光纤激光模式不稳定研究十年回顾与展望

王建军; 刘玙; 李敏; 冯曦; 楚秋慧; 张春; 高聪; 陶汝茂; 林宏奂; 景峰

doi:10.11884/HPLPB202032.200180

光纤激光模式不稳定研究十年回顾与展望

doi: 10.11884/HPLPB202032.200180

中国工程物理研究院激光聚变研究中心，四川绵阳 621900

基金项目: 国家自然科学基金项目（61905226）

详细信息

作者简介:
王建军（1974—），男，研究员，主要从事高功率光纤激光技术研究；wjjcaep@caep.cn

通讯作者:
陶汝茂（1987—），男，副研究员，主要从事高功率光纤激光技术研究；taorumao@sohu.com

中图分类号: TN248
计量
- 文章访问数: 1928
- HTML全文浏览量: 598
- PDF下载量: 307
- 被引次数: 0
出版历程
- 收稿日期: 2020-06-30
- 修回日期: 2020-11-06
- 刊出日期: 2020-11-19

Ten-year review and prospect on mode instability research of fiber lasers

Laser Fusion Research Center, CAEP, P. O. Box 919-988, Mianyang 621900, China

摘要

摘要: 2010年模式不稳定现象首次报道，开启了光纤激光与废热的斗争史。回顾了10年来模式不稳定现象的研究进展，概述了光纤激光模式不稳定物理表征、基本原理、理论研究、影响因素和抑制策略等，介绍了高功率光纤激光在模式不稳定抑制方面取得的最新成果，展望了高功率光纤激光模式不稳定研究的未来发展，对光纤激光模式不稳定未来可能的研究方向进行了展望。
- 模式不稳定 /
- 光纤激光 /
- 热效应 /
- 量子亏损 /
- 增益饱和
Abstract: The report about mode instability in 2010 has begun the history of struggling with the waste heat in fiber lasers. This paper presents a 10-year research progress of mode instability research, including physical demonstrations, physical mechanism, theoretical investigation, various impact factors and effective mitigating strategies. The most recent results on mode instability suppressing are also included as well as the future development trend of mode instability research.
- mode instability /
- fiber laser /
- thermal effect /
- quantum defect /
- gain saturation

HTML全文

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

参考文献(122)

