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In a large-scale ultra-fast and ultra-intensity laser system, with the increase of spectral bandwidth and beam aperture, the spatiotemporal coupling distortion will become more and more significant. This effect will not only degrade the beam quality and reduce the focusing intensity of the laser, but also invalidate the conventional evaluation method for laser far-field parameters. A pair of beam-expanding lenses, which may bring spatiotemporal coupling distortion to an ultrashort laser pulse, is taken as an example. And the influence of spatiotemporal coupling distortion on laser parameter measurement is analyzed in detail. It shows that in an ultrashort pulse laser system, an ordinary beam-expanding lens-pair can reduce the far-field peak intensity dramatically, and the actual pulse duration in the far field is more than 10 times longer than that measured at the near field by a single-shot autocorrelator. In this case, the focusing intensity estimated by using the measured value of near-field pulse width will be one order of magnitude bigger than the real value. It is expected that the results will be helpful in the optimal design of a laser system, the accurate characterization of an ultrafast laser pulse and relevant physical experiments.
[1] Perry M D, Pennington D, Stuart B C, Tietbohl G, Britten J A, Brown C, Herman S, Golick B, Kartz M, Miller J, Powell H T, Vergino M, Yanovsky V 1999 Opt. Lett. 24 160
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[2] Gaul E W, Ditmire T, Martinez M D, Douglas S, Gorski D, Hays G R, Henderson W, Erlandson A, Caird J, Ebbers C, Iovanovic I, Molander W 2005 Conference on Lasers and Electro-Optics Baltimore, Maryland United States, May 22–27, 2005 p2026
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Hu B L 2020 M. S. Thesis (Mianyang: China Academy of Engineering Physics) p13 (in Chinese)
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Google Scholar
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Yu S Q, Wang F, Huang X J 2010 J. Kashgar Univ. 31 44
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Wang X H, Zhang Q 2005 Res. Explor. Lab. 24 40
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[12] 王仕璠 2020 信息光学理论与应用(第四版)(北京: 北京邮电大学出版社) 第64页
Wang S F 2020 Information Optics Theory and Applications (Vol. 4) (Beijing: Beijing University of Posts and Telecommunications Press) p64 (in Chinese)
[13] 郝欣, 朱启华, 王逍, 耿远超, 周凯南, 黄征, 王凤蕊 2008 中国激光 35 1553
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Hao X, Zhu Q H, Wang X, Geng Y C, Zhou K N, Huang Z, Wang F R 2008 Chin. J. Lasers 35 1553
Google Scholar
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Google Scholar
[15] Zuo Y L, Zhou K N, Wu Z H, Wang X, Xie N, Su J Q, Zeng X M 2016 Laser Phys. Lett. 13 055302
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Li W, Wang X, Mu J, Hu B L, Zeng X M, Zuo Y L, Wu Z H, Wang X D, Li Z L, Su J Q 2021 Acta Phys. Sin. 70 234201
Google Scholar
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图 1 (a) 光路示意图; (b) 计算示意图
Figure 1. (a) Schematic of the optical path; (b) schematic of calculation.
图 2 单次自相关测试原理及分析模型示意图
Figure 2. Schematic diagram of the single-shot autocorrelation principle and analytical model.
图 3 扩束透镜组引入的时空耦合畸变 (a1) 考虑透镜组色差时远场光斑; (a2) 理想情况下的远场光斑; (b1) 考虑透镜组色差时远场环围能量曲线; (b2) 理想情况下远场环围能量曲线; 理想情况下近场(c1)及远场(c2)的光场时空分布; 激光脉冲经过透镜组并依据近场中心点进行色散补偿后的近场(d1)及远场(d2)时空耦合畸变
Figure 3. Spatiotemporal coupling distortion introduced by lens-pair: The far-field distribution with chromatic aberration of the lens-pair (a1) & without chromatic aberration (a2); circled energy graph of the far-field with chromatic aberration of the lens-pair (b1) & without chromatic aberration (b2); the spatio-temporal distribution of the laser pulse in the near-field (c1) and far-field (c2) without chromatic aberration; The spatio-temporal coupling distortion in the near-field (d1) and far-field (d2) in case of the laser pulse passing through the lens-pair with dispersion compensation according to the near-field centroid.
图 4 考虑色差(蓝色线)和不考虑色差(红色线)时远场脉宽、焦斑面积和远场功率密度随光束口径和带宽的变化 (a1) 远场脉宽随光束口径变化情况; (a2) 焦斑面积随光束口径变化情况; (a3) 远场功率密度随光束口径变化情况; (b1) 远场脉宽随带宽变化情况; (b2) 焦斑面积随带宽变化情况; (b3) 远场功率密度随带宽变化情况
Figure 4. Variation of far-field pulse width, focal spot area and far-field power density with beam aperture and bandwidth (blue line: with chromatic aberration; red line: without chromatic aberration): (a1) The variation of far-field pulse with beam aperture; (a2) the variation of focal spot area with beam aperture; (a3) the variation of far-field power density with beam aperture; (b1) the variation of far-field pulse width with bandwidth; (b2) the variation of focal spot area with bandwidth; (b3) the variation of far-field power density with bandwidth.
