1. INTRODUCTION

Nonlinear optical (NLO) responses can play an important role in light–matter interaction, and have attracted intense interest for use in versatile photonic and optoelectronic applications ^[1]. Optical materials under high-intensity laser field can show some fantastic NLO effects, including nonlinear absorption ^[2], Kerr nonlinearity, and Raman/Brillouin scattering ^[3,4]. Among them, nonlinear absorption effect (e.g., saturable ^{[5–10" target="_self" style="display: inline;">–10]} and multiphoton ^[11,12] absorption) is always one of most important and intensive research topics. For example, saturable absorption is usually used to generate short laser pulses by passive mode-locking ^{[13–20" target="_self" style="display: inline;">–20]} or Q-switching ^{[21–24" target="_self" style="display: inline;">–24]} techniques. Multiphoton absorption can be very useful for applications in optical limiting ^[25] and fluorescence microscopy ^[26]. Generally, these NLO responses are extremely dependent on the optical materials themselves. Therefore, there is always great interest in developing new NLO materials.

Recently, it was found that two-dimensional (2D) materials (e.g., graphene ^[7,11]) can possess extraordinary NLO properties. Graphene, as the first-discovered 2D nanomaterial, has impressively exhibited strong NLO responses with a large nonlinear refractive index (n2∼2×10−7cm2·W−1 ^[27]) and low saturable optical intensity of ∼0.7MW/cm2 ^[7]. The nonlinear saturable absorption of graphene has been widely used to mode-lock/Q-switch lasers for short-pulse generation ^{[28–36" target="_self" style="display: inline;">–36]}, and the Kerr nonlinearity (e.g., four-wave mixing) of graphene has also been applied to wavelength conversion ^[37].

The success of graphene has triggered a worldwide upsurge in research interest in 2D nanomaterials. In recent years, some new 2D materials [e.g., topological insulators (TIs)] have been successively discovered ^{[38–47" target="_self" style="display: inline;">–47]}. In particular, atomically thin group VIB transition metal dichalcogenides (TMDs; MX2; M=W, Mo; X=S, Se), as a new class of 2D materials, have recently stimulated a great deal of research due to their unique and exotic properties. TMDs possess bandgap tunability by reducing the layer number or introducing the defects ^[48], high carrier mobility, and strong spin-orbit coupling, making them appealing materials for various applications in electronics and optics. Recent experiments have demonstrated that layered molybdenum diselenide (MoSe2) has broadband saturable absorption from 400 to ∼2100nm ^[10,48], and exhibits a nonlinear refractive index (n2∼0.2×10−12cm2·W−1) ^[49]. Furthermore, mode-locking and Q-switching operations based on layered MoS2 have been achieved at around 1, 1.5, and 2 μm ^{[50–55" target="_self" style="display: inline;">–55]}. However, it should be noted that most studies on the TMDs were focused on MoS2 until now, and other TMDs (e.g., MoSe2) have not yet been fully investigated. Thin-layered MoSe2 actually possesses more attractive properties compared with MoS2, including narrower bandgap between 1.1 eV (indirect) and 1.5 eV (direct) ^[56], lower optical absorption coefficient ^[49], and larger spin-splitting energy of ∼180meV at the top of the valence bands. The narrow bandgap and low optical absorption coefficient could make MoSe2 more applicable than MoS2 to broadband saturable absorption for passively mode-locked lasers.

In this paper, we experimentally investigated the NLO absorption of few-layer MoSe2 at 1.56 μm wavelength and further demonstrated a MoSe2 passively mode-locked Er-doped fiber (EDF) soliton laser. Few-layer MoSe2 was fabricated by the liquid-phase exfoliation (LPE) method and then embedded in polymer composite, constructing few-layer MoSe2 films. Using a balanced twin-detector measurement system, the MoSe2 film exhibited saturable absorption with a relative modulation depth of 18% and two-photon absorption (TPA) under the input optical intensity of >260MW/cm2. Furthermore, a mode-locked Er-doped fiber laser (ML-EDFL) based on a few-layer MoSe2 film as saturable absorber (SA) was successfully achieved. The mode-locking operation could stably generate transform-limited pulses with a 1.45 ps duration, and was also interrupted by TPA under higher pumping level.

