1. Introduction

Ultrafast lasers have attracted great research interests due to their important applications in nonlinear optics, fiber optic communication, material processing, frequency comb and so on [1–3]. Q-switching and mode locking are common techniques for generating ultrashort pulses [4–7]. For passively mode locked fiber lasers, a mode locker is indispensable to sharpen the pulse in temporal domain. Various mode locking devices have been developed in past decades, such as Kerr lens [8], nonlinear optical loop mirror [9], nonlinear polarization rotation (NPR) [10, 11], semiconductor saturable absorber mirror (SESAM) [12, 13], carbon nanotube [14–16], graphene [17, 18], and topologic insulator [19, 20]. Among them, SESAM, carbon nanotube, graphene, and topologic insulator are based on the nonlinear saturable absorption of materials, in which the optical transmittance increases with the enhancement of the incident laser intensity and becomes saturated when the laser intensity rises to a certain value. Recently, molybdenum disulfide (MoS₂) has been proven to exhibit saturable absorption effect and found important applications in fiber lasers. Wang et al. demonstrated that MoS₂ nanosheets have better saturable absorption response than that of graphene at 800 nm [21]. Zhang et al. have proposed a mode locker by depositing few-layered MoS₂ nanosheets onto the end facet of an optical fiber, and demonstrated a mode-locked ytterbium-doped fiber laser with a pulse duration of 800 ps [22]. After that, they have fabricated an SA by coupling few-layer MoS₂ with fiber-taper evanescent light field [23]. Xia et al. and Liu et al. have realized picosecond- and femtosecond-pulses in erbium-doped fiber (EDF) lasers mode locked by MoS₂ SAs, respectively [24, 25]. Currently, Huang et al. reported the passively Q-switched EDF laser with a wide tuning range of 1519.6-1567.7 nm by utilizing a few-layer MoS₂ SA [26].

In the high pump regime, fiber lasers tend to operate at multiple-pulses state due to the peak power clamping effect [27]. Depending on the experimental settings, the multiple pulses exhibit several different distributions in fiber lasers. For example, the multiple pulses can rearrange themselves in a regular position and form the harmonic mode locking, in which the pulse repetition rate is the multiple of the fundamental repetition rate [28, 29]. In addition, the multiple pulses can constitute bound-state pulses, where each pulse has a stable location and the pulse separation is several times of pulse duration. So far, the harmonic mode locking and bound-state pulses have been observed in various laser systems [30–36]. Zhao et al. reported passive harmonic mode locking of twin-pulse solitons with different modes by using NPR technique [33]. Komarov et al. have simulated the formation mechanism of ultrahigh-repetition-rate pulse train in harmonically mode-locked fiber lasers [34]. Amrani et al. have demonstrated a gas, a supersonic gas flow, a liquid, a polycrystal and a crystal of solitons in a double-clad fiber laser [35]. They also showed that the equidistant distribution of ultrashort pulses filling the total laser cavity is due to bound-soliton mechanisms [36]. The bound-state soliton harmonic mode locking is mainly achieved in fiber laser based on NPR technique [33–36], while it is rarely observed in SA mode-locked fiber lasers.

In this paper, we demonstrate harmonic mode locking of bound-state solitons in an EDF laser based on MoS₂ SA. This SA, fabricated by depositing MoS₂ nanosheets on a D-shaped fiber (DF), can work stably at the pump power of 600 mW without damage. In the cavity, two solitons form bound-state pulses with temporal separation of 3.4 ps, and the bound-state pulses distribute equally with a repetition rate of 125 MHz, corresponding to 14th harmonic of fundamental cavity repetition rate. In addition, single- and multiple-pulses operations are also observed in the fiber laser by changing the pump power and optimizing the MoS₂-DF SA.