[1]	Snitzer E. Proposed fiber cavities for optical masers[J]. J Appl Phys, 1961, 32: 36-39. doi: 10.1063/1.1735955
[2]	Richardson D J, Nilsson J, Clarkson W A. High power fiber lasers: current status and future perspectives[J]. J Opt Soc Am B, 2010, 27(11): 63-92. doi: 10.1364/JOSAB.27.000B63
[3]	Mourou G, Brocklesby B, Tajima T, et al. The future is fibre accelerators[J]. Nat Photonics, 2013, 7: 258-261. doi: 10.1038/nphoton.2013.75
[4]	Jauregui C, Limpert J, Tünnermann A. High-power fibre lasers[J]. Nat Photonics, 2013, 7: 861-867. doi: 10.1038/nphoton.2013.273
[5]	Zervas M N, Codemard C A. High power fiber lasers: A review[J]. IEEE J Sel Top Quantum Electron, 2014, 20(11): 219-241.
[6]	Shi W, Fang Q, Zhu X, et al. Fiber lasers and their applications[J]. Appl Opt, 2014, 53: 6554-6568. doi: 10.1364/AO.53.006554
[7]	杨昌盛, 徐善辉, 周军, 等. 大功率光纤激光材料与器件关键技术研究进展[J]. 中国科学: 技术科学, 2017, 47:1038-1048. (Yang Changsheng, Xu Shanhui, Zhou Jun, et al. Research advance on the key technology of high-power fiber laser materials and components[J]. Scientia Sinica Technologica, 2017, 47: 1038-1048 doi: 10.1360/N092016-00437
[8]	Liu Z J, Jin X X, Su R T, et al. Development status of high power fiber lasers and their coherent beam combination[J]. Science China: Information Science, 2019, 62: 041301. doi: 10.1007/s11432-018-9742-0
[9]	Stiles E. New developments in IPG fiber laser technology[C]//Proc 5th Int Workshop Fiber Lasers. 2009.
[10]	Eidam T, Hanf S, Seise E, et al. Femtosecond fiber CPA system emitting 830 W average output power[J]. Opt Lett, 2010, 35: 94-96. doi: 10.1364/OL.35.000094
[11]	Shiner B. The impact of fiber laser technology on the world wide material processing market[C]//Proc Conf Lasers Electro-Opt. 2013: AF2J.1.
[12]	林宏奂, 唐选, 李成钰, 等. 全国产单纤激光系统获得10.6 kW激光输出[J]. 中国激光, 2018, 45:0315001. (Lin Honghuan, Tang Xuan, Li Chengyu, et al. 10.6 kW laser from totally-domestic fiber laser systems[J]. Chinese Journal of Laser, 2018, 45: 0315001 doi: 10.3788/CJL201845.0315001
[13]	林傲祥, 湛欢, 彭昆, 等. 国产复合功能光纤实现万瓦激光输出[J]. 强激光与粒子束, 2018, 30:060101. (Lin Aoxiang, Zhan Huan, Peng Kun, et al. 10 kW-level pump-gain integrated functional laser fiber[J]. High Power Laser and Particle Beams, 2018, 30: 060101 doi: 10.11884/HPLPB201830.180110
[14]	高聪, 代江云, 李峰云, 等. 自研万瓦级同带泵浦掺镱石英玻璃光纤[J]. 中国激光, 2020, 47:0315001. (Gao Cong, Dai Jiangyun, Li Fengyun, et al. Homemade 10-kW ytterbium-doped aluminophosphosilicate fiber for tandem pumping[J]. Chinese Journal of Laser, 2020, 47: 0315001 doi: 10.3788/CJL202047.0315001
[15]	陈晓龙, 楼风光, 何宇, 等. 高效率全国产化10 kW光纤激光器[J]. 光学学报, 2019, 39:0336001. (Chen Xiaolong, Lou Fengguang, He Yu, et al. Home-made 10-kW fiber laser with high efficiency[J]. Acta Optica Sinica, 2019, 39: 0336001 doi: 10.3788/AOS201939.0336001
[16]	Fang Q, Li J, Shi W, et al. 5 kW near-diffraction-limited and 8 kW high-brightness monolithic continuous wave fiber lasers directly pumped by laser diodes[J]. IEEE Photonics J, 2017, 9: 1506107.
[17]	Möller F, Krämer R, Matzdorf C, et al. Multi-kW performance analysis of Yb-doped monolithic single-mode amplifier and oscillator setup[C]//Proc of SPIE. 2019: 108970D.
[18]	Ye Y, Xi X, Shi C, et al. Experimental study of 5 kW high stability monolithic fiber laser oscillator with or without external feedback[J]. IEEE Photonics J, 2019, 11: 1503508.
[19]	Eidam T, Wirth C, Jauregui C, et al. Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers[J]. Opt Express, 2011, 19(14): 13218-13224. doi: 10.1364/OE.19.013218
[20]	Otto H J, Stutzki F, Jansen F, et al. Temporal dynamics of mode-instabilities in high power fiber lasers and amplifiers[J]. Opt Express, 2012, 20: 15710-15722. doi: 10.1364/OE.20.015710
