Research progress of stimulated Raman scattering effect in high power fiber lasers
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摘要:
由于具有高品质、高效率、高鲁棒性、结构紧凑等优点,光纤激光系统在近20年飞速发展,并得到广泛应用。然而发展至今,依旧存在着一些因素(如非线性效应、热效应、模式不稳定性等)限制着光纤激光系统功率的进一步提升。作为其中的一种主要限制因素,受激拉曼散射效应不仅降低了光纤激光器的输出效率,后向斯托克斯光还会提高系统的损毁风险。最近的研究结果表明,少模光纤中受激拉曼散射在引起模式不稳定性的同时,还会导致准静态的模式退化。因此,需要发展有效的拉曼抑制手段来突破现有瓶颈,促进高功率高光束质量光纤激光发展。在介绍高功率少模光纤激光中受激拉曼散射效应新表征的同时,从高功率光纤激光系统整体优化角度出发,总结整理了相关抑制技术研究新进展,并展望未来可能的研究方向。
Abstract:Due to themerits of high quality, high efficiency, high robustness and compact size, the fiber laser systems have developed rapidly in the past 20 years, and have been widely used. However, there are still some factors (such as nonlinear effect, thermal effect, transverse mode instability (TMI), etc.) that limit the scaling of output power of fiber lasers. As one of the main limitations, Stimulated Raman Scattering (SRS) effect not only reduces the fiber lasers’ efficiency, but also increases the risk of device damage with the backward-Stokes light. In addition, recent studies have shown that SRS effect in few-mode fiber lasers can result in TMI and another type of mode distortion, which is on a much slower time scale. Thereby, from the aspect of fiber design and laser systems, amounts of mitigation strategies have been carry out to suppress this nonlinear effect. In this paper, besides the concise description of SRS-induced mode distortion, the suppression strategies in the past decade are also summarized from the aspect of the fiber laser system optimization.
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Key words:
- stimulated Raman scattering /
- laser technique /
- fiber laser /
- mode distortion /
- suppression strategy
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图 9 时域抖动仿真和1 kW输出功率下仿真光谱[78]
Figure 9. Simulated temporal fluctuations and simulated spectra at the output power of ~1 kW[78]
(a)-(d) simulated temporal fluctuations of seed 1 (OSC), seed 2 (with 500 m fibers), seed 3 (with 0.5 nm OC-FBG), and seed 5 (with 0.5 nm OC-FBG+500 m fibers); (e)-(h) simulated temporal fluctuations of SRS lights (from 1080 to 1150 nm) in the corresponding amplifiers; (i)-(l) simulated spectra at the output power of ~1 kW.
表 1 近期光纤设计SRS抑制性能汇总
Table 1. Summary of the recent SRS mitigation performance by fiber design
strategy diameter/μm (core/clad) performance period materials — gain decrease ~3 dB 2013—2018 LMA confined-dope fiber ${A_{{\rm{eff}}}}$ 600 μm2 ~22 dB SNR (8 kW) 2012— tapered fiber 20/400 to 30/600 no Raman Stokes light when output power reached 2170 W 2019— SSC-YDF 20/400+30/600+20/400 no Raman Stokes light when output power reached 5008 W 2018— delocalization star-shaped
filter fiber10 (core) ~17 dB (net suppression ratio) 2006/2014 decreasing fiber length LCA-DCF 20/400 SRS threshold increase from 1.6 to 2.4 kW 2020— 表 2 光纤激光系统参数优化策略汇总
Table 2. Summary of the parameters optimization strategy in fiber laser system
parameter guideline/method parameter guideline/method wavelength of signal >1085 nm bandwidth of FBG in OSC wider fiber length <60 m reflective index of FBG in OSC lower core diameter >20 μm doping concentration lower seed power lower Raman noise of seed power <10−8 W pump methods backward gratings CTFBG/LPG external feedback large angle cleaving self-pulsation special designed seed sources FMW choosing the suitable dispersion value of fibers IM-FWM temporal stable pump -
