Here, few-layered W2C nanosheets and microfiber-based few-layered W2C-SA are fabricated by the magnetron sputtering deposition method. The third-order nonlinear optical responses of the prepared 2D W2C nanosheets are investigated by the Z-scan method with βeff and n2 determined to be −88.2 cm/MW and −1.112×10−13 m2/W, respectively, revealing its excellent nonlinear saturable absorption properties and optical modulation capabilities. In addition, by incorporating microfiber based few-layered W2C-SA into Yb-doped and Er-doped fiber lasers (YDFLs and EDFLs), the passively mode-locked operations at the central wavelength of 1035.1 and 1562 nm are realized, respectively. In addition, multi-soliton bound mode-locked operation in EDFLs with soliton pulses up to 36 is realized. Our results not only demonstrate the capability of few-layered W2C as a wideband optical modulator, but also provide a practical approach to explore soliton dynamics in fiber lasers.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Ultrafast pulsed lasers have attracted considerable attention in many applications such as remote sensing, micro-surgery, telecommunications, biomedical imaging, industrial processes and THz generation [1–4]. Passively mode-locked fiber lasers (PMFLs) are considered to be the most efficient way to generate ultrafast pulses due to the advantages of compactness, miniaturization and low cost. Saturable absorber (SA), a nonlinear optical material (or device) with absorption of light reducing as incident light intensity increasing, is the key element and plays a great role in the PMFLs. Since the first demonstration of graphene as a SA in PMFLs in 2009 , researches on nonlinear optical characteristics of two-dimensional (2D) or few-layered materials and their applications in PMFLs have experienced a rapid development [6–9].
Recently, 2D MXene, a large family of 2D transition metal carbides, carbonitrides, and nitrides, has been extensively studied due to the unique optical and electronic properties and their promising applications in supercapacitors, catalysis and Li-ion batteries [10–12]. The general formula of MXene is Mn+1XnTn (n=1-3), in which M represents a transition metal (e.g., Ti, Mo, W), X for either C and/or N, and T is the surface functional group (e.g., -OH, -O, and -F) . Some functionalized MXenes have been predicted to be 2D TIs, where electrons propagate along the edge states resulting in dissipation-less transport, such as Mo2C, Ti2C, W2C and double transition metal elements [14,15]. 2D MXenes are expected to have quantum spin Hall effect with one-dimensional helical edge states. Backscattering is prohibited when the time-reversal symmetry is not destroyed, thus ensuring the high-speed transmission for dissipation-less electron transport by the helical edge states . Compared with traditional TIs, MXenes host large bandgaps with quantum spin Hall effect that can support wider applications. Besides, the nonlinear optical properties of MXenes have also been extensively studied [16,17]. Jiang et al. systematically investigated the nonlinear optical response of Ti3C2Tx from 800 nm to 1800 nm, and PMFLs based on 2D Ti3C2Tx nanosheets were performed at 1.0 and 1.5 µm . In addition to Ti3C2Tx, the nonlinear optical properties of 2D Mo2C have also been studied and stable mode-locking operations have been achieved at 1.0 and 1.5 µm . 2D W2C, a newly developed MXene, has metal elements in the same main group as Mo2C. Simulation and density functional theory calculation results suggest that there is a Dirac point in the band structure and it has low diffusion barrier (∼0.045-0.13 eV) which benefits to ultrafast loading for lithium ions [14,20]. Furthermore, 2D W2C has very high melting points and good stability in the ambient environment, making it widely used in supercapacitor electrodes, superconductors and biomedical. However, up to date, the nonlinear saturable absorption properties of few-layered W2C and its applications in PMFLs have not yet been experimentally observed. Table 1 summarizes the output performance comparison of mode-locked fiber lasers based on MXene SA and shows that W2C SA has unique advantages in realizing mode-locked operation.
