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优化组合激光场驱动原子产生高次谐波及单个超短阿秒脉冲理论研究

汉琳 苗淑莉 李鹏程

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优化组合激光场驱动原子产生高次谐波及单个超短阿秒脉冲理论研究

汉琳, 苗淑莉, 李鹏程

Theoretical study of high-order harmonics and single ultrashort attosecond pulse generated by optimized combination of laser field

Han Lin, Miao Shu-Li, Li Peng-Cheng
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  • 高次谐波是获得阿秒紫外光源最主要的方法之一, 是强场超快领域研究的热点问题, 具有非常广泛的应用前景. 本文围绕如何产生超连续高次谐波平台及单个超短阿秒脉冲面临的问题, 概述了这方面研究的进展, 并从理论上展示了一种有效可行的方案, 即将强激光场中的含时薛定谔方程与非约束优化算法相结合, 以扩展谐波平台最宽为目标函数, 分别优化双色和三色组合激光场并驱动氦原子产生超连续高次谐波谱. 优化后的双色组合激光场驱动氦原子产生的超连续谐波谱平台达到了100阶, 叠加获得了最短25 as的单个阿秒脉冲; 优化后的三色组合激光场驱动氦原子产生的超连续谐波谱平台宽度达到了170阶, 叠加获得最短17 as的单个阿秒脉冲, 同时谐波转换效率也有所提高. 为了给实验提供切实可行的参考, 本文以优化的双色组合激光场情况为例, 基于同时求解含时薛定谔方程和麦克斯韦方程, 进一步考虑了介质宏观演化效应对单原子层次产生阿秒脉冲的影响, 发现利用远场轴外量子通道的空间选择性可以获得更短的单个阿秒脉冲.
    High-order harmonic generation, which is a hot topic of strong ultrafast fields, is one of the most important ways for obtaining the ultraviolet attosecond sources, and has a very wide application prospect. This work focuses on the challenges of the generation of either short or high attosecond pulses. We present the research progress of the high-order harmonics and attosecond pulse generation, and propose an effective and feasible method, and show some results. Specifically, combining the time-dependent Schrödinger equation and new unconstrained optimization algorithm, the objective function with the aim of the widest supercontinuum plateau of He atom is designed and the optimized two-color and three-color laser fields are obtained. The supercontinuum spectra extend up to 100 harmonic orders for the case of the optimized two-color laser field. As a result, a single ultrashort attosecond pulse of 25 as is produced. For the three-color case, the supercontinuum spectra reach up to 170 harmonic orders, and the width of single shortest attosecond pulse obtained by superposing pulses from low order (110 order) to high order (280 order) is obtained to be 17 as . Taking the optimized two-color laser field for example, the macroscopic medium propagation is discussed by solving the Maxwell equation. The results show that the selectivity of quantum trajectories from far-field space distribution can obtain the single ultra-short attosecond pulse.
      通信作者: 李鹏程, pchli@stu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 91850209, 12074239, 12047501)、广东省自然科学基金(批准号: 2020A1515010927)、广东省科技专项项目(批准号: 2020ST084)、广东省高校特色创新类项目(批准号: 2019KTSCX038, 2020KCXTD012)和汕头大学(批准号: NTF18030)资助的课题
      Corresponding author: Li Peng-Cheng, pchli@stu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 91850209, 12074239, 12047501), the Natural Science Foundation of Guangdong Province, China (Grant No. 2020A1515010927), the Science and Technology Project of Guangdong Province, China (Grant No. 2020ST084), the Special Innovation Program of Universities of Guangdong Province (Grant Nos. 2019KTSCX038, 2020KCXTD012), and the Shantou University, China (Grant No. NTF18030)
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  • 图 1  (a) 优化前和优化后的双色组合激光场; (b)优化前和优化后的双色组合激光场驱动He原子产生的高次谐波谱

    Fig. 1.  (a) Initial laser field and the optimized two-color laser field; (b) corresponding HHG power spectra

    图 2  (a) 优化前高次谐波时频分析图; (b)优化后高次谐波时频分析图

    Fig. 2.  Wavelet time-frequency of the HHG spectra for the cases of (a) initial and (b) optimized two-color laser fields

    图 3  (a) 优化后给定阶次高次谐波强度随时间变化关系; (b)对比优化前后单个阿秒脉冲的产生

    Fig. 3.  (a) Dipole time profiles of harmonics from the 70th to the 170th harmonic order; (b) attosecond pulse generation for the cases of the initial and optimized two-color laser fields

    图 4  (a) 优化前和优化后的三色组合激光场; (b)优化前和优化后的三色组合激光场驱动He原子产生的高次谐波谱

    Fig. 4.  (a) Initial laser field and the optimized three-color laser field; (b) corresponding HHG power spectra

    图 5  (a) 优化前高次谐波时频分析图; (b)优化后高次谐波时频分析图

    Fig. 5.  Wavelet time-frequency of the HHG spectra for the cases of (a) initial and (b) optimized three-color laser fields

    图 6  (a) 优化后给定阶次高次谐波强度随时间变化关系; (b)优化前后单个阿秒脉冲的产生

    Fig. 6.  (a) Dipole time profiles of harmonics from the 110th to the 200th harmonic order; (b) attosecond pulse generation for the cases of the initial and optimized three-color laser fields