[1] Snitzer E. Proposed fiber cavities for optical masers[J]. Journal of Applied Physics, 1961, 32(1): 36-39. doi: 10.1063/1.1735955 [2] Liu Zejin, Jin Xiaoxi, Su Rongtao, et al. Development status of high power fiber lasers and their coherent beam combination[J]. Science China Information Sciences, 2019, 62: 41301. doi: 10.1007/s11432-018-9742-0 [3] 周朴, 黄良金, 冷进勇, 等. 高功率双包层光纤激光器: 30周年的发展历程[J]. 中国科学:技术科学, 2020, 50(2):123-135. (Zhou Pu, Huang Liangjin, Leng Jinyong, et al. High-power double-cladding fiber lasers: a 30-year overview[J]. Scientia Sinica Technologica, 2020, 50(2): 123-135 doi: 10.1360/N092018-00409 [4] Dawson J W, Messerly M J, Beach R J, et al. Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power[J]. Optics Express, 2008, 16(17): 13240-13266. doi: 10.1364/OE.16.013240 [5] Zhu Jiajian, Zhou Pu, Ma Yanxing, et al. Power scaling analysis of tandem-pumped Yb-doped fiber lasers and amplifiers[J]. Optics Express, 2011, 19(19): 18645-18654. doi: 10.1364/OE.19.018645 [6] Khitrov V, Minelly J D, Tumminelli R, et al. 3kW single-mode direct diode-pumped fiber laser[C]//Proceedings of SPIE 8961, Fiber Lasers XI: Technology, Systems, and Applications. 2014: 89610V. [7] Möller F, Krämer R G, Matzdorf C, et al. Multi-kW performance analysis of Yb-doped monolithic single-mode amplifier and oscillator setup[C]//Proceedings of SPIE 10897, Fiber Lasers XVI: Technology and Systems. 2019: 108970D. [8] Wang Y, Kitahara R, Kiyoyama W, et al. 8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad[C]//Proceedings of SPIE 11260, Fiber Lasers XVII: Technology and Systems. 2020: 1126022. [9] Jauregui C, Limpert J, Tünnermann A. High-power fibre lasers[J]. Nature Photonics, 2013, 7(11): 861-867. doi: 10.1038/nphoton.2013.273 [10] Zervas M N, Codemard C A. High power fiber lasers: a review[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2014, 20(5): 219-241. doi: 10.1109/JSTQE.2014.2321279 [11] Jauregui C, Stihler C, Limpert J. Transverse mode instability[J]. Advances in Optics and Photonics, 2020, 12(2): 429-484. doi: 10.1364/AOP.385184 [12] 李淳飞. 非线性光学: 原理和应用[M]. 上海: 上海交通大学出版社, 2015: 134-143Li Chunfei. Nonlinear optics: principle and applications[M]. Shanghai: Shanghai Jiao Tong University Press, 2015: 134-143 [13] 王文亮. 大功率光纤激光器受激拉曼散射研究[D]. 长沙: 国防科技大学, 2014: 1-63Wang Wenliang. Stimulated Raman scattering in high power fiber lasers[D]. Changsha: National University of Defense Technology, 2014: 1-63 [14] Naderi S, Dajani I, Grosek J, et al. Theoretical and numerical treatment of modal instability in high-power core and cladding-pumped Raman fiber amplifiers[J]. Optics Express, 2016, 24(15): 16550-16565. doi: 10.1364/OE.24.016550 [15] Distler V, Möller F, Strecker M, et al. Transverse mode instability in a passive fiber induced by stimulated Raman scattering[J]. Optics Express, 2020, 28(15): 22819-22828. doi: 10.1364/OE.398882 [16] Distler V, Möller F, Yildiz B, et al. Experimental analysis of Raman-induced transverse mode instability in a core-pumped Raman fiber amplifier[J]. Optics Express, 2021, 29(11): 16175-16181. doi: 10.1364/OE.424842 [17] Zhang Hanwei, Xiao Hu, Wang Xiaolin, et al. Mode dynamics in high-power Yb-Raman fiber amplifier[J]. Optics Letters, 2020, 45(13): 3394-3397. doi: 10.1364/OL.393879 [18] Chu Qiuhui, Shu Qiang, Chen Zeng, et al. Experimental study of mode distortion induced by stimulated Raman scattering in high-power fiber amplifiers[J]. Photonics Research, 2020, 8(4): 595-600. doi: 10.1364/PRJ.383551 [19] Gao Wei, Fan Wenhui, Ju Pei, et al. Effective suppression of mode distortion induced by stimulated Raman scattering in high-power fiber amplifiers[J]. High Power Laser Science and Engineering, 2021, 9: e20. doi: 10.1017/hpl.2021.13 [20] Liu Wei, Ma Pengfei, Shi Chen, et al. Theoretical analysis of the SRS-induced mode distortion in large-mode area fiber amplifiers[J]. Optics Express, 2018, 26(12): 15793-15803. doi: 10.1364/OE.26.015793 [21] Agrawal G P. Nonlinear fiber optics[M]. 