In this work, few-layered W2C nanosheets and microfiber-based few-layered W2C-SA were fabricated by magnetron sputtering deposition method. The third-order nonlinear optical responses have been investigated by Z-scan measurements with the excited laser source operating at 1.06 µm for the first time. I-scan measurements were also performed to characterize the saturation absorption properties of few-layered W2C-SA at 1.06 and 1.56 µm, respectively. All above results indicated the as-prepared W2C nanosheets possess excellent saturable absorption properties and light modulation capability. In addition, microfiber-based few-layered W2C-SA was applied in fiber lasers to generate mode-locked pulses at 1.0 and 1.5 µm, respectively. The dissipative soliton mode-locked operation in YDFLs with pulse width of 250 ps and multi-soliton bound mode-locked operation in EDFLs with soliton pulses up to 36 were realized. All these results suggest that few-layered W2C nanosheets have excellent nonlinear optical responses and should be broadband SA in PMFLs for exploring soliton dynamics and ultrafast pulse generation.
2. Results and discussion
2.1 Synthesis and characterization of few-layer W2C nanosheets
Few-layered W2C nanosheets were synthesized on a k9-glass substrate by magnetron sputtering deposition mothed. Atomic force microscopy (AFM) and scanning electron microscopy (SEM) were performed to characterize the surface morphology of the prepared few-layered W2C nanosheets. As shown in Figs. 1(a) and 1(b), the average thickness of prepared few-layered W2C nanosheets was determined to be 15 nm, corresponding to the layer number of about ∼20 . The typical SEM image shown in Fig. 1(c) indicated the smooth and uniform distribution of few-layered W2C nanosheets. X-ray photoelectron spectroscopy (XPS) was used to further determine the surface terminations and binding energy. As shown in Fig. 1(d), C, W, and O elements existed in the few-layered W2C nanosheets. The C 1s component was split into three peaks [Fig. 1(e)]: the highest binding energy intensity peak located at 284.6 eV was C-C specie attributed to carbon; the peak with binding energy of 286.2 eV was attributed to C-O band; and the peak located at 282.7 eV was related to C-W band. The W 4f XPS spectrum was split into two peaks for W-C and W-O bands with binding energies of 31.8/34.1 eV and 35.7/37.9 eV, respectively, which was consistent with the previous research . The W-O bands could be assigned as the strong W spin-orbital doublet, which was fit well with the binding energies of WO3. We speculated that WO3 was decorated on top of few-layered W2C nanosheets in the form of ultra-small clusters or ultrathin film in pristine W-C. The co-existence of W-O and C-O indicated that the surface functional groups of prepared few-layered W2C nanosheets were oxygen-terminated. The prepared few-layered W2C nanosheets can be kept in the environment for a long time because of the protection of surface terminating functional groups, which ensures long-term stability of few-layered W2C nanosheets. What’s more, the Raman spectra of few-layered W2C nanosheets was measured by a 632 nm laser source and shown in Fig. 1(g). The strong intensity peaks were located at 695 and 807 cm−1, corresponding to the stretching mode of W-C . Figure 1(h) shows the UV-vis-NIR spectrometry of few-layered W2C nanosheets as well as the k9 glass substrate. The results indicated that few-layered W2C nanosheets had broadband absorption properties from 400-2000 nm.
2.2. Third-order nonlinear optical response of few-layered W2C nanosheets
Z-scan measurement is an effective way to characterize the third-order nonlinear optical response of nonlinear optical materials, as shown in Fig. 2. Here, the third-order nonlinearity was measured by open- and closed-aperture Z- scan method. The excited laser source was a homemade mode-locked Yb-doped fiber laser operating at 1064 nm with a pulse width of 10 ps and repetition rate of 200 kHz. A lens with a focal distance of 75 mm was used to focus the signal light with a Rayleigh length of 5.8 mm. Figure 3(a) shows the measured open-aperture Z-scan curves of the few-layered W2C nanosheets, exhibiting typical saturable absorption response with a sharp and narrow peak at the focus position. In order to better understand the third-order nonlinear optical properties, the absorption coefficient βeff can be obtained by fitting the open-aperture Z-scan curve with the following equations :22,27], indicating a strong saturable absorption ability and a strong interaction between few-layered W2C nanosheets and incident light.