[21]	Stutzki F, Otto H, Jansen F, et al. High-speed modal decomposition of mode instabilities in high-power fiber lasers[J]. Opt Lett, 2011, 36: 4572-4574. doi: 10.1364/OL.36.004572
[22]	Tao R M, Ma P F, Wang X L, et al. Study of mode instabilities in high power fiber amplifiers by detecting scattering light[C]//International Photonics and OptoElectronics Meetings. 2014.
[23]	陶汝茂, 周朴, 肖虎, 等. 高功率光纤激光中模式不稳定性现象研究进展[J]. 激光与光电子学进展, 2014, 51:020001. (Tao Rumao, Zhou Pu, Xiao Hu, et al. Progress of study on mode instability in high power fiber amplifiers[J]. Laser & Optoelectronics Progress, 2014, 51: 020001
[24]	史尘, 陶汝茂, 王小林, 等. 光纤激光模式不稳定的新现象与新进展[J]. 中国激光, 2017, 44:0201004. (Shi Chen, Tao Rumao, Wang Xiaolin, et al. New progress and phenomena of modal instability in fiber lasers[J]. Chinese Journal of Lasers, 2017, 44: 0201004 doi: 10.3788/CJL201744.0201004
[25]	陶汝茂, 周朴, 王小林, 等. 高功率全光纤结构主振荡功率放大器中模式不稳定现象的实验研究[J]. 物理学报, 2014, 63:085202. (Tao Rumao, Zhou Pu, Wang Xiaolin, et al. Experimental study on mode instability in high power all-fiber master oscillator power amplifier fiber lasers[J]. Acta Physica Sinica, 2014, 63: 085202
[26]	Tao R, Ma P, Wang X, et al. 1.4 kW all-fiber narrow-linewidth polarization-maintained fiber amplifier[C]//The 20th International Symposium on High-Power Laser Systems and Applications. 2014.
[27]	Tao R, Ma P, Wang X, et al. Mitigating of modal instabilities in linearly-polarized fiber amplifiers by shifting pump wavelength[J]. Journal of Optics, 2015, 17: 045504.
[28]	Wirth C, Schmidt O, Tsybin I, et al. High average power spectral beam combining of four fiber amplifiers to 8.2 kW[J]. Opt Lett, 2011, 36: 3118-3120. doi: 10.1364/OL.36.003118
[29]	Jansen F, Stutzki F, Otto H, et al. High-power thermally guiding index-antiguiding-core fibers[J]. Opt Lett, 2013, 38: 510-512. doi: 10.1364/OL.38.000510
[30]	Yang B L, Zhang H W, Shi C, et al. 3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability[J]. Journal of Optics, 2018, 20: 025802.
[31]	Malleville M, Benoît A, Dauliat R, et al. Experimental investigation of the transverse modal instabilities onset in high power fully-aperiodic-large-pitch fiber lasers[C]//Proc of SPIE. 2018: 1051206.
[32]	Scarnera V, Ghiringhelli F, Malinowski A, et al. Modal instabilities in high power fiber laser oscillators[J]. Opt Express, 2019, 27: 4386-4403. doi: 10.1364/OE.27.004386
[33]	Roohforouz A, Chenar R, Azizi S, et al. Effect of pumping configuration on the transverse mode instability power threshold in a 3.02 kW fiber laser oscillator[C]//OSA Laser Congress. 2019.
[34]	Chen H, Cao J, Huang Z, et al. Experimental investigations on TMI and IM-FWM in distributed side-pumped fiber amplifier[J]. IEEE Photonics J, 2020, 12: 1502413.
[35]	Jauregui C, Eidam T, Limpert J, et al. Impact of modal interference on the beam quality of high-power fiber amplifiers[J]. Opt Express, 2011, 19: 3258-3271. doi: 10.1364/OE.19.003258
[36]	Smith A V, Smith J J. Mode instability in high power fiber amplifiers[J]. Opt Express, 2011, 19(11): 10180-10192. doi: 10.1364/OE.19.010180
[37]	Hansen K R, Alkeskjold T T, Broeng J, et al. Thermally induced mode coupling in rare-earth doped fiber amplifiers[J]. Opt Lett, 2012, 37(12): 2382-2384. doi: 10.1364/OL.37.002382
[38]	Jauregui C, Eidam T, Otto H J, et al. Physical origin of mode instabilities in high-power fiber laser systems[J]. Opt Express, 2012, 20(12): 12912-12925. doi: 10.1364/OE.20.012912
[39]	Ward B, Robin C, Dajani I. Origin of thermal modal instabilities in large mode area fiber amplifiers[J]. Opt Express, 2012, 20(10): 11407-11422. doi: 10.1364/OE.20.011407
[40]	Dong L. Stimulated thermal Rayleigh scattering in optical fibers[J]. Opt Express, 2013, 21(3): 2642-2656. doi: 10.1364/OE.21.002642
