.5-nm narrow bandwidth filter and the artificial fiber birefringence filter could be the main reason for the formation of harmonic multipulse bunches and harmonic mode-locking.

Fig. 6
figure 6

The 4th, 8th harmonic mode-locking and 24th-order quasi-harmonic mode-locking state {(a), (b), (c)} and their corresponding spectra{(d), (e), (f)}

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3.4 Chaotic multipulse state

We also found the chaotic multipulse at the pump power of 185 mW. The feature of harmonic mode-locking is that all the pulses possess the same energy intensity and separation in the cavity, while the chaotic multipulse is different. Figure 7 shows a typical output. There are nine pulses coexisting in the cavity, but they have the diverse energy intensity. Besides, the separation is also chaotic. The chaotic pulses are scattered and moved randomly in the cavity. Additionally, the multipulse bunches states are also moved randomly in the cavity. The phenomenon can be explained as follows: The different pulses operation corresponds to different wavelengths, and the cavity dispersion is nonzero, so the pulse trains have different group velocities and round-trip times. In other words, the relative motion of pulses attributes to the phase shift, which corresponds to the instantaneous frequency at pulse peak to be nonzero [39].

Fig. 7
figure 7

The chaotic multipulse state and corresponding spectrum

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4 Conclusion

In conclusion, we have experimentally investigated multipulse operation in a passively mode-locked ytterbium-doped ring fiber laser with all-normal dispersion by GO as SA for the first time. Several other kinds of pulse states are also observed, including the single-pulse mode-locking, harmonic multipulse bunches, harmonic mode-locking, and chaotic multipulse state. The inserted 2.5-nm narrow bandwidth filter plays an important role in the formation of multipulse in all-normal dispersion fiber laser. The effective gain bandwidth of the laser is decided by both the 2.5-nm narrow bandwidth filter and the artificial fiber birefringence filter, so the multipulse operation states are sensitive to the orientation of PC. These results could extend the understanding of dissipative solitons dynamics in GOSA passively mode-locked fiber lasers.