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Owing to the advantages of high conversion efficiency, compactness and reliability, the fiber lasers are widely applied to many scientific areas, such as optical fiber communication, sensing and industrial processing. Beam quality is an important criterion for evaluating the performances of high-energy laser beam systems. Therefore, researchers have been constantly searching for the methods of evaluating the beam quality while pursuing higher output power. Until now, the researchers have proposed many definitions of beam quality. In practice, the evaluation parameters of beam quality include focused spot size, Strehl ratio, far-field divergence angle, diffraction limited β factor, energy circle rate, beam parameter product, and M 2 factor. Among them, the M 2 factor is the most suitable for the assessment of beam quality in both the near-field and far-field, which avoids the inaccuracy of the measurement of the beam quality only by the far-field radius or the far-field divergence angle. Thus, the M 2 factor is recognized as an important standard for evaluating beam quality by the International Organization for Standardization (ISO). However, it proves that the M 2 factor is not suitable for non-Gaussian distribution spot. On the other hand, in applications of high-energy laser beam transmission and laser industrial manufacturing, people pay more attention to the focusability of laser energy. In this case, the diffraction limited β factor is more suitable for evaluating beam quality. In this paper, we investigate the beam quality of LP01 mode of fiber laser by β factor, and a circular and solid homogenous beam with the energy of 99% of LP01 mode is considered as an ideal beam. The relationship between β factor and the parameters of LP01 mode in a step-index fiber is studied theoretically. It is found that the value of the beam quality β factor is lower than 1 when the normalized frequency V is bigger than 1.8, and the far-field energy focusability of LP01 mode is better than the case of ideal beam. Besides, the value of β factor decreases with the increase of normalized frequency V, core radius a or numerical aperture NA. In addition, the relationship between M 2 factor and β factor is non-linear.
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Keywords:
- fiber lasers /
- laser beam quality /
- diffraction limited β factor /
- M 2 factor
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Zhou J, Wang P, Zhou P 2017 Chin. J. Lasers 44 0201000
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Google Scholar
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Su Y, Wan M 2004 High Energy Laser System (Bejing: National Defense Industry Press) pp39−50 (in Chinese)
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Google Scholar
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Google Scholar
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Google Scholar
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Liao Y B, Jin H M 2000 Fiber Optics (Beijing: Tsinghua University Press) p28 (in Chinese)
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Google Scholar
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Google Scholar
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Lü B D 2003 Laser Optics (Beijing: Higher Education Press) p76 (in Chinese)
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Google Scholar
Rao R Z 2005 Chin. J. Lasers 32 53
Google Scholar
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图 1 不同归一化频率V下, 纤芯半径(洋红色实线)和包含LP01模99%能量的环围半径(黄色虚线)示意图
Figure 1. Schematic of core radius (magenta solid line) and the radius containing 99% of the energy of LP01 mode (yellow dotted line) for different values of normalized frequency V.
图 2 不同归一化频率V下, LP01模(蓝色实线)和理想光束(洋红色虚线)在出射面 ((a1)—(a4))和焦平面((b1)—(b4))的一维光强分布
Figure 2. For different values of normalized frequency V, 1D intensity distributions of LP01 mode (blue solid line) and ideal beam (magenta dotted line) in the initial plane ((a1)−(a4)) and focal plane((b1)−(b4)).
图 3 不同半径定义下β因子随归一化频率V的变化关系
Figure 3. β factor versus normalized frequency V for different definitions of radius.
图 4 β因子随纤芯半径a (a)和数值孔径NA (b)的变化关系图
Figure 4. β factor versus core radius a (a) and numerical aperture NA (b).
图 5 (a) 光束质量因子随归一化频率V和(b) β因子随
$ M^2 $ 因子的变化关系图Figure 5. (a) Beam quality factor versus normalized frequency V and (b) β factor versus
$ M^2 $ factor. -
[1] Shi W, Fang Q, Zhu X, Norwood R A, Peyghambarian N 2014 Appl. Opt. 53 6554
Google Scholar
