A commercial fiber taper system (SCS-4000) and flame brushing technique are used to fabricate the microfiber, as shown in Fig. 1(a). The taper system consists of two fiber holders, two stepper motors, a moveable torch, a computer controller, and a hydrogen generator. First, the coating of ∼ 3-cm long single mode fiber (SMF) was stripped by a fiberoptic stripper and fixed on two fiber holders after alcohol cleaning. Then the SMF was heated by a high temperature hydrogen flame and two stepper motors were controlled simultaneously. During the fabrication process, the stepper motor on the left was fixed and another stepper motor was controlled to pull the fiber. By adjusting the speed of the stepper motor and the flow of the hydrogen, a microfiber with different waist diameters can be obtained. Finally, the waist of the microfiber was tapered to a diameter of ∼ 10 μm and an interaction length of ∼ 1.2 cm, as shown in Fig. 1(b).

Fig. 1.

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	Fig. 1. (color online) (a) Experimental set up for fabricating the microfiber; (b) optical microscopic comparison image of standard fiber and microfiber.

The graphene film used in the TDFL was directly grown by chemical vapor deposition (CVD) method on a copper substrate. Figure 2 shows the Raman spectrum of graphene with three typical Raman peaks from the characteristic curve. The three prominent peaks are located at approximately 1350.21 cm⁻¹, 1587.48 cm⁻¹, and 2696.12 cm⁻¹, known as D, G, and 2D bands, respectively. The peak D band is associated with the stretching of the C–C bond with the sp³ electronic configuration of disordered graphite. The peak G band contributes to an E_2g phonon of sp² C atoms^[25] and is located at the Brillouin zone center.^[26] It was reported^[27] that the intensity ratio of 2D and G peak (I_2D/I_G) could be used to estimate the number of grapheme layer, while the intensity of D peak could reveal the defect of graphene. In general, the 2D peak of single-layer graphene is 2–3 times as strong as the G peak. As observed from the Raman spectrum, the I_2D/I_G is calculated to be about 2.1, which indicates that a single layer of graphene is used in our experiment. The relatively weak D peak reveals little defects existing in the graphene samples.

Fig. 2.

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	Fig. 2. (color online) Raman spectrum of the monolayer graphene film.

In order to reduce the contamination, a wetting transfer method was applied to transfer the monolayer graphene with a size of 1 cm × 0.5 cm from the copper substrate to PDMS film (∼ 1-mm thickness). The specific transfer process is shown in Fig. 3. Then, the fabricated graphene/PDMS film was covered on the upper surface of the microfiber, as shown in Fig. 4(a). In order to increase the interaction length of graphene, the waist is made into an S-shape on purpose, as depicted in Fig. 4(b), while the MgF₂ substrate with low refractive index is used to ensure the evanescent wave propagation along the graphene film.

Fig. 3.

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	Fig. 3. (color online) The transfer of monolayer graphene.

Fig. 4.

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	Fig. 4. (color online) (a) Schematic diagram of the cross-section of GCM. (b) The corresponding photo of GCM.

Figure 5 shows the SA properties of GCM, using a balanced twin-detector measurement technique. The laser source is a Tm/Ho-doped mode-locked fiber laser with a center wavelength of 1923.21 nm and a pulse width of 3.8 ps. A 60-dB attenuator was used to vary the input power during the experiment. A 3-dB coupler was used to separate the laser source into two beams equally. 50% of the laser was focused on the GCM and monitored by detector 1, and the other 50% of the laser as a reference beam was directly monitored by detector 2. By modifying the optical attenuator, the power of the incident laser on the GCM can be adjusted continuously. The nonlinear transmission can be measured by comparing the data of two detectors. Due to the difficulty of measurement of both the accurate optical power of the evanescent field and the effective mode area in the waist of the microfiber, we only provide the transmission curve versus the average power. Figure 6 shows the relation between the optical transmission and the average power of the input laser by using T(I) = 1 − ΔT · exp (−I/I_sat) − T_ns, where T(I) is transmission rate, ΔT is the modulation depth, I is the input intensity, I_sat is the saturable intensity, and T_ns is the non-saturable absorption loss. The fabricated GCM showed ∼ 7% modulation depth and ∼ 27% non-saturable loss.

Fig. 5.

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	Fig. 5. (color online) Schematic setup of the modulation depth measurement of GCM.

Fig. 6.

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	Fig. 6. (color online) Measured transmission data and the corresponding fitting curve of GCM.