The nonlinear refractive index of few-layered W2C nanosheets can be obtained based on the closed-aperture Z-scan measurement. Figure 3(b) shows the typical closed-aperture Z-scan curves of few-layered W2C nanosheets under different incident pulse energies baselined to the identical open-aperture Z-scan results. The valley-peak shape of the transmittance curve indicated positive nonlinear refractive index. The normalized transmittance can be described with the following formulas :
In addition, the I-scan measurements were constructed by using a mode-locked fiber laser operating at 1064 nm with a pulse width of 85 ps and repetition rate of 12.8 MHz and a mode-locked fiber laser operating at 1560 nm with a pulse width of 6 ps and repetition rate of 11.9 MHz, respectively. Figures 3(c) and 3(d) show the nonlinear transmittance of the few-layered W2C-SA with respect to the incident laser intensities, indicating the typical saturation absorption responses at the two wavelengths. The transmittance can be well fitted by a nonlinear transmission model:6), the modulation depths were determined to be 16.2% at 1.0 µm and 2.1% at 1.5 µm, and the saturation intensity were 74 MW/cm2 at 1.0 µm and 69 MW/cm2 at 1.5 µm, respectively. All the results suggest the strong nonlinear optical response and modulation abilities of few-layered W2C nanosheets, indicating the great potential as a SA for PMFLs.
2.3. Mode-locked fiber lasers operating at 1.0 and 1.5 µm
The strong nonlinear saturable absorption response of few-layered W2C nanosheets urges us to further explore its modulation function in PMFLs. Few-layered W2C was dispersed onto a microfiber by magnetron sputtering deposition method under the same situation to form the microfiber-based SA devices. The length of the YDFLs cavity is 13.7 m. Therein, a 0.5 m high concentration ytterbium-doped fiber (Yb-401) is gain medium and the rest is 13.2 m standard single-mode fiber (HI 1060) including the pigtailed fiber of a laser device. A 976-nm laser diode (LD) was employed as the pump source with the maximum output power of 400 mW. The function of the 980/1060-nm wavelength division multiplexer (WDM) was to couple two different wavelengths of light into fiber. To adjust the polarization state of propagation light, a three-paddle polarization controller (PC) was used in the cavity. The insensitive isolator (ISO) was placed to maintain the unidirectional transmission of light. In addition, a 90:10 output coupler (OC) was employed. An optical power meter (THORLABS S148C), a 4 GHz digital oscilloscope (Tektronix DPO 3052) coupled with a 4 GHz photodetector, an optical spectrum analyzer (Yokogawa AQ6370C) and a 3 GHz RF spectrum analyzer (Agilent N900A) were used to observe the laser performance. For EDFLs, 113.3 m cavity length was composed of 0.3 m EDF (LIEKKI Er 110-4/125) and 113 m single mode fiber (SMF-28). A 980/1560 nm WDM, PI-ISO, PC and 90:10 OC with operation wavelength at 1560 nm was used in the similar ring laser cavity. The net cavity dispersion of Yb- and Er-doped mode-locked fiber laser was calculated to be ∼ 0.231 ps2 and ∼−2.36 ps2, respectively.
By inserting the microfiber-based few-layered W2C-SA into the YDFLs, the stable mode-locking operation was realized at the pump power of 95 mW by slightly adjusting the PC. The mode-locked pulse width of 250 ps was obtained and shown in Fig. 4(b). The mode-locking operation was destroyed when the pump power exceeded 350 mW, no matter how changing the polarization state in the cavity. Figure 4(c) shows the pulse trains with a scale of 2 µs, indicating the high pulse stability of the mode-locked operation. The corresponding output optical spectra is presented in Fig. 4(d) with the central wavelength of 1035.1 nm and 3 dB bandwidth of 2.1 nm. Moreover, the typically square, steeply along the optical spectrum demonstrated that the cavity was in stable dissipative soliton state. To assess the mode-locking stability, the radio frequency (RF) spectrum was measured with different spans of at the pump power of 250 mW. Figure 4(f) shows the RF spectrum with a span of 12 MHz and the signal-to-noise ratio (SNR) of 65 dB. A wider span of 200 MHz is also presented in Fig. 4(e) with a resolution bandwidth of 5 kHz. Figure 4(g) represents the variation of output power with the pump power, and the maximum average output power of 6 mW was obtained with a slope efficiency of 2.4%.