4th ed. Oxford: Elsevier, 2007. [22] Dragic P D, Ballato J. Characterisation of Raman gain spectra in Yb: YAG-derived optical fibres[J]. Electronics Letters, 2013, 49(14): 895-896. doi: 10.1049/el.2013.1386 [23] Dragic P D, Ballato J, Hawkins T. Compositional tuning of glass for the suppression of nonlinear and parasitic fiber laser phenomena[C]//Proceedings of SPIE 9081, Laser Technology for Defense and Security X. 2014: 908109. [24] Ballato J, Dragic P. Materials approaches to mitigating parasitic effects in optical networks: towards the perfect optical fiber[C]//Proceedings of the 18th International Conference on Transparent Optical Networks. 2016: 1-4. [25] Ballato J, Cavillon M, Dragic P. A unified materials approach to mitigating optical nonlinearities in optical fiber. I. Thermodynamics of optical scattering[J]. International Journal of Applied Glass Science, 2018, 9(2): 263-277. doi: 10.1111/ijag.12327 [26] Ye Yun, Yang Baolai, Wang Peng, et al. Industrial 6 kW high-stability single-stage all-fiber laser oscillator based on conventional large mode area ytterbium-doped fiber[J]. Laser Physics, 2021, 31: 035104. doi: 10.1088/1555-6611/abdfc2 [27] Mashiko Y, Nguyen H K, Kashiwagi M, et al. 2 kW single-mode fiber laser with 20-m long delivery fiber and high SRS suppression[C]//Proceedings of SPIE 9728, Fiber Lasers XIII: Technology, Systems, and Applications. 2016: 972805. [28] Shima K, Ikoma S, Uchiyama K, et al. 5-kW single stage all-fiber Yb-doped single-mode fiber laser for materials processing[C]//Proceedings of SPIE 10512, Fiber Lasers XV: Technology and Systems. 2018: 105120C. [29] 张志伦, 张芳芳, 林贤峰, 等. 国产部分掺杂光纤实现3 kW全光纤激光振荡输出[J]. 物理学报, 2020, 69:234205. (Zhang Zhilun, Zhang Fangfang, Lin Xianfeng, et al. Home-made confined-doped fiber with 3-kW all-fiber laser oscillating output[J]. Acta Physica Sinica, 2020, 69: 234205 doi: 10.7498/aps.69.20200620 [30] Yang Baolai, Zhang Hanwei, Shi Chen, et al. High power monolithic tapered ytterbium-doped fiber laser oscillator[J]. Optics Express, 2019, 27(5): 7585-7592. doi: 10.1364/OE.27.007585 [31] Ye Yun, Xi Xiaoming, Shi Chen, et al. Comparative study on transverse mode instability of fiber amplifiers based on long tapered fiber and conventional uniform fiber[J]. Laser Physics Letters, 2019, 16: 085109. doi: 10.1088/1612-202X/ab2acf [32] Tian Yuan, Chen Yizhu, Leng Jinyong, et al. Numerical modeling and optimization of cladding-pumped tapered fiber Raman amplifiers[J]. Optics Communications, 2018, 423: 6-11. doi: 10.1016/j.optcom.2018.03.084 [33] Zeng Lingfa, Xi Xiaoming, Ye Yun, et al. A 1.8 kW fiber laser oscillator employing a section of spindle-shaped core ytterbium-doped fiber[J]. Laser Physics Letters, 2020, 17: 095104. doi: 10.1088/1612-202X/aba62d [34] 奚小明, 曾令筏, 叶云, 等. 基于国产双锥形光纤实现3 kW单模全光纤振荡器[J]. 