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This study presents an optimization method of generating a wide stable-zone, large mode field operation nanosecond laser oscillator based on artificial intelligence algorithms. The work is motivated by the need of the large mode field laser cavities in compact size with variable thermal focal length. A physics model of light field propagation inside the resonator is established by combining thermal lensing tolerance. A multi-objective optimization function is designed to simultaneously balance the beam quality, thermal stability, and cavity compactness. Several algorithms, such as simulated annealing, particle swarm optimization, and genetic algorithms are compared, and ultimately, efficient searching for optimal solutions in complex multi-dimensional parameter spaces is achieved. In the system design, the parameters of cavity segment length, intracavity lens, and Gaussian mirror (VRM) are optimized. Therefore, an optimized cavity structure is experimentally implemented and Q-switching operations are perform. The results demonstrate stable laser output at 100 Hz repetition rate with 190 mJ pulse energy and 7 ns pulse width, and beam quality factors $ M_x^2 $ = 2.1 and $ M_y^2 $ = 1.9 respectively, and the total length of the cavity is only 540 mm, which demonstrates the compactness of laser design. Furthermore, numerical simulations are conducted to compare a variety of resonator configurations and assess the influence of different parameters on the cavity’s thermal stability. After the optimization, the thermal stability curve of the laser resonator shows a significant decrease in slope near the large-mode-field region, indicating an improvement in thermal length adaptability. This enhancement is crucial for ensuring long-term stable operation of high-repetition-rate nanosecond laser oscillators. In summary, this study provides an efficient approach for designing compact, thermally stable, large-mode-area resonators, and valuable insights into designing compact laser with high power output.
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Keywords:
- solid-state laser /
- large mode area /
- artificial intelligence /
- multi-parameter optimization
[1] Zhu Z D, Lv S W, Zhang H Y, Hui Y L, Lei H, Li Q 2021 Opt. Express 29 32325
Google Scholar
[2] Li C Y, Lu C Q, Li C, Yang N, Li Y, Yang Z, Han S, Shi J F, Zhou Z W 2017 Opt. Commun. 394 1
Google Scholar
[3] Li C Y, Lu C Q, Li C, Zang Y N, Yang Z, Han S, Li Y, Yang N, Shi J F, Zhou Z W 2017 Opt. Commun. 56 116115
Google Scholar
[4] Fan Z W, Qiu J S, Kang Z J, Chen Y Z, Ge W Q, Tang X X 2017 Light-Sci. Appl. 6 e17004
Google Scholar
[5] Lu S W, Gao M, Yang Y, Zhu R, Hou X, Sun J F, Chen W B, Zhu X L 2019 Appl. Opt. 58 7517
Google Scholar
[6] Qi Y F, Zhu X L, Lou Q H, Ji J H, Dong J X, Wei R R 2007 J. Opt. Soc. Am. B-Opt. Phys. 24 1042
Google Scholar
[7] 沈骁, 邹辉, 郑锐林, 郑加金, 韦玮 2015 物理学报 64 024210
Google Scholar
Shen X, Zhou H, Zhen R L, Zhen J J, Wei W 2015 Acta Phys. Sin. 64 024210
Google Scholar
[8] 周王哲, 李雪鹏, 杨晶, 杨天利, 王小军, 刘炳杰, 王浩竹, 杨俊波, 彭钦军 2023 物理学报 72 014204
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Zhou W Z, Li X P, Yang J, Yang T L, Wang X J, Liu B J, Wang H Z, Yang J B, Peng Q J 2023 Acta Phys. Sin. 72 014204
Google Scholar
[9] Murdough M P, Denman C A 1996 Appl. Opt. 35 5925
Google Scholar
[10] Cerullo G, Desilvestri S, Magni V, Svelto O 1993 Opt. Quantum Electron. 25 489
Google Scholar
[11] 薄勇, 耿爱丛, 毕勇, 孙志培, 杨晓东, 李瑞宁, 崔大复, 许祖彦 2006 物理学报 55 1171
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Bo Y, Geng A C, Bi Y, Sun Z P, Yang X D, Li R N, Cui D F, Xu Z Y 2006 Acta Phys. Sin. 55 1171
Google Scholar
[12] 何广源, 郭靖, 焦中兴, 王彪 2012 物理学报 61 094217
Google Scholar
He G Y, Guo J, Jiao Z X, Wang B 2012 Acta Phys. Sin. 61 094217
Google Scholar
[13] Siegman A E 1974 Appl. Opt. 13 353
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[14] Liu Q, Liu J, Gong M 2011 Appl. Opt. 50 1186
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[15] 韩昌昊, 穆宇, 罗辉, 韩隆, 方聪, 王思博, 魏磊 2024 激光与红外 54 179
Han C H, Mu Y, Luo H, Han L, Fang C, Wang S B, Wei L 2024 Laser Infrared 54 179
[16] Hauck R, Kortz H P, Weber H 1980 Appl. Opt. 19 598
Google Scholar
[17] Woodward R I, Kelleher E J R 2016 Sci. Rep. 6 37616
Google Scholar
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Google Scholar
[19] Shi H D, Fan R H, He C F, Wang J Y, Yang S, Xu M, Sun H Y, Li Y C, Fu Q 2024 Photonics 11 164
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[21] 王宁, 陆雨田, 孔勇 2004 中国激光 31 1317
Wang N, Lu Y T, Kong Y 2004 Chin. J. Lasers 31 1317
[22] Kirkpatrick S, Gelatt C, Vecchi M 1983 Science 220 671
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[23] 赵知劲, 徐世宇, 郑仕链, 杨小牛 2009 物理学报 58 5118
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Zhao Z J, Xu S Y, Zheng S L, Yang X N 2009 Acta Phys. Sin. 58 5118
Google Scholar
[24] Shapiro J 2001 Machine Learning and Its Applications: Advanced Lectures (Berlin, Heidelberg) 2001 pp146–168
[25] Li X P, Yang J, Zhang M S, Yang T L, Wang X J, Peng Q J 2022 Chin. Phys. B 31 084207
Google Scholar
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图 1 高斯镜非稳腔的优化示意图
Figure 1. Optimization environment for Gaussian mirror unstable cavities.