To further demonstrate the broadband saturable absorption properties of few-layered W2C-SA, the EDFLs was constructed by incorporating the microfiber-based few-layered W2C-SA. The mode-locking operation was easily realized by adjusting the PC when the pump power reaching to the 70 mW. Figure 5 summarizes the corresponding results of microfiber-based few-layered W2C-SA PMFLs, where the multi-soliton pulse was obtained. To better understand the generation of multi-soliton, we analyze the formation of soliton and quantization of soliton energy. When the peak power of the pulse increased to a certain value, the pulse width caused by the dispersion effect in the cavity can be balanced by self-phase modulation (SPM) effect, and then the pulse can propagate stably in the laser cavity. In this case, the mode-locked pulse became a soliton, and thus generated the Kelly sideband . The soliton pulse was independent to the mode-locked pulse, showing that multi-soliton pulse always appeared with the same pulse width and single pulse energy under the condition of strong pump power. The inherent characteristic was the so-called quantization effect of soliton energy . As shown in Fig. 5(b), the single pulse width is determined to be ∼310 ps. And the pulse trains with a scale of 10 µs at the pump power of 300 mW is shown in Fig. 5(c).
The multi-soliton pulse was obtained when the pump power reached up to 100 mW. As shown in Fig. 5(d), the number of soliton pulse increased from 9 to 36 as the pump power increased from 150 to 350 mW. Once the soliton pulse was formed in the laser cavity, the peak power of the soliton would increase as the pump power increases. However, the higher the soliton peak power increased, the smaller the actual cavity transmission became . In this case, further increasing the peak power of the soliton would cause the actual transmission quantity of the soliton in the cavity to be small, meaning that soliton peak power would be limited. At this time, the background noise, such as the dispersion wave, would be amplified until it formed a continuous wave component, which can be seen from the narrow peak of spectra [shown in Fig. 5(f)]. Under the function of saturation absorption, the strongest local pulse would be amplified and formed an additional soliton [32–34]. The soliton energy balance process in the cavity dominated other parameters of the soliton.
As shown in Fig. 5(d), the spacing of the soliton pulse varied as the function of pump power, indicating that there were interactions between different solitons in the cavity. However, the repulsive forces dominated by the dispersion wave, gain loss and recovery and acoustic wave were not enough to offset the attraction between adjacent pulses, so the pulses were not completely separated . Compared to other multi-solitons fiber lasers, EDFLs based on microfiber-based few-layered W2C-SA can support a greater number of soliton pulse outputs, indicating fascinating potential in optical fiber communications and coherent pulse stacking amplification [36–38]. The pulse interval was short when soliton close to the center. And the pulse separations were several times larger than pulse width and the phase differences was unfixed . Therefore, the multi-soliton pulse realized in the experiment was the loosely bound soliton pairs. In general, the peak power limiting effect gave rise to the multiple soliton pulses in the resonator. The long cavity structure (∼113 m) and the small modulation depth (2.1%) of microfiber-based few-layered W2C-SA at 1.5 µm were conducive to the generation of multiple solitons, as the same as previous reports . By analyzing the spectrum [shown in Fig. 5(e)], the mode-locking operation was in a good stable state with SNR of ∼65 dB. And with increasing the number of soliton pulses, the RF components increased, and the RF period became shorter. What’s more, pump power hysteresis was also observed. After the soliton operation was realized, the pump power could be reduced to a very low level while the soliton operation still existed. All the experimental results show that few-layered W2C nanosheets is an excellent SA for exploring soliton dynamics in fiber lasers.