    图 7  优化的宏观双色组合激光场空间传播效应 (a)演化前激光场; (b)演化后激光场; (c)轴上演化前和演化后激光场对比; (d)驱动单原子激光场与宏观演化后轴上激光场对比

    Fig. 7.  Macroscopic propagation effects of the optimized two-color laser fields: (a) Entrance; (b) exit; (c) comparison of entrance and exit on axis; (d) comparison of the fields for single-atom case and mac-field on axis

    图 8  (a) 远场高次谐波空间分布; (b)单原子与远场高次谐波对比; (c)远场阿秒脉冲空间分布

    Fig. 8.  (a) Spatial distribution of far-field HHG; (b) comparison of single atom and far-field HHG; (c) spatial distribution of far-field attosecond pulse.

    图 9  (a) 轴上高次谐波时频分析; (b)轴外0.37 mm处高次谐波时频分析; (c)轴上与轴外0.37 mm处获得的单个最短阿秒脉冲

    Fig. 9.  (a) Wavelet time-frequency of the HHG spectra on axis; (b) wavelet time-frequency of the HHG spectra at 0.37 mm off axis; (c) on-axis and off-axis attosecond pulse generation

    图 10  轴上不同气体靶位置产生的单个阿秒脉冲对比

    Fig. 10.  Comparison of single attosecond pulse for the different target position

    表 1  He原子模型势参数(原子单位制)[65]

    Table 1.  Model potential parameters for He (in a.u.)[65]

    $ l $ $ \alpha $ $r_{\rm{c}}$ S $ A_1 $ $ A_2 $ $ B_1 $ $ B_2 $
    $ 0 $ $ 0.28125 $ $ 2.0 $ $ -7.9093912 $ $ -10.899664 $ 0 $ 1.7 $ $ 3.8 $
    $ 1 $ $ 0.28125 $ $ 2.0 $ $ 1.50094970 $ $ 0.11297684 $ 0 $ 1.3 $ $ 3.8 $
    $ 2 $ $ 0.28125 $ $ 2.0 $ $ 0.88294766 $ $ -0.032043029 $ 0 $ 1.3 $ $ 3.8 $
    $ 3 $ $ 0.28125 $ $ 2.0 $ $ 0.41193110 $ $ -0.129391180 $ 0 $ 1.3 $ $ 3.8 $
    $ \geqslant 3 $ $ 0.28125 $ $ 2.0 $ $0$ $0$ 0 $ 1.3 $ $ 0 $
    下载: 导出CSV
  • [1]

    Telnov D A, Chu S I 2009 Phys. Rev. A 79 041401Google Scholar

    [2]

    Garcia Ruiz R F, Vernon A R, Binnersley C L, Sahoo B K, Bissell M, Billowes J, Cocolios T E, Gins W, de Groote R P, Flanagan K T, Koszorus A, Lynch K M, Neyens G, Ricketts C M, Wendt K D A, Wilkins S G, Yang X F 2018 Phys. Rev. X 8 041005

    [3]

    Wang R, Zhang Q, Li D, Xu S, Cao P, Zhou Y, Cao W, Lu P 2019 Opt. Express 27 6471Google Scholar

    [4]

    Ge P, Fang Y, Guo Z, Ma X, Yu X, Han M, Wu C, Gong Q, Liu Y 2021 Phys. Rev. Lett. 126 223001Google Scholar

    [5]

    De Silva A H N C, Atri-Schuller D, Dubey S, Acharya B P, Romans K L, Foster K, Russ O, Compton K, Rischbieter C, Douguet N, Bartschat K, Fischer D 2021 Phys. Rev. Lett. 126 023201Google Scholar

    [6]

    Liu M M, Shao Y, Han M, Ge P, Deng Y, Wu C, Gong Q, Liu Y 2018 Phys. Rev. Lett. 120 043201Google Scholar

    [7]

    Li W K, Lei Y, Li X, Yang T, Du M, Jiang Y, Li J L, Luo S Z, Liu A H, He L H, Ma P, Zhang D D, Ding D J 2021 Chin. Phys. Lett. 38 053202Google Scholar

    [8]

    Kelvich S A, Becker W, Goreslavski S P 2017 Phys. Rev. A 96 023427Google Scholar

    [9]

    Brennecke S, Lein M 2018 Phys. Rev. A 98 063414Google Scholar

    [10]

    Brennecke S, Lein M 2018 J. Phys. B: At. Mol. Opt. Phys. 51 094005Google Scholar

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    Shi M, Lai X, Yu S, Wang Y, Quan W, Liu X 2022 Phys. Rev. A 105 013118Google Scholar

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    Yang Q, Leng J, Wang Y H, Sun Y N, Du H B, Zhang D D, Song L L, He L H, Liu F C 2022 Chin. Phys. Lett. 39 023301Google Scholar

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出版历程
  • 收稿日期:  2022-06-30
  • 修回日期:  2022-08-24
  • 上网日期:  2022-11-18
  • 刊出日期:  2022-12-05

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