[2] Zervas M N, Codemard C A 2014 IEEE J. Sel. Top. Quant. 20 0904123
Google Scholar
[3] 周军, 王璞, 周朴 2017 中国激光 44 0201000
Zhou J, Wang P, Zhou P 2017 Chin. J. Lasers 44 0201000
[4] 杨永强, 吴世彪, 张越, 朱勇强 2020 中国激光 47 0500012
Google Scholar
Yang Y Q, Wu S B, Zhang Y, Zhu Y Q 2020 Chin. J. Lasers 47 0500012
Google Scholar
[5] 陈良惠, 杨国文, 刘育衔 2020 中国激光 47 0500001
Google Scholar
Chen L H, Yang G W, Liu Y X 2020 Chin. J. Lasers 47 0500001
Google Scholar
[6] Jauregui C, Limpert J, Tuennermann A 2013 Nat. Photonics 7 861
Google Scholar
[7] 陶汝茂, 周朴, 王小林, 司磊, 刘泽金 2014 63 085202
Google Scholar
Tao R M, Zhou P, Wang X L, Si L, Liu Z J 2014 Acta Phys. Sin. 63 085202
Google Scholar
[8] 杨昌盛, 徐善辉, 周军, 何兵, 杨依枫, 渠红伟, 赵智德, 杨中民 2017 中国科学: 技术科学 47 1038
Google Scholar
Yang C S, Xu S H, Zhou J, He B, Yang Y F, Qu H W, Zhao Z D, Yang Z M 2017 Scientia Sin. Technol. 47 1038
Google Scholar
[9] Siegman A E 1993 Laser Resonators and Coherent Optics: Modeling, Technology, and Applications Los Angeles, CA, United States, August 13, 1993 pp1−12
[10] 杜祥琬 1997 中国激光 24 327
Google Scholar
Du X W 1997 Chin. J. Lasers 24 327
Google Scholar
[11] 刘泽金, 周朴, 许晓军 2009 中国激光 36 773
Google Scholar
Liu Z J, Zhou P, Xu X J 2009 Chin. J. Lasers 36 773
Google Scholar
[12] 苏毅, 万敏 2004 高能激光系统 (北京: 国防工业出版社) 第39−50页
Su Y, Wan M 2004 High Energy Laser System (Bejing: National Defense Industry Press) pp39−50 (in Chinese)
[13] 冯国英, 周寿桓 2009 中国激光 36 1643
Google Scholar
Feng G Y, Zhou S H 2009 Chin. J. Lasers 36 1643
Google Scholar
[14] International Organization for Standardization. Laser and Laser-Related Equipment: Test Methods for Laser Beam Parameters, Beam Width, Divergence Angle and Beam Propagation Factor 1999 ISO11146
[15] Ophir-Spiricon’s M2-200 s Automated M2 Laser Beam Propagation Analyzer Enhances Robust Packaging for 24/7 Operation, Gary Wagner https://www.ophiropt.com/ laser-measurement/node/9283 [2021-6-9]
[16] Beier F, Hupel C, Nold J, Kuhn S, Hein S, Ihring J, Sattler B, Haarlammert N, Schreiber T, Eberhardt R 2016 Opt. Express 24 6011
Google Scholar
[17] Flores A, Robin C, Lanari A, Dajani I 2014 Opt. Express 22 17735
Google Scholar
[18] Gray S, Liu A, Walton D T, Wang J, Li M J, Chen X, Ruffin A B, DeMeritt J A, Zenteno L A 2007 Opt. Express 15 17044
Google Scholar
[19] Ma P F, Tao R M, Su R T, Wang X L, Zhou P, Liu Z Z 2016 Opt. Express 24 4187
Google Scholar
[20] Huang L J, Wang W L, Leng J Y, Guo S F, Xu X J, Cheng X A 2014 IEEE Photon. Technol. Lett. 26 33
Google Scholar
[21] 陈子伦, 雷成敏, 王泽锋, 周朴, 马阎星, 肖虎, 冷进勇, 王小林, 许晓军, 陈金宝, 刘泽金 2018 中国激光 45 324
Chen Z L, Lei C M, Wang Z F, Zhou P, Ma Y X, Xiao H, Leng J Y, Wang X L, Xu X J, Chen J B, Liu Z J 2018 Chin. J. Lasers 45 324
[22] Siegman A E 1998 Diode Pumped Solid State Lasers: Applications and Issues Washington D.C., United States, January 1, 1998 pp184−199
[23] Chen Z Z, Xu Y T, Guo Y D, Wang B S, Xu J, Xu J L, Gao H W, Yuan L, Yuan H T, Lin Y Y 2015 Appl. Opt. 54 5011
Google Scholar
[24] Sean Ross T 2013 Laser Beam Quality Metrics (Bellingham: SPIE Press) pp42−51
[25] 刘泽金, 陆启生, 赵伊君 1998 中国激光 25 193
Google Scholar
Liu Z J, Lu Q S, Zhao Y J 1998 Chin. J. Lasers 25 193
Google Scholar
[26] 高卫, 王云萍, 李斌 2003 红外与激光工程 32 61
Google Scholar
Gao W, Wang Y P, Li B 2003 Infrared Laser Eng. 32 61
Google Scholar
[27] Yan P, Wang X J, Gong M L, Xiao Q R 2016 Appl. Opt. 55 6145
Google Scholar
[28] Tan Y, Li X Y 2012 High-Power Lasers and Applications VI Beijing, China November 5–7, 2012 p85511 C
[29] Ji Z Y, Zhang X F 2017 2017 International Conference on Optical Instruments and Technology Beijing, China, October 28−30, 2017 p10619
[30] 高卫 2003 光子学报 32 1038
Gao W 2003 Acta Photon. Sinica 32 1038
[31] 周朴 2018 强激光与粒子束 30 060201
Google Scholar
Zhou P 2018 High Power Laser Part. Beams 30 060201
Google Scholar
[32] Belanger P A 1993 Opt. Eng. 32 2107
Google Scholar
[33] 廖延彪, 金慧明 1992 光纤光学 (北京: 清华大学出版社) 第28页
Liao Y B, Jin H M 2000 Fiber Optics (Beijing: Tsinghua University Press) p28 (in Chinese)
[34] Jain D, Jung Y, Kim J, Sahu J K 2014 Opt. Lett. 39 5200
Google Scholar
[35] Marciante J R, Roides R G, Shkunov V V, Rockwell D A 2010 Opt. Lett. 35 1828
Google Scholar
[36] 吕百达 1992 激光光学 (北京: 高等教育出版社) 第76页
Lü B D 2003 Laser Optics (Beijing: Higher Education Press) p76 (in Chinese)
[37] 饶瑞中 2005 中国激光 32 53
Google Scholar
Rao R Z 2005 Chin. J. Lasers 32 53
Google Scholar
[38] Siegman A E 1990 Optical Resonators Los Angeles, CA, United States, June 1 pp1−14
[39] Yoda H, Polynkin P, Mansuripur M 2006 J. Lightwave Technol. 24 1350
Google Scholar
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