2. PREPARATION AND CHARACTERIZATION OF MoSe2

2.1 A. Few-Layer MoSe2 Fabricated by the LPE Method

The few-layer MoSe2 used in our experiment was prepared by the LPE method ^[57]. The LPE process for obtaining thin-layered 2D materials has two steps. Namely, bulk material is first mixed with a solvent and then sonicated under strong ultrasound field for overcoming the interlayer van der Waals forces. In this process, it is very key that a suitable solvent is chosen for easily exfoliating bulk crystals and stabilizing thin-layered material. It is required that the solvent surface energy be similar to the exfoliated material (e.g., MoSe2). N-methyl-pyrrolidone, chitosan acetic, and Li+ solutions were widely used to exfoliate graphene, TIs, and MoS2 ^{[38,44,50,55]}, but these solvents could be harmful to human health. In contrast, lysine is indispensable to human body and its surface energy is close to MoSe2. Therefore, we used lysine as the dispersant to exfoliate and stabilize MoSe2 in our experiment. Initially, the bulk MoSe2 (325 mesh power, Alfa Aesar) was added into the 1mg/mL lysine solution and sonicated for 20 h to produce the few-layer MoSe2 suspension. The exfoliated MoSe2 suspension was centrifuged for 30 min at 1000 rpm to remove bulk MoSe2. Subsequently, the supernatant was decanted to another centrifuge tube. After centrifuging the supernatant at 13,000 rpm for 30 min to remove free lysine, the as-obtained product was collected into vials.

2.2 B. Characterization of Few-Layer MoSe2

After exfoliation, the color of solution was deepened, manifesting that the exfoliated MoSe2 had been well dispersed in lysine solution [Fig. 1(a)]. The purchased bulk MoSe2 was first characterized by x ray diffraction (XRD). As shown in Fig. 1(b), all labeled peaks of the bulk material can be readily indexed to rhombohedral MoSe2 (JCPDS no. 29-0914). Then, we measured the XRD pattern of the exfoliated MoSe2. As given in Fig. 1(b), the high [002] orientation still exists and some characteristic peaks disappeared (compared to bulk structure), indicating that bulk MoSe2 had been successfully exfoliated as we expected. The thickness of the as-prepared few-layer MoSe2 was also characterized by atomic force microscopy (AFM), as shown in Fig. 1(c). The average thickness from the height profile diagram [inset of Fig. 1(c)] was measured to be ∼2–3nm. This indicates that the exfoliated MoSe2 nanosheets are around 2–3 layers, because the single-layer thickness of MoSe2 is about 0.8 nm ^[56]. In addition, it is well known that the location of Raman modes can also determine the thickness of 2D materials. Therefore, we further measured the Raman spectra [Fig. 1(d)] of MoSe2 before and after exfoliation. We observed the prominent Ag1 Raman mode, which is associated with the out-of-plane vibration of Se atoms. As shown in Fig. 1(d), the Ag1 Raman mode of the as-exfoliated MoSe2 is redshifted slightly, also confirming the few-layered structure of the as-prepared MoSe2 ^[58]. Actually, the redshift phenomenon has been reported in other 2D materials (e.g., graphene, TIs, MoS2), possibly originating from the decreasing the van der Waals forces between layers.

Fig. 1. Characterization of few-layer MoSe2 by the LPE method. (a) MoSe2 solution before (left) and after (right) sonication. (b) XRD patterns of the bulk MoSe2 (top) and exfoliated few-layer MoSe2 (bottom). (c) Typical AFM image and the height profile diagram (inset) of the few-layer MoSe2 nanosheets. (d) Raman spectrum of the exfoliated MoSe2.