中国激光, 2020, 47:0916001. (Xi Xiaoming, Zeng Lingfa, Ye Yun, et al. Single-mode all-fiber oscillator based on home-made dual-tapered fiber with 3kW output[J]. Chinese Journal of Lasers, 2020, 47: 0916001 doi: 10.3788/CJL202047.0916001 [35] Zeng Lingfa, Pan Zhiyong, Xi Xiaoming, et al. 5 kW monolithic fiber amplifier employing homemade spindle-shaped ytterbium-doped fiber[J]. Optics Letters, 2021, 46(6): 1393-1396. doi: 10.1364/OL.418194 [36] Zenteno L A, Wang J, Walton D T, et al. Suppression of Raman gain in single-transverse-mode dual-hole-assisted fiber[J]. Optics Express, 2005, 13(22): 8921-8926. doi: 10.1364/OPEX.13.008921 [37] Fini J M, Mermelstein M D, Yan M F, et al. Distributed suppression of stimulated Raman scattering in an Yb-doped filter-fiber amplifier[J]. Optics Letters, 2006, 31(17): 2550-2552. doi: 10.1364/OL.31.002550 [38] Fini J M, Nicholson J W. Fibers design with a bend-compensated cladding for distributed wavelength filtering[C]//Proceedings of SPIE 8961, Fiber Lasers XI: Technology, Systems, and Applications. 2014: 89610S. [39] Liu Rui, Yan Dapeng, Chen Ming, et al. Enhanced cladding pump absorption of ytterbium-doped double cladding fiber with internally modified cladding structures[J]. Optical Materials Express, 2020, 10(1): 36-45. doi: 10.1364/OME.10.000036 [40] Wang Yong, Martinez-Rios A, Po H. Experimental study of stimulated Brillouin and Raman scatterings in a Q-switched cladding-pumped fiber laser[J]. Optical Fiber Technology, 2004, 10(2): 201-214. doi: 10.1016/j.yofte.2003.11.004 [41] Wang Yong, Xu Changqing, Po Hong. Analysis of Raman and thermal effects in kilowatt fiber lasers[J]. Optics Communications, 2004, 242(4/6): 487-502. [42] Wang Yong. Stimulated Raman scattering in high-power double-clad fiber lasers and power amplifiers[J]. Optical Engineering, 2005, 44: 114202. doi: 10.1117/1.2128147 [43] Ye Yun, Xi Xiaoming, Shi Chen, et al. Experimental study of 5-kW high-stability monolithic fiber laser oscillator with or without external feedback[J]. IEEE Photonics Journal, 2019, 11: 1503508. [44] Lai P Y, Chang Chunlin, Huang S L, et al. Effective suppression of stimulated Raman scattering in high power fiber amplifiers using double-pass scheme[C]//Proceedings of SPIE 8961, Fiber Lasers XI: Technology, Systems, and Applications. 2014: 89612T. [45] Zhang Tianzi, Ding Yingchun, Liu Zhongxuan, et al. An optimization of Raman effects in tandem-pumped Yb-doped kilowatt fiber amplifiers[C]//Proceedings of SPIE 9524, International Conference on Optical and Photonic Engineering. 2015: 95240Y. [46] 叶云, 王小林, 史尘, 等. 高功率掺镱光纤激光振荡器研究进展[J]. 激光与光电子学进展, 2018, 55:120006. (Ye Yun, Wang Xiaolin, Shi Chen, et al. Research progress in high power ytterbium doped fiber laser oscillator[J]. Laser & Optoelectronics Progress, 2018, 55: 120006 [47] Ye Yun, Yang Baolai, Wang Xiaolin, et al. Experimental study of SRS threshold dependence on the bandwidths of fiber Bragg gratings in co-pumped and counter-pumped fiber laser oscillator[J]. Journal of Optics, 2019, 21: 025801. doi: 10.1088/2040-8986/aafa65 [48] Schreiber T, Liem A, Freier E, et al. Analysis of stimulated Raman scattering in cw kW fiber oscillators[C]//Proceedings of SPIE 8961, Fiber Lasers XI: Technology, Systems, and Applications. 2014: 89611T. [49] Liu Wei, Ma Pengfei, Lv Haibin, et al. General analysis of SRS-limited high-power fiber lasers and design strategy[J]. Optics Express, 2016, 24(23): 26715-26721. doi: 10.1364/OE.24.026715 [50] Lin Weixuan. Stimulated Raman scattering and intermodal coupling in continuous-wave high power fiber lasers[D]. Montreal: McGill University, 2018. [51] Jansen F, Nodop D, Jauregui C, et al. Suppression of stimulated Raman scattering in high-power fiber laser systems by lumped spectral filters[C]//Proceedings of SPIE 7580, Fiber Lasers VII: Technology, Systems, and Applications. 