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激光介质热效应引起的谐振腔模场结构变化成为高功率涡旋激光器的一个关键问题. 本文建立了环形光泵浦薄片激光晶体的温度场及热形变计算模型, 将热效应像差作为谐振腔衍射积分方程的微扰, 研究热效应对激光器模场结构的影响规律. 具体研究了Nd:YAG, Nd:YLF和Nd:YVO4薄片涡旋激光器的模场结构随泵浦功率、晶体吸收系数、晶体厚度的变化规律. 研究结果表明, 热效应使涡旋激光器模谱产生径向展宽, 模式纯净度下降. 泵浦功率越大, 高阶径向模式占比越大, 模场结构越复杂. 泵浦功率升高时, Nd:YVO4激光器的模谱展宽最大, Nd:YAG激光器的模谱展宽最小. 晶体吸收系数越大, 模谱展宽越严重; 激光晶体厚度减小时, 模谱展宽呈增宽趋势.Optical vortex beam has wide applications in areas of optical communication, lidar detection and optical trapping. To increase the operating distance, a high-power vortex laser source is necessary in these applications. However, the purity of the output vortex beam decreases with the pump power increasing due to the thermal effect of the laser medium. Therefore, modal field degeneration induced by thermal effect of laser medium has become a key problem in high-power vortex solid-state laser. To investigate this modal field degeneration, the heat transfer and thermal deformation model of an annular beam end pumped thin-disk vortex laser (Fig. (a)) is established. The phase difference of the thermal effect is calculated based on this model. Then, the quadratic term is separated from the phase difference. The non-quadratic term, as a small perturbation, is substituted into the diffraction integral equation of the laser cavity. The modal field structure is obtained by using the perturbation method. The variations of the modal structure with pump power, absorption coefficient and crystal thickness are investigated for three kinds of laser crystals, i.e. Nd:YAG, Nd:YLF and Nd:YVO4. The results show that the modal field under thermal effect presents obvious deviation from the ideal mode at high power, and the modal structure shows that it contains many higher-order radial modes, with the angular mode order unchanged. Hence, the radial modal spectrum is broadened by the thermal effect. For an ideal vortex laser without thermal effect operating on the radial mode order 0 and angular mode order 1, Fig. (b) shows the modal structures with thermal effect under different pump power values with a laser crystal thickness of 1 mm. The ratio of the higher-order modes increases and the modal structure becomes more and more complex with the pump power increasing. The ratios of the ideal mode are 0.99, 0.97, 0.90, 0.79 and 0.61, under the pump power of 10 W, 20 W, 40 W, 60 W and 100 W, respectively. Moreover, the Nd:YVO4 laser has the largest and the Nd:YAG laser has the smallest modal spectrum broadening under the same pump power. Figure (c) shows the variation of the modal purity with the pump power. The modal purity of the Nd:YVO4 and the Nd:YLF laser decrease to 0.35 and 0.44 at the pump power of 100 W, respectively. We also investigate the modal structures under different absorption coefficients and crystal thickness values. A larger absorption coefficient or a smaller crystal thickness leads to a larger radial modal spectrum broadening and a smaller modal purity. These results indicate that in the design of high-power thin-disk vortex laser, it is necessary to comprehensively optimize the disk thickness and the absorption coefficient, and consider modal spectrum broadening as well.
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Keywords:
- solid-state laser /
- vortex beam /
- thermal effect /
- radial modal spectrum broadening
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图 1 环形光端面泵浦薄片涡旋激光器结构
Fig. 1. Schematic of an annular beam end pumped thin-disk vortex laser.
图 2 Nd:YAG温度和热形变分布 (a)三维温度分布; (b)三维热形变分布; (c)剖面温度; (d)剖面形变
Fig. 2. Temperature and thermal deformation of Nd:YAG crystal: (a) 3D temperature distribution; (b) 3D deformation distribution; (c) temperature in the section plane; (d) deformation in the section plane.
图 3 不同泵浦功率下3种晶体的温度及热形变 (a) Nd:YAG温度; (b) Nd:YAG形变; (c) Nd:YLF温度; (d) Nd:YLF形变; (e) Nd:YVO4温度; (f) Nd:YVO4形变
Fig. 3. Temperature and thermal deformation of the three laser crystals under different pump power: (a) Temperature of Nd:YAG; (b) deformation of Nd:YAG; (c) temperature of Nd:YLF; (d) deformation of Nd:YLF; (e) temperature of Nd:YVO4; (f) deformation of Nd:YVO4.