[41]	Hu I N, Zhu C, Zhang C, et al. Analytical time-dependent theory of thermally-induced modal instabilities in high power ﬁber amplifiers[C]//Proc of SPIE. 2013: 860109.
[42]	Jauregui C, Eidam T, Otto H J, et al. Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems[J]. Opt Express, 2012, 21(1): 440-451.
[43]	Chi M, Huignard J P, Petersen P M. A general theory of two-wave mixing in nonlinear media[J]. J Opt Soc Am B, 2009, 26(8): 1578-1584. doi: 10.1364/JOSAB.26.001578
[44]	Smith A V, Smith J J. Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers[J]. Opt Express, 2012, 20(22): 24545-24558. doi: 10.1364/OE.20.024545
[45]	Smith A V, Smith J J. Spontaneous Rayleigh seed for stimulated Rayleigh scattering in high power fiber amplifiers[J]. IEEE Photonics J, 2013, 5: 7100807. doi: 10.1109/JPHOT.2013.2280526
[46]	Smith A V, Smith J J. Review of models of mode instability in fiber amplifiers[EB/OL]. http://as-photonics.com.
[47]	Ward B. Numerical analysis of modal instability onset in fiber amplifiers[C]//Proc of SPIE. 2014: 89611U.
[48]	Naderi S, Dajani I, Grosek J, et al. Theoretical treatment of modal instability in high power cladding-pumped Raman amplifiers[C]//Proc of SPIE. 2015: 93442X.
[49]	Ward B. Finite element steady periodic beam propagation analysis of mode instability in high power fiber amplifiers[J]. Opt Express, 2018, 26: 16875-16883. doi: 10.1364/OE.26.016875
[50]	Smith A V, Smith J J. Steady-periodic method for modeling mode instability in fiber amplifiers[J]. Opt Express, 2013, 21(3): 2606-2623. doi: 10.1364/OE.21.002606
[51]	Naderi S, Dajani I, Madden T, et al. Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations[J]. Opt Express, 2013, 21(13): 16111-16129. doi: 10.1364/OE.21.016111
[52]	Eznaveh Z S, Lopez-Galmiche G, Antonio-Lopez E, et al. Bi-directional pump configuration for increasing thermal modal instabilities threshold in high power fiber amplifiers[C]//Proc of SPIE. 2015: 93442G.
[53]	Xia N, Yoo S. Mode instability in ytterbium-doped non-circular fibers[J]. Opt Express, 2017, 25: 13230-13251. doi: 10.1364/OE.25.013230
[54]	Wang Y, Liu Q, Ma Y, et al. Research of the mode instability threshold in high power double cladding Yb-doped fiber amplifiers[J]. Ann Phys, 2017: 1600398.
[55]	Zhu S, Li J, Li L, et al. Mode instabilities in Yb: YAG crystalline fiber amplifiers[J]. Opt Express, 2019, 27: 35065-35078. doi: 10.1364/OE.27.035065
[56]	Hansen K R, Alkeskjold T T, Broeng J, et al. Theoretical analysis of mode instability in high-power ﬁber ampliﬁers[J]. Opt Express, 2013, 21(2): 1944-1971. doi: 10.1364/OE.21.001944
[57]	Hansen K R, Lægsgaard J. Impact of gain saturation on the mode instability threshold in high-power fiber amplifiers[J]. Opt Express, 2014, 22(9): 11267-11278. doi: 10.1364/OE.22.011267
[58]	Mermelstein M. Laser linewidth dependence to the transverse mode instability (TMI) nonlinear gain in kW-class fiber amplifiers[C]//Proc of SPIE. 2018: 1051221.
[59]	Jauregui C, Otto H-J, Stutzki F, et al. Simplified modelling the mode instability threshold of high power fiber amplifiers in the presence of photodarkening[J]. Opt Express, 2015, 23: 20203-20218. doi: 10.1364/OE.23.020203
[60]	Tao R, Ma P, Wang X, Zhou P, et al. 1.3 kW monolithic linearly polarized single-mode master oscillator power amplifier and strategies for mitigating mode instabilities[J]. Photonics Research, 2015, 3: 86-93. doi: 10.1364/PRJ.3.000086
[61]	Kong L, Leng J, Zhou P, et al. Numerical modeling of the thermally induced core laser leakage in high power co-pumped ytterbium doped fiber amplifier[J]. High Power Laser Science and Engineering, 2018, 6: e25. doi: 10.1017/hpl.2018.15