2010: 75802I. [52] Nodop D, Jauregui C, Jansen F, et al. Suppression of stimulated Raman scattering employing long period gratings in double-clad fiber amplifiers[J]. Optics Letters, 2010, 35(17): 2982-2984. doi: 10.1364/OL.35.002982 [53] Heck M, Bock V, Krämer R G, et al. Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings[C]//Proceedings of SPIE 10512, Fiber Lasers XV: Technology and Systems. 2018: 105121I. [54] Jiao Kerong, Shen Hua, Guan Zhiwen, et al. Suppressing stimulated Raman scattering in kW-level continuous-wave MOPA fiber laser based on long-period fiber gratings[J]. Optics Express, 2020, 28(5): 6048-6063. doi: 10.1364/OE.384760 [55] Wang Meng, Zhang Yujing, Wang Zefeng, et al. Fabrication of chirped and tilted fiber Bragg gratings and suppression of stimulated Raman scattering in fiber amplifiers[J]. Optics Express, 2017, 25(2): 1529-1534. doi: 10.1364/OE.25.001529 [56] Wang Meng, Hu Qihao, Liu Le, et al. Suppression of stimulated Raman scattering in a monolithic fiber laser oscillator using chirped and tilted fiber Bragg gratings[C]//Proceedings of SPIE 10811, High-Power Lasers and Applications IX. 2018: 108110V. [57] Wang Zefeng, Wang Meng, Hu Qihao. Filtering of stimulated Raman scattering in a monolithic fiber laser oscillator using chirped and tilted fiber Bragg gratings[J]. Laser Physics, 2019, 29: 075101. doi: 10.1088/1555-6611/ab1537 [58] Jiao Kerong, Shu Jian, Shen Hua, et al. Fabrication of kW-level chirped and tilted fiber Bragg gratings and filtering of stimulated Raman scattering in high-power CW oscillators[J]. High Power Laser Science and Engineering, 2019, 7: 02000e31. [59] Zhao Xiaofan, Tian Xin, Hu Qihao, et al. Raman suppression in a high-power single-mode fiber oscillator using a chirped and tilted fiber Bragg grating[J]. Laser Physics Letters, 2021, 18: 035103. doi: 10.1088/1612-202X/abe46f [60] Wang Meng, Liu Le, Wang Zefeng, et al. Mitigation of stimulated Raman scattering in kilowatt-level diode-pumped fiber amplifiers with chirped and tilted fiber Bragg gratings[J]. High Power Laser Science and Engineering, 2019, 7: e18. doi: 10.1017/hpl.2019.1 [61] Tian Xin, Zhao Xiaofan, Wang Meng, et al. Effective suppression of stimulated Raman scattering in direct laser diode pumped 5 kilowatt fiber amplifier using chirped and tilted fiber bragg gratings[J]. Laser Physics Letters, 2020, 17: 085104. doi: 10.1088/1612-202X/aba051 [62] Wang Meng, Wang Zefeng, Liu Le, et al. Effective suppression of stimulated Raman scattering in half 10 kW tandem pumping fiber lasers using chirped and tilted fiber Bragg gratings[J]. Photonics Research, 2019, 7(2): 167-171. doi: 10.1364/PRJ.7.000167 [63] Tian Xin, Zhao Xiaofan, Wang Meng, et al. Influence of Bragg reflection of chirped tilted fiber Bragg grating on Raman suppression in high-power tandem pumping fiber amplifiers[J]. Optics Express, 2020, 28(13): 19508-19517. doi: 10.1364/OE.396250 [64] 张俊, 冯莹, 陈爽. 大功率双包层光纤激光器拉曼效应分析[J]. 量子电子学报, 2007, 24(6):757-762. (Zhang Jun, Feng Ying, Chen Shuang. Analysis of Raman effects in high power double-clad fiber laser[J]. Chinese Journal of Quantum Electronics, 2007, 24(6): 757-762 doi: 10.3969/j.issn.1007-5461.2007.06.019 [65] Chen Heng, Cao Jianqiu, Huang Zhihe, et al. Experimental investigations on multi-kilowatt all-fiber distributed side-pumped oscillators[J]. Laser Physics, 2019, 29: 075103. doi: 10.1088/1555-6611/ab1de4 [66] Chen Heng, Cao Jianqiu, Huang Zhihe, et al. 3-kilowatt all-fiber distributed side-pumped oscillator with high SRS suppression[C]//Proceedings of 2018 Asia Communications and Photonics Conference. 