In conclusion, few-layered W2C nanosheets and microfiber-based few-layered W2C-SA were fabricated by magnetron sputtering deposition method. The third-order nonlinear optical properties were studied by Z-scan technique for the first time. The βeff and n2 were measured to be −88.2 cm/MW and −1.112×10−13 m2/W, corresponding to the imaginary part and real part of the third-order susceptibility of −0.98×10−8 esu and 1.146×10−7 esu, respectively. The results were orders of magnitude higher than other low dimensional nanomaterials, indicating that few-layered W2C has strong nonlinear optical response and excellent light modulation capabilities. In addition, few-layered W2C nanosheets-decorated microfiber composite structure was applied in YDFLs and EDFLs, respectively. Based on the YDFLs, mode-locked pulses at central wavelength of 1035.1 nm with the pulse duration of 250 ps have been obtained. In addition, multiple-soliton pulse was obtained in EDFLs with the central wavelength of 1562 nm and pulse width of 310 ps. The number of soliton pulse increased from 9 to 36 as the pump power increased from 150 to 350 mW. Our work reveals the excellent nonlinear optical properties of few-layered W2C and provide a practical approach to explore soliton dynamics in fiber lasers.
National Research Foundation of China (61975095, 61675116, 61575110); the Young Scholars Program of Shandong University (2017WLJH48); the Youth Cross Innovation Group of Shandong University (2020QNQT); Shenzhen Science and Technology Research and Development Funds (JCYJ20180305163932273); Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices (KF201908).
The authors declare no conflicts of interest.
1. V. S. Letokhov, “Laser biology and medicine,” Nature 316(6026), 325–330 (1985). [CrossRef]
2. S. W. Lanigan, “Editorial,” Laser Med. Sci. 17(4), 221 (2002). [CrossRef]
3. Y. Liang and H. P. Zeng, “Single-photon detection and its applications,” Sci. China: Phys., Mech. Astron. 57(7), 1218–1232 (2014). [CrossRef]
4. R. Chen, P. Jiang, X. Y. Shao, G. Y. Mi, and C. M. Wang, “Effect of static magnetic field on microstructures and mechanical properties of laser-MIG hybrid welding for 304 stainless steel,” Int. J. Adv. Manuf. Tech. 91(9-12), 3437–3447 (2017). [CrossRef]
5. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009). [CrossRef]
6. A. Autere, H. Jussila, Y. Y. Dai, Y. D. Wang, H. Lipsanen, and Z. P. Sun, “Nonlinear optics with 2D layered materials,” Adv. Mater. 30(24), 1705963 (2018). [CrossRef]
7. N. R. Hemanth and B. Kandasubramanian, “Recent advances in 2D MXenes for enhanced cation intercalation in energy harvesting Applications: A review,” Chem. Eng. J 392, 123678 (2020). [CrossRef]
8. W. J. Liu, M. L. Liu, X. M. Liu, X. T. Wang, H. X. Deng, M. Lei, Z. M. Wei, and Z. Y. Wei, “Recent advances of 2D materials in nonlinear photonics and fiber lasers,” Adv. Opt. Mater. 8(8), 1901631 (2020). [CrossRef]
9. Y. F. Song, X. J. Shi, C. F. Wu, D. Y. Tang, and H. Zhang, “Recent progress of study on optical solitons in fiber lasers,” Appl. Phys. Rev. 6(2), 021313 (2019). [CrossRef]