[62]	Li Z, Huang Z, Xiang X, et al. Experimental demonstration of transverse mode instability enhancement by a counter-pumped scheme in a 2 kW all-fiberized laser[J]. Photonics Research, 2017, 5: 77-81. doi: 10.1364/PRJ.5.000077
[63]	Zervas M. Transverse mode instability analysis in fibre amplifiers[C]//Proc of SPIE. 2017: 100830M.
[64]	Gao W, Zhao B, Fan W, et al. Instability transverse mode phase transition of fiber oscillator for extreme power lasers[J]. Opt Express, 2019, 27: 22393-22407. doi: 10.1364/OE.27.022393
[65]	Smith A V, Smith J J. Mode instability thresholds of fiber amplifiers[C]//Proc of SPIE. 2013: 860108.
[66]	Laurila M, Jørgensen M M, Hansen K R, et al. Distributed mode filtering rod fiber amplifier delivering 292 W with improved mode stability[J]. Opt Express, 2012, 20(5): 5742-5753. doi: 10.1364/OE.20.005742
[67]	Tao R, Ma P, Wang X, et al. Study of wavelength dependence of mode instability based on a semi-analytical model[J]. IEEE J Quantum Electron, 2015, 51: 1600106.
[68]	Filippov V, Ustimchik V, Chamorovskiy Y, et al. Impact of axial profile of the gain medium on the mode instability in lasers: regular versus tapered fibers[C]//Cleo/europe-eqec P Cj-105 1 P Cj. 2015.
[69]	Stihler C, Otto H-J, Jauregui C, et al. Experimental investigation of transverse mode instabilities in a double-pass Yb-doped rod-type fiber amplifier[C]//Proc of SPIE. 2017: 100830R.
[70]	Bobkov K, Bubnov M, Aleshkina S, et al. Long-term mode shape degradation in large mode area Yb-doped pulsed fiber amplifers[J]. Laser Phys Lett, 2017, 14: 015102.
[71]	Lupi J, Johansen M, Michieletto M, et al. Static and dynamic mode coupling in double-pass rod-type fiber amplifier[J]. Opt Lett, 2018, 43(22): 5535-5538. doi: 10.1364/OL.43.005535
[72]	Chen Y, Xu H, Xing Y, et al. Impact of gamma-ray radiation-induced photodarkening on mode instability degradation of an ytterbium-doped fiber amplifier[J]. Opt Express, 2018, 26: 20430-20441. doi: 10.1364/OE.26.020430
[73]	Gaida C, Gebhardt C, Heuermann T, et al. Observation of transverse-mode instabilities in a thulium-doped fiber amplifier[C]//Proc of SPIE. 2019: 1089702.
[74]	Distler V, Möller F, Strecker M, et al. High power narrow-linewidth Raman amplifier and its limitation[C]//Proc of SPIE. 2020: 1126005.
[75]	Zhang H, Xiao H, Wang X, et al. Mode dynamics in high power Yb-Raman fiber amplifier[J]. Opt Lett, 2020, 45(13): 3394-3397. doi: 10.1364/OL.393879
[76]	Lægsgaard J. Static thermo-optic instability in double-pass fiber amplifiers[J]. Opt Express, 2016, 24: 13429-13443. doi: 10.1364/OE.24.013429
[77]	Ward B. Theory and modeling of photodarkening-induced quasi static degradation in fiber amplifiers[J]. Opt Express, 2016, 24: 3488-3501. doi: 10.1364/OE.24.003488
[78]	Smith A V, Smith J J. Mode instability thresholds for Tm-doped fiber amplifiers pumped at 790 nm[J]. Opt. Express, 2016, 24: 975-992. doi: 10.1364/OE.24.000975
[79]	Shi C, Wang X, Zhang H, et al. Simulation investigation of impact factors in photodarkening-induced beam degradation in fiber amplifers[J]. Laser Phys, 2017, 27: 105102. doi: 10.1088/1555-6611/aa77be
[80]	Tao R, Wang X, Zhou P. Comprehensive theoretical study of mode instability in high-power fiber lasers by employing a universal model and its implications[J]. IEEE J Sel Top Quant Electron, 2018, 24: 0903319.
[81]	Tao R, Ma P, Wang X, et al. Study of dopant concentrations on thermally induced mode instability in high-power fiber amplifiers[J]. Laser Phys, 2016, 26: 065103. doi: 10.1088/1054-660X/26/6/065103
[82]	Ward B. Accurate modeling of rod-type photonic crystal fiber amplifiers[C]//Proc of SPIE. 2015: 97280F.
[83]	Xia N. Investigation of transverse mode instability suppression in large mode area fibre[D]. Singapore: Nanyang Technological University Library. 2019.