图 4 温度及热形变随泵浦功率的变化 (a) 最高温度; (b) 最高温度与中心温差; (c) 最大热形变; (d) 最大热形变与中心热形变差
Fig. 4. Variation of temperature and thermal deformation with pump power: (a) Maximum temperature; (b) difference between the maximum temperature and the center temperature; (c) maximum thermal deformation; (d) difference between the maximum thermal deformation and the center thermal deformation.
图 5 不同泵浦功率下的模场分布和模谱结构 (a) Nd:YAG模场; (b) Nd:YAG模谱; (c) Nd:YLF模场; (d) Nd:YLF模谱; (e) Nd:YVO4模场; (f) Nd:YVO4模谱
Fig. 5. Mode distribution and mode structure under different pump power: (a) Nd:YAG mode distribution; (b) Nd:YAG mode structure; (c) Nd:YLF mode distribution; (d) Nd:YLF mode structure; (e) Nd:YVO4 mode distribution; (f) Nd:YVO4 mode structure.
图 7 不同吸收系数下3种晶体的温度及形变 (a) Nd:YAG温度; (b) Nd:YAG形变; (c) Nd:YLF温度; (d) Nd:YLF形变; (e) Nd:YVO4温度; (f) Nd:YVO4形变
Fig. 7. Temperature and deformation of the three laser crystals under different absorption coefficient: (a) Temperature of Nd:YAG; (b) deformation of Nd:YAG; (c) temperature of Nd:YLF; (d) deformation of Nd:YLF; (e) temperature of Nd:YVO4; (f) deformation of Nd:YVO4.
图 8 温度及热形变随吸收系数的变化 (a) 最高温度; (b) 最高温度与中心温度差值; (c) 最大热形变; (d) 最大热形变与中心热形变差值
Fig. 8. Variation of temperature and thermal deformation with absorption coefficient: (a) Maximum temperature; (b) difference between the maximum temperature and the center temperature; (c) maximum thermal deformation; (d) difference between the maximum thermal deformation and the center thermal deformation.
图 9 不同吸收系数下的模场分布和模谱结构 (a) Nd:YAG模场; (b) Nd:YAG模谱; (c) Nd:YLF模场; (d) Nd:YLF模谱; (e) Nd:YVO4模场; (f) Nd:YVO4模谱
Fig. 9. Mode distribution and mode structure under different absorption coefficient: (a) Nd:YAG mode distribution; (b) Nd:YAG mode structure; (c) Nd:YLF mode distribution; (d) Nd:YLF mode structure; (e) Nd:YVO4 mode distribution; (f) Nd:YVO4 mode structure.
图 10 模式纯净度随吸收系数的变化
Fig. 10. Variation of the modal purity with absorption coefficient.
图 11 不同厚度下3种晶体的温度及热形变 (a) Nd:YAG温度; (b) Nd:YAG形变; (c) Nd:YLF温度; (d) Nd:YLF形变; (e) Nd:YVO4温度; (f) Nd:YVO4形变
Fig. 11. Temperature and thermal deformation of the three laser crystals under different crystal thickness: (a) Temperature of Nd:YAG; (b) deformation of Nd:YAG; (c) temperature of Nd:YLF; (d) deformation of Nd:YLF; (e) temperature of Nd:YVO4; (f) deformation of Nd:YVO4.
图 12 温度及热形变随晶体厚度的变化 (a) 最高温度; (b) 最高温度与中心温度差值; (c) 最大热形变; (d) 最大热形变与中心热形变差值
Fig. 12. Variation of temperature and thermal deformation with crystal thickness: (a) Maximum temperature; (b) difference between the maximum temperature and the center temperature; (c) maximum thermal deformation; (d) difference between the maximum thermal deformation and the center thermal deformation.
图 13 不同厚度下的模场分布和模谱结构 (a) Nd:YAG模场; (b) Nd:YAG模谱; (c) Nd:YLF模场; (d) Nd:YLF模谱; (e) Nd:YVO4模场; (f) Nd:YVO4模谱
Fig. 13. Mode distribution and mode structure under different thickness: (a) Nd:YAG mode distribution; (b) Nd:YAG mode structure; (c) Nd:YLF mode distribution; (d) Nd:YLF mode structure; (e) Nd:YVO4 mode distribution; (f) Nd:YVO4 mode structure.