In the experiment, the fiber laser starts to operate in the CW state when the pump power is fixed at 1.25 W. The optical spectrum generated by the seed is shown in Fig. 9. It is centered at 1990.02 nm and has a full width at half maximum (FWHM) of 0.15 nm.

Fig. 9.

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	Fig. 9. (color online) Output spectrum of TDFL operated in CW state.

The self-starting CSML operation is achieved at the pumping power of 1.45 W when the pump power continues to increase. To optimize the mode-locked operation, the best performance is observed at a pump power of 1.50 W. Figure 10 shows the corresponding mode-locked oscilloscope trace, optical spectrum, and radio-frequency (RF) spectrum, respectively. Meanwhile, the laser pulse traces are measured using an oscilloscope with a high-speed photodetector, as shown in Fig. 10(a). The time interval between adjacent pulses is ∼ 144.5 ns. The blue line in Fig. 10(b) shows the typical mode-locking spectrum with a central wavelength of 1992.17 nm and a FWHM of 2.02 nm. Kelly sidebands of the spectrum are clearly observed, demonstrating that the TDFL is operated in the soliton regime. To investigate the stability of the laser, the RF spectrum of CSML has been measured with a resolution bandwidth (RBW) of 1 kHz, as presented in Fig. 10(c). The fundamental repetition rate of the laser is 6.92 MHz, corresponding to the cavity length of ∼ 29 m. In Figs. 10(c) and 10(d), the signal-to-noise ratio (SNR) of ∼ 40 dB at the fundamental repetition rate and flat wideband RF spectrum indicates good mode-locking stability and no Q-switching instabilities.^[28,29] Limited to the laboratory conditions, the current self-correlation curves of the output pulse is estimated. Assuming that the pulses are operated in a transform-limited soliton form, the pulse-width of output laser is calculated to be ∼ 1.36 ps using the time-bandwidth product value 0.315, which is transform-limited hyperbolic secant pulses.^[30]

Fig. 10.

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	Fig. 10. (color online) The output characteristics of the CSML in TDFL: (a) oscilloscope trace; (b) optical spectrum; (c) the fundamental RF spectrum with the resolution of 1 kHz and the span of 2 MHz; (d) wideband RF spectrum up to 1 GHz.

When the pump power exceeds 1.55 W, the stable CSML state is broken and the laser turns into the MSML state. In contrast to CSML, the MSML have two or more pulse sequences, but the period of the round-trip is constant. As the pumping increases from 1.55 W to 1.85 W, the operation states of 2 to 6 soliton pulses are obtained, under a pump power of 1.60 W, 1.64 W, 1.69 W, 1.75 W, and 1.83 W, respectively, as depicted in Fig. 11. Although these pulses are grouped together, they are separated from each other in time-domain. Meanwhile, all the multi-soliton pulses have exactly similar pulse quality at the same pump power. Due to the sensitivity of the photodetector and the accuracy of the oscilloscope, there is a slight difference between the pulses. In order to further explore the difference between the MSML and CSML, we also observe the corresponding optical spectrum. As can be seen, the spectrum of MSML shows an obvious CW component relative to CSML.

Fig. 11.

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	Fig. 11. (color online) The characteristics of mode-locked TDFL: (a)–(e) pulse sequences under different conditions of the pump power (left) and the corresponding optical spectrum (right).

In addition, mode-locking operation is still maintained by slightly decreasing the pump power to a relatively low value, generally known as pump hysteresis. For the MSML operation, the generation and annihilation of new soliton pulses also show the pump hysteresis, as shown in Fig. 12. When multi-soliton pulses already exist in the laser cavity, the pump power is slowly increased and new soliton pulses are generated one by one. On the contrary, the pump power is slowly reduced and the existing soliton pulses will annihilate one by one. The laser will remain in the mode-locking state as long as there is a soliton in the cavity. In the experiment, with the increase of the pump power (1.55 W–1.85 W), the 2–6 order multi-soliton pulse corresponding to a pump power ranges from 1.55 W–1.61 W (2 solitons), 1.62 W–1.68 W (3 solitons), 1.69 W–1.74 W (4 solitons), 1.75 W–1.80 W (5 solitons), and 1.81 W–1.85 W (6 solitons), while carefully decreasing the pump strength (1.85 W–1.53 W), the pump power range obtained is 1.79 W–1.85 W (6 solitons), 1.73 W–1.78 W (5 solitons), 1.66 W–1.72 W (4 solitons), 1.59 W–1.65 W (3 solitons), and 1.53 W–1.58 W (2 solitons).