图 5 单次自相关脉宽测试分析对比 (a1) 有色差时基频光信号; (a2) 有色差时单次自相关倍频信号(空-时分布); (a3) 有色差时单次自相关仪信号; (b1) 理想条件下的基频信号; (b2) 理想条件下自相关倍频信号空-时分布; (b3) 理想条件下单次自相关仪信号; (c1) 通过透镜组后远场处(焦平面内)的积分通量时间波形; (c2) 通过理想无像差透镜组时远场处的积分通量时间波形
Figure 5. Analysis and comparison between the results from single-autocorrelation method and the actual far-field pulse shape: Fundamental frequency signal (a1), second harmonic signal (a2) and signal of an auto-correlator (a3) in case of the pulse passing through the lens-pair with chromatic aberration; fundamental frequency signal (b1), second harmonic signal (b2) and signal of an auto-correlator (b-3) in case of ideal condition without chromatic aberration; (c1) actual temporal shape of the pulse at the far field with chromatic aberration of lens-pair; (c2) actual temporal shape of the pulse at the far field without chromatic aberration of lens-pair
表 1 计算参数
Table 1. Parameters for calculation.
对象 项目 具体参数 输入光束 口径/m 0.12 × 0.12 中心波长/nm 800 光谱范围/nm ± 80 近场超高斯分布阶数 6 频谱超高斯分布阶数 6 透镜1 尺寸/m 0.2 × 0.2 材料 K9 前球面曲率半径 ∞ 后球面曲率半径/m 1.1789 中心厚度/m 0.03 透镜2 尺寸/m 0.4 × 0.4 材料 K9 前球面曲率半径/m 3.5367 后球面曲率半径 ∞ 中心厚度/m 0.05 抛物聚焦镜 尺寸/m 0.5 × 0.5 焦距/m 1 
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[1] Perry M D, Pennington D, Stuart B C, Tietbohl G, Britten J A, Brown C, Herman S, Golick B, Kartz M, Miller J, Powell H T, Vergino M, Yanovsky V 1999 Opt. Lett. 24 160
Google Scholar
[2] Gaul E W, Ditmire T, Martinez M D, Douglas S, Gorski D, Hays G R, Henderson W, Erlandson A, Caird J, Ebbers C, Iovanovic I, Molander W 2005 Conference on Lasers and Electro-Optics Baltimore, Maryland United States, May 22–27, 2005 p2026
[3] Danson C N, Brummitt P A, Clarke R J, Collier J L, Fell B, Frackiewicz A J, Hancock S, Hawkes S, Hernandez-Gomez C, Holligan P 2004 Nucl. Fusion 44 p239
Google Scholar
[4] 彭翰生 2006 中国激光 33 865
Google Scholar
Peng H S 2006 Chin. J. Lasers 33 865
Google Scholar
[5] Center for Relativistic Laser Science, Ultrahigh Intensity Lasers https://www.ibs.re.kr/corels/ [2020-1-1]
[6] Bor Z 1989 Opt. Lett. 14 119
Google Scholar
[7] 胡必龙 2020 硕士学位论文 (绵阳: 中国工程物理研究院) 第13页
Hu B L 2020 M. S. Thesis (Mianyang: China Academy of Engineering Physics) p13 (in Chinese)
[8] Kempe M, Rudolph W 1993 Opt. Lett. 18 137
Google Scholar
[9] 俞胜清, 黄晓俊 2011 科技创新导报 2011 216
Google Scholar
Yu S Q, Huang X J 2011 Sci. Technol. Innov. Her. 2011 216
Google Scholar
[10] 俞胜清, 王峰, 黄晓俊 2010 喀什大学学报 31 44
Google Scholar
Yu S Q, Wang F, Huang X J 2010 J. Kashgar Univ. 31 44
Google Scholar
[11] 王小怀, 张庆 2005 实验室研究与探索 24 40
Google Scholar
Wang X H, Zhang Q 2005 Res. Explor. Lab. 24 40
Google Scholar
[12] 王仕璠 2020 信息光学理论与应用(第四版)(北京: 北京邮电大学出版社) 第64页
Wang S F 2020 Information Optics Theory and Applications (Vol. 4) (Beijing: Beijing University of Posts and Telecommunications Press) p64 (in Chinese)
[13] 郝欣, 朱启华, 王逍, 耿远超, 周凯南, 黄征, 王凤蕊 2008 中国激光 35 1553
Google Scholar
Hao X, Zhu Q H, Wang X, Geng Y C, Zhou K N, Huang Z, Wang F R 2008 Chin. J. Lasers 35 1553
Google Scholar
[14] Raghuramaiah M, Sharma A K, Naik P A, Gupta P D, Ganeev R A 2001 Sadhana 26 603
Google Scholar
[15] Zuo Y L, Zhou K N, Wu Z H, Wang X, Xie N, Su J Q, Zeng X M 2016 Laser Phys. Lett. 13 055302
Google Scholar
[16] 李伟, 王逍, 母杰, 胡必龙, 曾小明, 左言磊, 吴朝辉, 王晓东, 李钊历, 粟敬钦 2021 物理学报 70 234201
Google Scholar
Li W, Wang X, Mu J, Hu B L, Zeng X M, Zuo Y L, Wu Z H, Wang X D, Li Z L, Su J Q 2021 Acta Phys. Sin. 70 234201
Google Scholar
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