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3. NLO ABSORPTION OF FEW-LAYER MoSe2

To flexibly use the as-prepared MoSe2 for practical applications, the polyvinyl alcohol (PVA) polymer was further dispersed into the few-layer MoSe2 solution. Therefore, the MoSe2 PVA film can be easily formed and transferred onto a fiber end-facet for constructing a fiber-compatible MoSe2 device (see the MoSe2 sample in Fig. 2).

Fig. 2. Balanced twin-detector measurement system for measuring the NLO absorption of the fiber-compatible PVA-MoSe2 film.

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Then, we measured the NLO absorption of the fiber-compatible MoSe2 device using the balanced twin-detector measurement system (Fig. 2). The system consists of a femtosecond seed laser, erbium-doped fiber amplifier (EDFA), tunable optical attenuator, 50∶50 coupler, and two optical powermeters. The seed laser from a homemade passively mode-locked fiber laser has a center wavelength of 1566 nm, pulse duration of ∼650fs, repetition rate of 22.15 MHz, and average output power of ∼400μW. When amplified by the EDFA, the optical power could reach ∼10mW, and the pulse duration was slightly broadened to ∼1ps. The amplified power was further divided by the 50∶50 coupler and the 50% optical power could be injected into the few-layer MoSe2 film (the other 50% being the reference beam). The tunable attenuator was used to continuously change the input optical intensity (I) into the MoSe2 film. The maximum optical intensity into the MoSe2 film can be ∼500MW/cm2. As we increased the input optical intensity from 0.3 to 500MW/cm2, we recorded the optical absorbance of the few-layer MoSe2 film. As shown in Fig. 3, the optical absorbance gradually reduces from 4.20% to 3.57% in the initial stage, but sharply increases when the input optical intensity is more than 260MW/cm2. The experimental data at the input optical intensity I<260MW/cm2 can be well fitted by the formula

Fig. 3. Measured nonlinear absorption characteristics of the few-layer MoSe2 film at 1566 nm wavelength. SA, saturable absorption.

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Here, Δα, Isat, and αlinear represent the modulation depth, saturated optical intensity, and the nonsaturable loss, respectively. This clearly indicates that the saturable absorption behavior happens at I<260MW/cm2, and has Δα=0.63%, Isat=19.8MW/cm2, and a low nonsaturable loss αlinear=3.57%. The normalized modulation depth can be calculated to be ∼18%, comparable to that of graphene ^[7], TIs ^[41], and MoS2 ^[52]. It is well known that, from the bulk to single-layer MoSe2, the energy gap of MoSe2 is between 1.1 eV (1.12 μm) and 1.5 eV (0.82 μm). It is noted that the 1.56 μm photon energy is less than the bandgap of MoSe2, and one could question why the few-layer MoSe2 has saturable absorption at the longer 1.56 μm wavelength. Similar to the few-layer MoS2 reported previously ^{[48–55" target="_self" style="display: inline;">–55]}, the saturable absorption of few-layer MoSe2 at 1.56 μm can be well understood as being due to the following possible reasons: (1) the defects induced by the LPE fabrication process ^[48], and (2) the edge-state or surface absorption ^[55] (i.e., the coexistence of both semiconducting and metallic phases) ^{[51–54" target="_self" style="display: inline;">–54]}.

Interestingly, we found that the experimental data at I>260MW/cm2 can be well fitted by the quadratic equation as follows: This shows that the TPA process in the few-layer MoSe2 has been excited under the higher optical intensity, and the TPA coefficient β is 3.4×10−6cm4/MW2. Note that the increasing of optical absorbance can be attributed to the TPA rather than the thermal damage of the MoSe2 samples. This can be confirmed by the MoSe2-based mode-locking operation features, and the reason will be further analyzed.

4. MoSe2 PASSIVELY MODE-LOCKED FIBER SOLITON LASER

In this section, we will try to further exploit the NLO absorption effects (Fig. 3) of the few-layer MoSe2 for laser application. The saturable absorption characteristic of few-layer MoSe2 will especially be used for a passively mode-locked fiber laser.