Fig. 12.

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	Fig. 12. (color online) Hysteresis phenomenon of the MSML pulses numbers versus the pump power.

Under the 6-solitons mode-locked operation, the pump power is further increased to 1.86 W. An interesting phenomenon, namely the soliton rain consisting of noise background, drifting pulses, and condensed soliton phase, has been observed, as shown in Fig. 13(a). In recent years, the soliton rain has been found in the 1-μm band of ytterbium-doped fiber laser (YDFL) and the 1.5-μm band erbium-doped fiber laser (EDFL).^[31] In contrast to the preceding MSML pulses, the soliton rain regime is not only increasing the number of pulses, but also accompanied by the increase of the intensity of the condensed soliton phase. The remaining pulses present a tendency to flow slowly from right to left. Next, by increasing the pump power from 1.86 W to 2.02 W, these drifting pulses can be moved faster and event gather together, forming an NLML in the cavity, as shown in Fig. 13(d).

Fig. 13.

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	Fig. 13. (color online) The evolution of the soliton rain to NLML.

In order to illustrate the difference between CSML and NLML, figure 14 gives the output characteristics of NLML, including oscilloscope trace, optical spectrum, the fundamental RF spectrum, and wideband RF spectrum under a pump power of 2.03 W. It is clear that NLML shows a stronger pulse intensity (almost twice of CSML) and a higher SNR of ∼ 50 dB. Note that NLML presents a smooth optical spectrum with a center wavelength of 1992.23 nm and an FWHM of ∼ 12.58 nm. In addition, obvious shoulder and fluctuations of high-order harmonics are exhibited on the fundamental RF spectrum and wideband RF spectrum, respectively. These characteristics also indicate that the output pulse is noise-like at the pump power of 2.03 W, similar to the previously reported pulsed laser.^[32,33]

Fig. 14.

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	Fig. 14. (color online) The characteristics of the NLML in TDFL: (a) optical spectrum (inset is the comparison of oscilloscope trace between CSML and NLML); (b) the fundamental RF spectrum with the resolution of 1 kHz and the span of 0.8 MHz (inset is the fundamental RF spectrum with the span of 6 MHz); (c) wideband RF spectrum up to 1 GHz.

In this paper, by covering a graphene/PDMS film on the microfiber as an SA, an all-fiber thulium-doped fiber system with five different output characteristics that can be adjusted by increasing the pump power is presented. Firstly, the laser operates in the CW state and soon enters CSML as the pump power increases. When the pump power exceeds 1.55 W, the laser is converted from CSML pulse to MSML pulse with the same energy in the steady state. This phenomenon can be found in all kinds of mode-locked lasers, such as NALM mode-locked laser, NPR mode-locked laser, and other real SA mode-locked laser. That is, it is a common feature of the laser and has nothing to do with mode-locking. The generation of MSML pulses can be attributed to the peak power clamping effect.^[34] In general, the soliton energy is related to the cavity structure of the laser. Under the constant cavity parameters, the maximum energy contained by the soliton will be determined. If the SA effect in the cavity is strong enough, increasing the pump power will only cause the formation of MSML pulses at a certain threshold. At the same time, due to the soliton energy quantization effect,^{[30,31,35,36]} the weak soliton pulse becomes stronger by the positive feedback, and the strong soliton behaves oppositely and is weakened. In the end, all pulses reach a steady state with the same peak power.

Meanwhile, the pump hysteresis effect is also found in the process of the MSML. In the past reports,^[37,38] Komarov et al.^[38] have made an intensive study on the pump hysteresis of passively mode-locked fiber lasers. According to their research, the pump hysteresis stems from the competition between the positive feedback from the nonlinear transmittance of the SA and the negative feedback related to the modulation effect of the pulsed phase modulation. And the generation and annihilation of solitons must go through a continuous increase or decrease of the pump power, which is consistent with our experiment. In addition, there is obvious jitter in switching between adjacent pulses of multi-soliton mode-locking in the experiment. It is necessary to increase or decrease a certain amount of power to stabilize the current state. Hence, when drawing the graph of hysteresis, the switching between adjacent pulses of multi-soliton mode-locking is based on the current stable value. When the pump power is between 1.85 W and 2.02 W, the output pulse shows the evolution of soliton rain to NLML. Compared with CSML, higher pulse energy, larger FWHM, smooth spectrum, and obvious fluctuation of wideband RF are important characteristics of laser operation in a NLML regime.^[32,33]