2. Preparation and characterization of MoS₂ deposited on D-shaped fiber (MoS₂-DF)

To integrate MoS₂ nanosheets onto a DF, we first disperse the MoS₂ nanosheets into the water-ethanol mixture via sonication and centrifugation processing, and then obtain MoS₂ solution with a concentration of ~0.1 mg/ml. Figure 1(a) shows the dispersed MoS₂ solution, which presents sepia color and can keep unchanged for tens of days. By depositing MoS₂ solution on a quartz plate, we characterize the layered structure of the MoS₂ nanosheets, as shown in the scanning electron microscope image of Fig. 1(b). The employed DFs are fabricated by side-polishing single-mode fibers [37]. We paste a standard single-mode fiber on an arched plate and grind its side cladding of fiber using abrasive papers. The whole procedure is monitored by an optical power meter to estimate the distance from polished surface to the fiber core. We then integrate the MoS₂ nanosheets onto the DF using an optical-deposition technique [38]. The MoS₂ solution is dropped on a DF and a continuous wave with power of 10 dBm at 1550 nm is simultaneously launched into the DF. The output power is monitored using a power meter to evaluate the deposition thickness of MoS₂. The insertion loss of the MoS₂-DF is measured as 3.15 dB. Figure 1(c) displays the DF coated with MoS₂, where the top image shows the polished surface with a magnification of 20-fold and the left bottom is the cross profile of DF with a magnification of 200-fold after inputting 632.8 nm laser. From the side view of the DF, shown in the right bottom image, we can observe the scattering of the 632.8 nm laser, indicating strong interaction between the evanescent field and the MoS₂ nanosheets.

 

Fig. 1 (a) Image of MoS₂ dispersed in ethanol and water, (b) scanning electron microscopic image of MoS₂ nanosheets, (c) fabricated DF coated with MoS₂, (d) nonlinear absorption of MoS₂-DF SA.

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We then study the nonlinear saturable absorption of the MoS₂-DF SA via a power-dependent transmission technique based on a balanced twin-detector measurement [23]. A home-made pulsed laser (central wavelength: 1550 nm, pulse duration: 400 fs, repetition rate: 25 MHz) works as the illumination source. Figure 1(d) shows the measurement result, in which the nonsaturable loss, modulation depth, and saturable optical intensity of the MoS₂-DF SA are 75.4%, 1.2%, and 158 MW/cm², respectively. Comparing with the SA coated on the facet of an optical fiber, the DF based SA exhibits some inherent advantages, such as long interaction length and high damage threshold [39].

3. Experimental setup and results

Figure 2 shows the experimental setup of MoS₂ mode-locked fiber laser. A 975-nm laser diode provides pump by a wavelength division multiplexer (WDM). A polarization-independent isolator (PI-ISO) is used to realize the unidirectional operation, and a polarization controller (PC) is used to optimize mode-locking state. The 5% port of the optical coupler (OC) is employed to output the laser. The laser cavity includes a standard single-mode fiber (SMF) with a total length of 20.3 m and a 3 m EDF as the gain medium. The group velocity dispersions at 1550 nm for the SMF and EDF are 17 ps/(nm.km) and –16 ps/(nm.km), respectively. The net cavity dispersion β₂ is calculated to be –0.381 ps², which provides the possibility to generate the standard soliton. The total cavity length is 23.3 m, which gives a fundamental repetition rate of 8.968 MHz.

 

Fig. 2 Experimental setup of the fiber laser with MoS₂-DF SA as a mode locker. LD: laser diode; PI-ISO: polarization-independent isolator; SMF: single-mode fiber; OC: optical coupler; EDF: erbium-doped fiber; WDM: wavelength division multiplexer; PC: polarization controller.