图 2 不同优化算法在迭代过程中的收敛曲线 (a) 模拟退火算法和粒子群优化算法; (b)遗传算法
Figure 2. Convergence curves of different optimization algorithms: (a) Simulated annealing algorithm and particle swarm optimization algorithm; (b) genetic algorithm.
图 3 基于遗传算法的谐振腔参数优化过程 (a)腔段长度$ {x_1} $随进化代数的变化; (b) 腔段长度${x_2}$随进化代数的变化; (c)腔段长度${x_3}$随进化代数的变化; (d)可调透镜焦距$f$的优化轨迹; (e) 光学参数组$({w_{\text{m}}}, {R_0}, {R_{\text{c}}})$选择随代数的演化, 算法在20代后趋于稳定, 最终选定参数组2 (${w_{\text{m}}} = 3{\mkern 1 mu} {\text{ mm}}, {R_{\text{c}}}{\text{ }} = - 1500{\mkern 1 mu} {\text{ mm}}, {R_0} = 0.3$).
Figure 3. Optimization process of resonator parameters via genetic algorithm: (a) Evolution of cavity segment ${x_1}$; (b) evolution of cavity segment ${x_2}$; (c) evolution of cavity segment ${x_3}$; (d) optimization trajectory of adjustable lens focal length $f$; (e) selection of optical parameter groups $({w_{\text{m}}}, {R_0}, {R_{\text{c}}})$ across generations, the algorithm converges after 20 generations, ultimately selecting parameter group 2 (${w_{\text{m}}} = 3{\mkern 1 mu} {\text{ mm}}, {R_{\text{c}}}{\text{ }} = - 1500{\mkern 1 mu} {\text{ mm}}, {R_0} = 0.3$).
图 4 实验装置示意图. M为高反射后镜, L为平凸透镜, TFP为1064 nm薄膜偏振片, QWP为1/4波片, LM为激光模块, OC为输出耦合镜
Figure 4. Experimental setup. M represents high-reflectivity rear mirror, L represents plano-convex lens, TFP represents thin-film polarizer at 1064 nm, QWP represents quarter-wave plate, LM represents laser module, OC represents output coupler.
图 5 谐振腔内各平面束宽半径分布. M为高反镜, L为透镜, LM为激光模块, OC为高斯耦合输出镜
Figure 5. Beam radius distribution at different planes within the resonator. M represents high-reflection mirror, L represents lens, LM represents laser module, OC represents Gaussian mirror output coupler.
图 6 (a)晶体中心位置基模光斑半径与热焦距的关系, 其中红虚线OC为非高斯镜, 蓝实线OC为高斯镜, I为传统热近非稳区, II为高斯镜非稳区; (b)不同耦合输出器下, 谐振腔模场半径$\omega $对焦距${f_{\text{t}}}$的导数变化趋势
Figure 6. (a) Relationship between the fundamental mode beam radius at the crystal center and the thermal focal length, red dashed line OC as a non-Gaussian mirror, blue solid line OC as a Gaussian mirror, I represents traditional thermal near-unstable region, II represents Gaussian mirror unstable region; (b) the derivative of the resonator mode radius $\omega $ with respect to focal length ${f_{\text{t}}}$ under different output couplers.
图 7 不同腔型的模式直径与最高输出功率关系图
Figure 7. Mode diameter vs. maximum output power for different cavity types.
图 8 (a) 输出能量与泵浦能量的关系及光光转换效率; (b) 输出稳定性在60 min内的测量结果
Figure 8. (a) Output energy and O-O efficiency as a function of pump energy; (b) output stability measurement over 60 min.
图 9 (a) 激光的典型脉冲列; (b) 单个脉冲的扩展轮廓
Figure 9. (a) Typical pulse train of laser; (b) an expanded single pulse profile.
图 10 典型的优化后 M2测量结果, 插图为相应的远场二维光束空间分布图
Figure 10. Typical optimized M2 measurement results, with the corresponding far-field 2D beam spatial distribution shown in the inset.