10. J. Halim, I. Persson, E. J. Moon, P. Kuhne, V. Darakchieva, P. O. A. Persson, P. Eklund, J. Rosen, and M. W. Barsoum, “Electronic and optical characterization of 2D Ti2C and Nb2C (MXene) thin films,” J. Phys.: Condens. Matter 31(16), 165301 (2019). [CrossRef]
11. Y. Yoon, M. Lee, S. K. Kim, G. Bae, W. Song, S. Myung, J. Lim, S. S. Lee, T. Zyung, and K. S. An, “A strategy for synthesis of carbon nitride induced chemically doped 2D MXene for high-performance supercapacitor electrodes,” Adv. Energy Mater. 8(15), 1703173 (2018). [CrossRef]
12. G. Yan, C. X. Wu, H. Q. Tan, X. J. Feng, L. K. Yan, H. Y. Zang, and Y. G. Li, “N-Carbon coated P-W2C composite as efficient electrocatalyst for hydrogen evolution reactions over the whole pH range,” J. Mater. Chem. A 5(2), 765–772 (2017). [CrossRef]
13. F. Shahzad, M. Alhabeb, C. B. Hatter, B. Anasori, S. M. Hong, C. M. Koo, and Y. Gogotsi, “Electromagnetic interference shielding with 2D transition metal carbides (MXenes),” Science 353(6304), 1137–1140 (2016). [CrossRef]
14. N. N. Zhao, P. J. Guo, X. Q. Lu, Q. Han, K. Liu, and Z. Y. Lu, “Topological properties of Mo2C and W2C superconductors,” Phys. Rev. B 101(19), 195144 (2020). [CrossRef]
15. H. M. Weng, A. Ranjbar, Y. Y. Liang, Z. D. Song, M. Khazaei, S. Yunoki, M. Arai, Y. Kawazoe, Z. Fang, and X. Dai, “Large-gap two-dimensional topological insulator in oxygen functionalized MXene,” Phys. Rev. B 92(7), 075436 (2015). [CrossRef]
16. X. Sun, B. Zhang, B. Yan, G. Li, H. Nie, K. Yang, C. Zhang, and J. He, “Few-layer Ti3C2Tx (T = O, OH, or F) saturable absorber for a femtosecond bulk laser,” Opt. Lett. 43(16), 3862–3865 (2018). [CrossRef]
17. J. Yi, L. Du, J. Li, L. Yang, L. Hu, S. Huang, Y. Dong, L. Miao, S. Wen, V. N. Mochalin, C. Zhao, and A. M. Rao, “Unleashing the potential of Ti2CTx MXene as a pulse modulator for mid-infrared fiber lasers,” 2D Mater. 6(4), 045038 (2019). [CrossRef]
18. Y. C. Dong, S. Chertopalov, K. Maleski, B. Anasori, L. Y. Hu, S. Bhattacharya, A. M. Rao, Y. Gogotsi, V. N. Mochalin, and R. Podila, “Saturable absorption in 2D Ti3C2 MXene thin films for passive photonic diodes,” Adv. Mater. 30(10), 1705714 (2018). [CrossRef]
19. M. Tuo, C. Xu, H. Mu, X. Bao, Y. Wang, S. Xiao, W. Ma, L. Li, D. Tang, H. Zhang, M. Premaratne, B. Sun, H.-M. Cheng, S. Li, W. Ren, and Q. Bao, “Ultrathin 2D transition metal carbides for ultrafast pulsed fiber lasers,” ACS Photonics 5(5), 1808–1816 (2018). [CrossRef]
20. J. Tian, Y. Q. Shi, W. Fan, and T. X. Liu, “Ditungsten carbide nanoparticles embedded in electrospun carbon nanofiber membranes as flexible and high-performance supercapacitor electrodes,” Compos. Commun. 12, 21–25 (2019). [CrossRef]
21. Y. Shi, N. Xu, and Q. Wen, “Ti2CTx (T = O, OH or F) nanosheets as new broadband saturable absorber for ultrafast photonics,” J. Lightwave Technol. 38(7), 1975–1980 (2020). [CrossRef]
22. X. T. Jiang, S. X. Liu, W. Y. Liang, S. J. Luo, Z. L. He, Y. Q. Ge, H. D. Wang, R. Cao, F. Zhang, Q. Wen, J. Q. Li, Q. L. Bao, D. Y. Fan, and H. Zhang, “Broadband nonlinear photonics in few-layer MXene Ti3C2Tx (T = F, O, or OH),” Laser Photonics Rev. 12(2), 1700229 (2018). [CrossRef]