4.2 A. Experimental Setup

Figure 4 shows the experimental setup of the EDFL passively mode-locked by the few-layer MoSe2 film. A 974 nm laser diode (LD) is used to pump a section of 4.6 m EDF (Nufern, EDFC-980-HP) through a 975/1550 nm wavelength division multiplexer. The EDF has an absorption coefficient of 3dB/m at 980 nm and group velocity dispersion (GVD) of 53.6×10−3ps2/m at 1550 nm. The as-fabricated few-layer MoSe2 device in the cavity acts as SA for passive mode locking. A polarization-independent isolator ensures the unidirectional laser operation. A polarization controller (PC) is used to fine tune the cavity birefringence for optimizing the mode-locking operation. A 10/90 optical coupler extracts 10% intracavity signal as laser output. In addition, a section of 15 m single-mode fiber with GVD of −22×10−3ps2/m at 1550 nm is used for ensuring the cavity operating in the anomalous dispersion region. The total cavity length is about 26 m, with net cavity dispersion of −0.224ps2. For measuring the laser outputs, the laser optical spectrum was monitored by an optical spectrum analyzer (HP 70951B), and a 10 GHz InGaAs photodetector (Nortel PP-10G-FAC) together with a 1 GHz digital oscilloscope used to detect the pulse trains and pulse waveforms. Moreover, the radio frequency (RF) output characteristics of the laser pulses were observed by a RF spectrum analyzer (Gwinstek GSP-930, 9 kHz–3 GHz), and the pulse duration was measured by an autocorrelator (FR-103XL, Femtochrome Research Inc.).

Fig. 4. Experiment setup of the proposed EDFL passively mode-locked by the few-layer MoSe2 film.

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4.3 B. Experimental Results and Discussions

Because the net GVD of the cavity is anomalous, it can be expected that the ML-EDFL emits soliton pulses by the interplay between anomalous cavity dispersion and the fiber nonlinear Kerr effect. In our experiment, the laser oscillation started initially at continuous-wave (CW) regime at a low pump threshold of 5.5 mW. Then, the CW operation transited to a pulsed regime when the pump power exceeded 10.0 mW. Moreover, as we gradually increased the pump power from 10 to 30.2 mW, we found that the pulse repetition rate enlarged and pulse duration decreased, exhibiting the typical features of passive Q switching ^[21]. Actually, such passive Q switching under the lower pump power was observed usually in some passively mode-locked fiber lasers previously reported ^[18], mainly resulting from the few number of oscillating longitudinal modes and the insufficient nonlinearity in low pumping intensity. At the pump power of 17.4 mW, Fig. 5 gives the typical characteristics of the passive Q switching. The Q-switched optical spectrum [Fig. 5(a)] has a center wavelength of 1558.25 nm and a narrow 3 dB bandwidth of 0.28 nm. The typical oscilloscope trace [Fig. 5(b)] shows that the Q-switched pulse trains with an uniform pulse intensity have a periodic interval of 101 μs (corresponding to the repetition rate of 9.9 kHz). The inset of Fig. 5(b) further gives the single pulse envelope. The Gaussian-profile pulse has a pulse duration as broad as ∼13.6μs. The low repetition rate (kHz) and the relative broad pulses also suggest the occurrence of passive Q switching.

Fig. 5. (a) Optical spectrum and (b) typical oscilloscope trace of the passive Q-switching operation at the pump power of 17.4 mW. Inset, single-pulse envelope.