表 1 高斯镜规格参数
Table 1. Specifications of Gaussian mirrors.
高斯镜
编号N曲率半径
Rc/mm中心反射率 膜斑半径
${\omega _{\text{m}}}$/mm1 –700 0.35 4 2 –1500 0.3 3 3 –2000 0.2 2 
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[1] Zhu Z D, Lv S W, Zhang H Y, Hui Y L, Lei H, Li Q 2021 Opt. Express 29 32325
Google Scholar
[2] Li C Y, Lu C Q, Li C, Yang N, Li Y, Yang Z, Han S, Shi J F, Zhou Z W 2017 Opt. Commun. 394 1
Google Scholar
[3] Li C Y, Lu C Q, Li C, Zang Y N, Yang Z, Han S, Li Y, Yang N, Shi J F, Zhou Z W 2017 Opt. Commun. 56 116115
Google Scholar
[4] Fan Z W, Qiu J S, Kang Z J, Chen Y Z, Ge W Q, Tang X X 2017 Light-Sci. Appl. 6 e17004
Google Scholar
[5] Lu S W, Gao M, Yang Y, Zhu R, Hou X, Sun J F, Chen W B, Zhu X L 2019 Appl. Opt. 58 7517
Google Scholar
[6] Qi Y F, Zhu X L, Lou Q H, Ji J H, Dong J X, Wei R R 2007 J. Opt. Soc. Am. B-Opt. Phys. 24 1042
Google Scholar
[7] 沈骁, 邹辉, 郑锐林, 郑加金, 韦玮 2015 物理学报 64 024210
Google Scholar
Shen X, Zhou H, Zhen R L, Zhen J J, Wei W 2015 Acta Phys. Sin. 64 024210
Google Scholar
[8] 周王哲, 李雪鹏, 杨晶, 杨天利, 王小军, 刘炳杰, 王浩竹, 杨俊波, 彭钦军 2023 物理学报 72 014204
Google Scholar
Zhou W Z, Li X P, Yang J, Yang T L, Wang X J, Liu B J, Wang H Z, Yang J B, Peng Q J 2023 Acta Phys. Sin. 72 014204
Google Scholar
[9] Murdough M P, Denman C A 1996 Appl. Opt. 35 5925
Google Scholar
[10] Cerullo G, Desilvestri S, Magni V, Svelto O 1993 Opt. Quantum Electron. 25 489
Google Scholar
[11] 薄勇, 耿爱丛, 毕勇, 孙志培, 杨晓东, 李瑞宁, 崔大复, 许祖彦 2006 物理学报 55 1171
Google Scholar
Bo Y, Geng A C, Bi Y, Sun Z P, Yang X D, Li R N, Cui D F, Xu Z Y 2006 Acta Phys. Sin. 55 1171
Google Scholar
[12] 何广源, 郭靖, 焦中兴, 王彪 2012 物理学报 61 094217
Google Scholar
He G Y, Guo J, Jiao Z X, Wang B 2012 Acta Phys. Sin. 61 094217
Google Scholar
[13] Siegman A E 1974 Appl. Opt. 13 353
Google Scholar
[14] Liu Q, Liu J, Gong M 2011 Appl. Opt. 50 1186
Google Scholar
[15] 韩昌昊, 穆宇, 罗辉, 韩隆, 方聪, 王思博, 魏磊 2024 激光与红外 54 179
Han C H, Mu Y, Luo H, Han L, Fang C, Wang S B, Wei L 2024 Laser Infrared 54 179
[16] Hauck R, Kortz H P, Weber H 1980 Appl. Opt. 19 598
Google Scholar
[17] Woodward R I, Kelleher E J R 2016 Sci. Rep. 6 37616
Google Scholar
[18] Fang Z W, Pu G Q, Xu Y X, Hu W S, Yi L L 2023 Opt. Express 31 41794
Google Scholar
[19] Shi H D, Fan R H, He C F, Wang J Y, Yang S, Xu M, Sun H Y, Li Y C, Fu Q 2024 Photonics 11 164
Google Scholar
[20] Liu Z C, Dang Z B, Liu Z X, Li Y, He X, Dai Y C, Chen Y X, Peng P, Fang Z Y 2023 Photonics Res. 11 695
Google Scholar
[21] 王宁, 陆雨田, 孔勇 2004 中国激光 31 1317
Wang N, Lu Y T, Kong Y 2004 Chin. J. Lasers 31 1317
[22] Kirkpatrick S, Gelatt C, Vecchi M 1983 Science 220 671
Google Scholar
[23] 赵知劲, 徐世宇, 郑仕链, 杨小牛 2009 物理学报 58 5118
Google Scholar
Zhao Z J, Xu S Y, Zheng S L, Yang X N 2009 Acta Phys. Sin. 58 5118
Google Scholar
[24] Shapiro J 2001 Machine Learning and Its Applications: Advanced Lectures (Berlin, Heidelberg) 2001 pp146–168
[25] Li X P, Yang J, Zhang M S, Yang T L, Wang X J, Peng Q J 2022 Chin. Phys. B 31 084207
Google Scholar
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