[84]	Tao R, Wang X, Zhou P, et al. Seed power dependence of mode instabilities in high-power fiber amplifiers[J]. Journal of Optics, 2017, 19: 065202. doi: 10.1088/2040-8986/aa6902
[85]	Karow M, Tünnermann H, Neumann J, et al. Beam quality degradation of a single-frequency Yb-doped photonic crystal fiber amplifier with low mode instability threshold power[J]. Opt Lett, 2012, 37: 4242-4244. doi: 10.1364/OL.37.004242
[86]	Chu Q, Tao R, Li Chen, et al. Experimental study of the influence of mode excitation on mode instability in high power fiber amplifier[J]. Scientific Reports, 2019, 9: 9396. doi: 10.1038/s41598-019-45787-8
[87]	Zhang F, Xu H, Xing Y, et al. Bending diameter dependence of mode instabilities in multimode fiber amplifier[J]. Laser Phys Lett, 2019, 16: 035104. doi: 10.1088/1612-202X/aaff4b
[88]	Tao R, Ma P, Wang X, et al. A novel theoretical model for mode instability in high power fiber lasers[C]//Advanced Solid State Lasers. 2014: AM5A20.
[89]	陶汝茂. 高功率窄线宽近衍射极限光纤激光放大器热致模式不稳定研究[D]. 长沙: 国防科学技术大学, 2015. Tao Rumao. Study of thermal-induced modal instabilities in high power narrow-linewidth fiber amplifiers with near diffraction-limited beam quality[D]. Changsha: Graduate School of National University of Defense Technology, 2015
[90]	Stihler C, Jauregui C, Kholaif S, et al. The sensitivity of the mode instability threshold to different types of intensity noise[C]//Proc of SPIE. 2020, 11260: 1126018.
[91]	Tao R, Liu Y, Xie L, et al. Static and dynamic mode evolution behavior in high power distributed side-coupled cladding-pumped fiber amplifiers[J]. submitted.
[92]	Tao R, Ma P, Wang X, et al. Influence of core NA on thermal-induced mode instabilities in high power fiber amplifiers[J]. Laser Phys Lett, 2015, 12: 085101. doi: 10.1088/1612-2011/12/8/085101
[93]	Yu C, Shatrovoy O, Fan T, et al. Diode-pumped narrow linewidth multi-kilowatt metalized Yb fiber amplifier[J]. Opt Lett, 2016, 41: 5202-5205. doi: 10.1364/OL.41.005202
[94]	Tao R, Ma P, Wang X, et al. Comparison of the threshold of thermal-induced mode instabilities in polarization-maintaining and non-polarization-maintaining active fibers[J]. Journal of Optics, 2016, 18: 065501. doi: 10.1088/2040-8978/18/6/065501
[95]	Goodno G D, McNaught S, Thielen P, et al. Polarization control with mode stability: US8922877B1[P]. 2014-XX-XX.
[96]	Lei M, Qi Y, Liu C, et al. Mode controlling study on narrow-linewidth and high power all-fiber amplifier[C]//Proc of SPIE. 2015, 9543: 95431L.
[97]	Nicholson J, Fini J, Yablon A, et al. Demonstration of bend-induced nonlinearities in large-mode-area fibers[J]. Opt Lett, 2007, 32: 2562-2564. doi: 10.1364/OL.32.002562
[98]	Li M J, Chen X, Liu A, et al. Limit of effective area for single-mode operation in step-index large mode area laser fibers[J]. IEEE J Lightwave Tech, 2009, 27: 3010-3016. doi: 10.1109/JLT.2009.2020682
[99]	Walorny M, Abramczyk J, Jacobson N, et al. Mechanical reliability of double clad fibers in typical fiber laser deployment conditions[C]//Proc of SPIE. 2016: 97283A.
[100]	Beier F, Möller F, Sattler B, et al. Experimental investigations on the TMI thresholds of low-NA Yb-doped single mode fibers[J]. Opt Lett, 2018, 43: 1291-1294. doi: 10.1364/OL.43.001291
[101]	Hansen K, Alkeskjold T, Broeng J, et al. Thermo-optical effects in high-power Ytterbium-doped fiber amplifiers[J]. Opt Express, 2011, 19: 23965-23980. doi: 10.1364/OE.19.023965
[102]	Rosales-Garcia A, Tobioka H, Abedin K, et al. 2.1 kW single mode continuous wave monolithic fiber laser[C]//Proc of SPIE. 2015: 93441G.