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We interestingly found that, once the pump power is more than 30.3 mW, the passive Q-switching operation became unstable and could abruptly evolve into the mode-locking regime. Stable self-started mode-locking could be readily achieved by slightly adjusting the PC in the cavity. At the pump power of 33.4 mW, we measured the typical optical spectrum of this mode locking with a spectral resolution of 0.08 nm. As shown in Fig. 6(a), the mode-locked optical spectrum (solid line) was obviously broadened, compared with the passive Q-switching one (dashed line). This implies that the mode-locking operation excited more longitudinal modes and also induced stronger optical nonlinearity in the laser. The mode-locking operation has a center wavelength of 1558.25 nm and a wide 3 dB bandwidth of 1.76 nm. Meanwhile, we clearly observed the symmetrical Kelly sidebands originating from the spectral interference of dispersive waves, manifesting that this operation was at the conventional solitary mode locking ^[59]. Moreover, the absence of additional narrow spectral peak also suggests that the soliton mode locking almost has no CW component. As shown in Fig. 6(b), we also measured the mode-locked pulse trains at the same pump power of 33.4 mW. The pulse interval of 124.5 ns matches well with the cavity roundtrip time (i.e., the cavity length of ∼26m), suggesting that only one soliton was generated per roundtrip. Furthermore, once the stable mode locking was obtained under the initial adjustment of the PC, we found in our experiment that the single soliton operation was always observed so long as the passive mode-locking state is not interrupted.

Fig. 6. (a) Mode-locked optical spectrum and (b) mode-locked pulse trains at the pump power of 33.4 mW.

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As shown in Fig. 7, the mode-locking operation at the pump power of 33.4 mW was further characterized by the RF spectrum analyzer and the autocorrelator. Figure 7(a) gives the output RF spectrum of the mode-locked pulses at the fundamental frequency peak for a scanning range of 50 kHz and RF resolution bandwidth of 10 Hz. The fundamental RF peak locates at 8.028 MHz, corresponding to the fundamental cavity repetition rate. This further confirms the occurrence of the passive mode locking. The RF signal-to-noise ratio (SNR) is more than 61.5 dB. We also measured the broadband RF spectrum with a large frequency span of 600 MHz. As can be seen in Fig. 7(b), the measured RF peaks from the 2nd- to 74th-order harmonic exhibit almost uniform intensity without spectral modulation. Both the higher RF SNR (>60dB) and the absence of modulation in the 600 MHz broad RF spectrum evidently indicate the good stability and CW mode-locking state of the proposed ML-EDFL. Figure 7(c) shows the measured autocorrelation trace of the mode-locked pulses with a narrow scanning range of 32 ps and time resolution of 100 fs. The full width at half maximum (FWHM) of the pulse was measured to be 2.23 ps. If the fit of sech2 pulse shape is assumed, the corresponding pulse duration (τ) is 1.45 ps. The time–bandwidth product (TBP) of the mode-locked pulses can be further calculated by the equation TBP=τ×c·Δλ/λ02,(3)where c, λ0, and Δλ represent the light speed, center wavelength, and 3 dB bandwidth of the mode-locked optical spectrum. In our experiment, these parameters are τ=1.45ps, λ0=1558.25nm, and Δλ=1.76nm, respectively. Therefore, the TBP of the mode-locked pulses is ∼0.316. This manifests that the soliton mode locking of the proposed ML-EDFL generated the transform-limited pulses. Furthermore, an autocorrelation trace with a broad scanning range of 800 ps is given in Fig. 7(d). Note that no pedestal was shown on the autocorrelation trace [Fig. 7(d)], which reveals the excellent quality of the mode locking.

Fig. 7. (a) RF spectrum of the mode-locked pulses at the fundamental RF peak. (b) Broadband RF spectrum with a frequency span of 600 MHz. The autocorrelation traces of the mode-locked pulses with the (c) narrow and (d) broad scanning range are also shown.