2018. [67] Huang Zhihe, Cao Jianqiu, An Yingye, et al. A kilowatt all-fiber cascaded amplifier[J]. IEEE Photonics Technology Letters, 2015, 27(16): 1683-1686. doi: 10.1109/LPT.2015.2426191 [68] Ying Hanyuan, Yu Yu, Cao Jianqiu, et al. 2 kW pump-light-stripper-free distributed side-coupled cladding-pumped fiber oscillator[J]. Laser Physics Letters, 2017, 14: 065102. doi: 10.1088/1612-202X/aa6dc8 [69] Wang Jianming, Yan Dapeng, Xiong Songsong, et al. High power all-fiber amplifier with different seed power injection[J]. Optics Express, 2016, 24(13): 14463-14469. doi: 10.1364/OE.24.014463 [70] Tec P S, Lewis R J, Alam S U, et al. 200 W Diffraction limited, single-polarization, all-fiber picosecond MOPA[J]. Optics Express, 2013, 21(22): 25883-25889. doi: 10.1364/OE.21.025883 [71] Ying Hanyuan, Cao Jianqiu, Yu Yu, et al. Raman-noise enhanced stimulated Raman scattering in high-power continuous-wave fiber amplifier[J]. Optik, 2017, 144: 163-171. doi: 10.1016/j.ijleo.2017.06.098 [72] Hu Shuling, Zhang Chunxi, Wang Shouchao, et al. Self-pulsing behavior in high-power ytterbium-doped fiber lasers[C]//Proceedings of SPIE 6823, High-Power Lasers and Applications IV. 2008: 68230D. [73] Bock V, Schultze T, Liem A, et al. The influence of different seed sources on Stimulated Raman Scattering in fiber amplifiers[C]//The European Conference on Lasers and Electro-Optics 2017. 2017: CJ_4_3. [74] Li Tenglong, Zha Congwen, Sun Yinhong, et al. 3.5 kW bidirectionally pumped narrow-linewidth fiber amplifier seeded by white-noise-source phase-modulated laser[J]. Laser Physics, 2018, 28: 105101. doi: 10.1088/1555-6611/aace37 [75] Lin H, Tao R, Li C, et al. 3.7 kW monolithic narrow linewidth single mode fiber laser through simultaneously suppressing nonlinear effects and mode instability[J]. Optics Express, 2019, 27(7): 9716-9724. doi: 10.1364/OE.27.009716 [76] Liu Wei, Ma Pengfei, Lv Haibin, et al. Investigation of stimulated Raman scattering effect in high-power fiber amplifiers seeded by narrow-band filtered superfluorescent source[J]. Optics Express, 2016, 24(8): 8708-8717. doi: 10.1364/OE.24.008708 [77] Bock V, Liem A, Schreiber T, et al. Explanation of Stimulated Raman Scattering in high power fiber systems[C]//Proceedings of SPIE 10512, Fiber Lasers XV: Technology and Systems. 2018: 105121F. [78] Li Tenglong, Ke Weiwei, Ma Yi, et al. Suppression of stimulated Raman scattering in a high-power fiber amplifier by inserting long transmission fibers in a seed laser[J]. Journal of the Optical Society of America B, 2019, 36(6): 1457-1465. doi: 10.1364/JOSAB.36.001457 [79] Wang Yanshan, Peng Wanjing, Ke Weiwei, et al. Influence of seed instability on the stimulated Raman scattering of high power narrow linewidth fiber amplifier[J]. Optical and Quantum Electronics, 2020, 52: 193. doi: 10.1007/s11082-020-02299-4 [80] Yin Lu, Han Zhigang, Shen Hua, et al. Suppression of inter-modal four-wave mixing in high-power fiber lasers[J]. Optics Express, 2018, 26(12): 15804-15818. doi: 10.1364/OE.26.015804 [81] Babin S A, Churkin D V, Ismagulov A E, et al. Four-wave-mixing-induced turbulent spectral broadening in a long Raman fiber laser[J]. Journal of the Optical Society of America B, 2007, 24(8): 1729-1738. doi: 10.1364/JOSAB.24.001729 [82] Hu Man, Ke Weiwei, Yang Yifeng, et al. Low threshold Raman effect in high power narrowband fiber amplifier[J]. Chinese Optics Letters, 2016, 14: 011901. doi: 10.3788/COL201614.011901 [83] Liu Wei, Ma Pengfei, Zhou Pu, et al. Effects of four-wave-mixing in high-power Raman fiber amplifiers[J]. Optics Express, 2020, 28(1): 593-606. doi: 10.1364/OE.381761