[103]	Kanskar M, Zhang J, Koponen J, et al. Narrowband transverse-modal-instability (TMI)-free Yb-doped fiber amplifiers for directed energy application[C]//Proc of SPIE. 2018: 105120F.
[104]	Tao R, Ma P, Wang X, et al. Theoretical study of pump power distribution on modal instabilities in high power fiber amplifiers[J]. Laser Phys Lett, 2017, 14: 025002. doi: 10.1088/1612-202X/aa4f8e
[105]	HansJürgen Otto, Jauregui C, Stutzki F, et al. Dependence of mode instabilities on the extracted power of fiber laser systems[C]//Advanced Solid State Lasers. 2013.
[106]	Xiao H, Leng J, Zhang H, et al. High-power 1018 nm ytterbium-doped fiber laser and its application in tandem pump[J]. Appl Opt, 2015, 54: 8166-8169. doi: 10.1364/AO.54.008166
[107]	Yagodkin R, Platonov N, Yusim A, et al. ＞1.5 kW narrow linewidth CW diffraction-limited fiber amplifier with 40 nm bandwidth[C]//Proc of SPIE. 2015: 972807.
[108]	Platonov N, Shkurikhin O, Fomin V, et al. Highly efficient kW level single-mode ytterbium fiber lasers in all-fiber format with diffraction-limited beam at wavelengths in 1000-1030 nm spectral range[C]//Proc of SPIE. 2020: 1126003.
[109]	Johansen M M, Laurila M, Maack M D, et al. Frequency resolved transverse mode instability in rod fiber amplifiers[J]. Opt Express, 2013, 21: 21847-21856. doi: 10.1364/OE.21.021847
[110]	Otto H-J, Modsching N, Jauregui C, et al. Impact of photodarkening on the mode instability threshold[J]. Opt Expres, 2015, 23: 15265-15277. doi: 10.1364/OE.23.015265
[111]	Chen Y, Xu H, Xing Y, et al. Mitigation of mode instability in laser oscillators based on deuterium loading[J]. Opt Express, 2019, 27: 25964-25973. doi: 10.1364/OE.27.025964
[112]	Ballato J, Dragic P. Materials development for next generation optical fiber[J]. Materials, 2014, 7: 4411-4430. doi: 10.3390/ma7064411
[113]	陈瑰, 侯超奇, 郭海涛, 等. 用于高功率系统的掺镱石英光纤研究进展及发展趋势[J]. 光子学报, 2019, 48:1148012. (Chen Gui, Hou Chaoqi, Guo Haitao, et al. Ytterbium-doped silica fiber for high power system: a review of research progress and development trend[J]. Acta Photonica Sinica, 2019, 48: 1148012 doi: 10.3788/gzxb20194811.1148012
[114]	杨保来, 王小林, 叶云, 等. 全光纤激光振荡器输出功率突破6 kW[J]. 中国激光, 2020, 47:0116001. (Yang Baolai, Wang Xiaolin, Ye Yun, et al. Laser power from all-fiber oscillators breaks through 6 kW[J]. Chinese Journal of Lasers, 2020, 47: 0116001 doi: 10.3788/CJL202047.0116001
[115]	Möller F, Krämer R, Matzdorf C, et al. Multi-kW performance analysis of Yb-doped monolithic single-mode amplifier and oscillator setup[C]//Proc of SPIE. 2019: 108970D.
[116]	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]//Proc of SPIE. 2020: 1126022.
[117]	Möller F, Distler V, Schreiber T, et al. Manipulating the heat load distribution by laser gain competition in TMI-limited fiber amplifiers[C]//Proc of SPIE. 2020: 1126019.
[118]	Gaida C, Gebhardt M, Heuermann T, et al. Observation of transverse-mode instabilities in a thulium-doped fiber amplifier[C]//Proc of SPIE. 2019: 1089702.
[119]	Distler V, Möller F, Strecker M, et al. High power narrow-linewidth Raman amplifier and its limitation[C]//Proc of SPIE. 2020: 1126005.
[120]	于海龙, 王小林, 张汉伟, 等. 300 W线偏振飞秒全光纤啁啾脉冲放大系统[J]. 强激光与粒子束, 2016, 28:050101. (Yu Hailong, Wang Xiaolin, Zhang Hanwei, et al. 300 W linearly polarized femtosecond all-fiber chirped pulse amplification system[J]. High Power Laser and Particle Beams, 2016, 28: 050101 doi: doi:10.11884/HPLPB201628.050101
[121]	Stihler C, Jauregui C, Kholaif S, et al. The sensitivity of the mode instability threshold to different types of intensity noise[C]//Proc of SPIE. 2020: 1126018.
[122]	Smith A V, Smith J J. Overview of a steady-periodic model of modal instability in fiber amplifiers[J]. IEEE J Sel Topics Quantum Electron, 2014, 20(5): 472-483. doi: 10.1109/JSTQE.2013.2296372