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As we increased the pump power from 0 to 75 mW, we also recorded the average output power of the laser. One can see from Fig. 8(a) that the laser operation underwent four phases as follows: (1) the CW regime (pump power <10mW); (2) the passive Q-switching regime (pump power in the range of 10−30.2mW); (3) the soliton mode-locking regime (pump power from 30.3 to 73.5 mW); and (4) the CW regime (pump power >73.5mW). The maximum average output power for passive mode locking is 440 μW, corresponding to the maximum pulse energy of 54.8 pJ. The obtained pulse energy is close to the theoretical calculation value of limited pulse energy (Ep) for a single soliton based on the formula ^[60] Ep≈3.11λ02/2πcγ|Dav|/τ.(4)Here, γ and |Dav| represent the nonlinear coefficient and the average dispersion of the laser cavity. In addition, one could question why the soliton mode locking degenerated in the case of pump power >50mW (i.e., output average power >400μW), and was even extinguished with pump power >73.5mW. This phenomenon should be attributed to the TPA process of the few-layer MoSe2 under intracavity high peak intensity. As shown in Fig. 3, when the optical intensity injected into the few-layer MoSe2 film exceeds ∼260MW/cm2, the SA performance becomes worse and the TPA process happens. In our experiment, when the output average power exceeds 400 μW, the intracavity power injected into the few-layer MoSe2 film is more than 4 mW with 1.45 ps pulse duration, corresponding to the input optical intensity of ∼300MW/cm2. Therefore, once the pump power is above 50 mW, TPA of the few-layer MoSe2 film happens and the SA-based passive mode locking becomes worse. Decreasing the pump power from 75 mW to 0, we found in our experiment that the ML-EDFL exhibited optical bistability. Namely, when turning on or off the pump power, the processes of the laser operation are very different, as shown in Figs. 8(a) and 8(b). Laser operation with the decrease of pump power only underwent two phases, i.e., the soliton mode-locking (pump power from 73.5 to 8.5 mW) and CW regime (pump power <8.5mW). Optical bistability has usually been observed in passively mode-locked fiber lasers based on other SAs (e.g., graphene ^[61] or TIs ^[41]), or the nonlinear amplifying loop mirror ^[62] or nonlinear polarization rotation techniques ^[63,64]. Komarov et al. ^[65,66] have numerically demonstrated that the optical bistability between the CW and mode-locked regimes is a common feature in fiber lasers independently of the exact optical configuration. Moreover, they also claimed that the mode locking would occur when the nonlinear transmission of the SA works as a positive feedback. The positive feedback means that the greater intensity produces the lower losses. In our experiment, when the fiber laser operated under the CW condition, the intracavity power intensity was much lower than that of mode-locking operation with the same pump power. Namely, the nonlinear loss caused by the SA is relatively larger than that of mode-locking operation. In order to initiate the mode locking from CW based on the saturable absorption of SAs, higher pump power is needed. Then the bistability can be observed in the fiber laser, which is in accordance with the numerical analyses ^[65,66] and experimental results ^[41,61–64].

Fig. 8. Average output power as a function of the pump power when (a) turning on and (b) turning off the pump power.

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In order to evaluate the long-term stability of the passive mode locking, we recorded the mode-locked optical spectrum in 10-min intervals for 70 min at the fixed pump power of 33.4 mW. Figure 9 gives the eight series of spectral data. Neither the central wavelength drift nor the power variation was significantly observed, further confirming that the mode-locked operation possesses good long-term stability.

Fig. 9. Stability measurement of soliton mode locking by repeatedly scanning the output optical spectra at 10-min intervals.

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5. CONCLUSION

We propose a new SA material, MoSe2, for efficient mode locking of an EDFL. In our experiment, bulk MoSe2 is exfoliated to a few-atomic-layer structure by the liquid phase exfoliation method. Then, the few-layer MoSe2 is composited with PVA to construct PVA–MoSe2 film as a fiber-compatible SA. The MoSe2 SA is measured to have a modulation depth of 0.63% and a nonsaturable loss of 3.5% (i.e., the relative modulation depth of 18%). When inserting the MoSe2 SA into an EDFL, stable mode locking is initiated to emit soliton pulses with duration of 1.45 ps. Moreover, the TPA of the few-layer MoSe2 has also been observed, and we found that the TPA could significantly influence the mode-locking operation. The experimental results show that apart from MoS2, few-layer MoSe2, as one of the atomic-layered TMDs, can also serve as a potential SA for ultrafast photonics.