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With increasing the pump power to 15 mW, we observe the continuous wave emission in the fiber laser. Self-started soliton mode locking is obtained by increasing the pump power to 340 mW with the optimization of the polarization state. The fiber laser exhibits clear hysteresis phenomenon, in which mode locking vanishes by decreasing pump power to 230 mW. Figure 3 shows the mode-locking results at the pump power of 385 mW. The sidebands of the output spectrum shown in Fig. 3(a) verify the solitons mode locking state of the laser. The spectrum also shows a regular modulation with a period of 2 nm, which is an important characteristic of bound-state solitons. The corresponding autocorrelation trace shown in Fig. 3(b) has three peaks with an intensity ratio of 1:2:1, indicating the two solitons in the bound-state pulses have the same intensity [30]. The pulse duration and pulse-pulse separation of the solitons are measured as 1.2 ps and 3.4 ps, respectively. Figure 3(c) demonstrates the radio frequency spectrum of the bound-state solitons mode locking. The interval between two peaks is 125.5 MHz, which is 14th harmonics of the fundamental repetition rate (8.968 MHz). The high-order harmonic mode locking is then confirmed by the oscilloscope trace of the pulses, as shown in Fig. 3(d). In one cavity round trip time of 112 ns, we observe 14 bound-state pulses with a separation of 8 ns. As each bound-state pulse consists of two solitons, there are 28 solitons co-propagating in the fiber laser. The formation process can be described as follows: two solitons form the bound-state pulses, and then, the bound-state pulses rearrange themselves and distribute regularly in the laser cavity. This operation is different from typical bound-state pulses or harmonic mode-locking reported previously [40, 41]. Based on the aforementioned results, we conclude that the fiber laser operates at the bound-state harmonic mode locking operation.

 

Fig. 3 (a) Spectrum, (b) auto-correlation trace, (c) radio frequency spectrum, and (d) oscilloscope trace of bound-state harmonic mode-locked pulses.

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Decreasing the pump power and adjusting the polarization state, we have also observed the multiple-pulses mode locking. As shown in Fig. 4(a), the output spectrum is centered at 1530.4 nm with a 3-dB spectral bandwidth of 2.1 nm. The auto-correlation trace of the output solitons is plotted in Fig. 4(b), which has a full width at half maximum of about 2.04 ps. By fitting the auto-correlation trace with a sech² function, the pulse duration is estimated to be 1.21 ps. The time bandwidth product is calculated as 0.33, indicating that the output pulse is near-chirp-free. Figure 4(c) shows the radio frequency spectrum at a resolution of 9.1 Hz and a span of 1 kHz. The fundamental repetition rate is given as 8.968 MHz, matching exactly with the cavity length of ~23.2 m. The signal-to-noise ratio is about 60 dB, indicating a good mode locking stability. In this state, there are three pulses in the fiber cavity, as shown in the upward image of Fig. 4(d). The interval of adjacent multi-pulses train is about 112 ns, which is equal to the cavity round-trip time. By optimizing the MoS₂-DF SA, we have also observed single-pulse mode locking at 43 mW, as shown in the downward image of Fig. 4(d).

 

Fig. 4 (a) Spectrum, (b) auto-correlation trace, (c) radio frequency spectrum, and (d) multiple- and single-pulse mode locking operations.

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A notable feature of the MoS₂-DF SA is the ultra-high optical damage threshold. During the experiment, mode locking always can be maintained when the pump power changes from the self-starting threshold to the maximum available power (600 mW). To verify whether MoS₂ purely contributes to the mode locking operation, we have purposely removed the SA or replaced the SA by a clean DF in the laser cavity. In both cases, no mode locking was observed, despite that the PC and the pump power were tuned over a large range. Based on aforementioned results, we conclude that the mode locking operation is induced by MoS₂ SA rather than other components.

4. Conclusions

We have observed the harmonic mode locking of bound-state solitons in an EDF laser based on MoS₂ SA. The mode locker is formed by depositing MoS₂ on a DF using optically-driven deposition method. In the fiber laser, two solitons form bound-state pulses with temporal separation of 3.4 ps. Then, the bound-state pulses rearrange themselves and distribute regularly with a repetition rate of 125 MHz, corresponding to 14th harmonic of fundamental cavity repetition rate. Our results also show that MoS₂-DF SA can work as a promising mode locker in ultrafast fiber lasers. Combining with the previous reports [33–36], one can infer that bound-state soliton harmonic mode locking is a general operation, which is independent of mode-locking devices in fiber lasers.