激光晶体 密度/
(kg·m–3)杨氏模量/GPa 泊松比 热膨胀系数/K–1 热导率/
(W·m–1·K–1)$ {{{\text{d}}n} \mathord{\left/ {\vphantom {{{\text{d}}n} {{\text{d}}T}}} \right. } {{\text{d}}T}} $/K–1 Nd:YAG 4560 317 0.25 7.5×106 14 7.3×10–6 Nd:YLF 3990 85 0.33 8.3×106 6.3 –6.6×10–6 Nd:YVO4 4220 133 0.33 4.43×106 5.2 8.5×10–6 
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[1] Wang J, Yang J Y, Fazal I M, et al. 2012 Nat. Photonics 6 488
Google Scholar
[2] Gibson G, Courtial J, Padgett M J, Vasnetsov M, Pas’ko V, Barnett S M, Franke-Arnold S, 2004 Opt. Express 12 5448
Google Scholar
[3] Willner A E, Zhao Z, Ren Y X, Li L, Xie G D, Song H Q, Liu C, Zhang R Z, Bao C J, Pang K 2018 Opt. Commun. 408 21
Google Scholar
[4] Lavery M P J, Speirits F C, Barnett S M, Padgett M J 2013 Science 341 537
Google Scholar
[5] Belmonte A, Rosales-Guzman C, Torres J P 2015 Optica 2 1002
Google Scholar
[6] 杨伟东, 邱晓东, 陈理想 2020 中国激光 47 0500013
Google Scholar
Yang W D, Qiu X D, Chen L X 2020 Chin. J. Lasers 47 0500013
Google Scholar
[7] 杨苏辉, 廖英琦, 林学彤, 刘欣宇, 齐若伊, 郝燕 2021 红外与激光工程 50 20211040
Google Scholar
Yang S H, Liao Y Q, Lin X T, Liu X Y, Qi R Y, Hao Y 2021 Infrared Laser Eng. 50 20211040
Google Scholar
[8] Jantzi A, Jemison W, Laux A, Mullen L, Cochenour B 2018 Opt. Express 26 2668
Google Scholar
[9] Baghdady J, Miller K, Morgan K, et al. 2016 Opt. Express 24 9794
Google Scholar
[10] Shen Y J, Wang X J, Xie Z W, Min C J, Fu X, Liu Q, Gong M L, Yuan X C 2019 Light Sci. Appl. 8 90
Google Scholar
[11] 柳强, 潘婧, 万震松, 申艺杰, 张恒康, 付星, 巩马理 2020 中国激光 47 0500006
Google Scholar
Liu Q, Pan J, Wan Z S, Shen Y J, Zhang H K, Fu X, Gong M L 2020 Chin. J. Lasers 47 0500006
Google Scholar
[12] Forbes A 2019 Laser Photonics Rev. 13 1900140
Google Scholar
[13] Forbes A, Oliveira M D, Dennis M R 2021 Nat. Photonics 15 253
Google Scholar
[14] 孙喜博, 朱启华, 刘兰琴, 黄晚晴, 张颖, 王文义, 耿远超 2017 激光与光电子学进展 54 070001
Google Scholar
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Google Scholar
[15] 付时尧, 高春清 2019 光学学报 39 0126014
Google Scholar
Fu S Y, Gao C Q 2019 Acta Opt. Sin. 39 0126014
Google Scholar
[16] 常宁, 金立伟, 高玮 2019 光学学报 39 0319001
Google Scholar
Chang N, Jin L W, Gao W 2019 Acta Opt. Sin. 39 0319001
Google Scholar
[17] Zhao Y G, Chen B, Zheng C S, Jia D W, Dong J F, Guo J, Wang Z X, Yu H H, Zhang H J 2024 Laser Photonics Rev. 18 2301089
Google Scholar
[18] Pan J, Shen Y J, Wan Z S, Fu X, Zhang H K, Liu Q 2020 Phys. Rev. Appl. 14 044048
Google Scholar
[19] Zhao Y G, Wang L, Chen W D, et al. 2021 Photonics Res. 9 357
Google Scholar
[20] Qiao Z, Xie G Q, Wu Y H, Yuan P, Ma J G, Qian L J, Fan D Y 2018 Laser Photonics Rev. 12 1800019
Google Scholar
[21] 宋小鹿, 李兵斌, 王石语, 蔡德芳, 文建国, 过振 2008 红外与激光工程 37 73
Google Scholar
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Google Scholar
[22] 姚育成, 刘丹琳, 黄楚云, 徐国旺, 王贝 2016 光子学报 45 131
Google Scholar
Yao Y C, Liu D L, Huang C Y, Xu G W, Wang B 2016 Acta Photonica Sin. 45 131
Google Scholar
[23] 方洪烈 2014 光学谐振腔与引力波探测 (北京: 科学出版社) 第78—80页
Fang H L 2014 Optical Resonators and Gravitational Wave Detection (Beijing: Science Press ) pp78–80
[24] Koechner W 2013 Solid-State Laser Engineering (New York: Springer) pp46–83
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