23. Y. Wang, Y. Wang, K. Chen, K. Qi, T. Xue, H. Zhang, J. He, and S. Xiao, “Niobium carbide MXenes with broad-band nonlinear optical response and ultrafast carrier dynamics,” ACS Nano 14(8), 10492–10502 (2020). [CrossRef]
24. S. C. Liu, Y. G. Wang, R. D. Lv, J. Wang, H. Z. Wang, Y. Wang, and L. N. Duan, “2D molybdenum carbide (Mo2C)/fluorine mica (FM) saturable absorber for passively mode-locked erbium-doped all-fiber laser,” Nanophotonics 9(8), 2523–2530 (2020). [CrossRef]
25. H. Lin, X. G. Wang, L. D. Yu, Y. Chen, and J. L. Shi, “Two-dimensional ultrathin MXene ceramic nanosheets for photothermal conversion,” Nano Lett. 17(1), 384–391 (2017). [CrossRef]
26. T. Dash and B. B. Nayak, “Preparation of WC-W2C composites by arc plasma melting and their characterisations,” Ceram. Int. 39(3), 3279–3292 (2013). [CrossRef]
27. L. F. Gao, H. L. Chen, F. Zhang, S. Mei, Y. Zhang, W. L. Bao, C. Y. Ma, P. Yin, J. Guo, X. T. Jiang, S. X. Xu, W. C. Huang, X. B. Feng, F. M. Xu, S. R. Wei, and H. Zhang, “Ultrafast relaxation dynamics and nonlinear response of few-layer niobium carbide MXene,” Small Methods 4(8), 2000250 (2020). [CrossRef]
28. X. Jiang, A. V. Kuklin, A. Baev, Y. Ge, H. Agren, H. Zhang, and P. N. Prasad, “Two-dimensional MXenes: From morphological to optical, electric, and magnetic properties and applications,” Phys. Rep. 848, 1–58 (2020). [CrossRef]
29. D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005). [CrossRef]
30. A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Passive harmonic modelocking of a fiber soliton ring lasers,” Electron. Lett. 29(21), 1860–1861 (1993). [CrossRef]
31. Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10(1), 830 (2019). [CrossRef]
32. L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B: Lasers Opt. 65(2), 277–294 (1997). [CrossRef]
33. D. Y. Tang, L. M. Zhao, and B. Zhao, “Soliton collapse and bunched noise-like pulse generation in a passively mode-locked fiber ring laser,” Opt. Express 13(7), 2289–2294 (2005). [CrossRef]
34. B. A. Malomed, “Bound solitons in the nonlinear Schrödinger–Ginzburg-Landau equation,” Phys. Rev. A 44(10), 6954–6957 (1991). [CrossRef]
35. X. Liu and M. Pang, “Revealing the buildup dynamics of harmonic mode-locking states in ultrafast lasers,” Laser Photonics Rev. 13(9), 1800333 (2019). [CrossRef]
36. Z. H. Wang, X. J. Wang, Y. F. Song, J. Liu, and H. Zhang, “Generation and pulsating behaviors of loosely bound solitons in a passively mode-locked fiber laser,” Phys. Rev. A 101(1), 013825 (2020). [CrossRef]
37. Z. H. Wang, Z. Wang, Y. G. Liu, R. J. He, J. Zhao, G. D. Wang, and G. Yang, “Self-organized compound pattern and pulsation of dissipative solitons in a passively mode-locked fiber laser,” Opt. Lett. 43(3), 478–481 (2018). [CrossRef]
38. S. A. Hussain, “Tunable bound solitons from carbon nanotube saturable absorber,” Optik 217, 164733 (2020). [CrossRef]
39. T. Y. Zhu, Z. K. Wang, D. N. Wang, F. Yang, and L. J. Li, “Observation of controllable tightly and loosely bound solitons with an all-fiber saturable absorber,” Photonics Res. 7(1), 61–68 (2019). [CrossRef]