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Low-coherece laser based lens array beam smoothing techique

Gao Yan-Qi Zhao Xiao-Hui Jia Guo Li Fu-Jian Cui Yong Rao Da-Xing Ji Lai-Lin Liu Dong Feng Wei Huang Xiu-Guang Ma Wei-Xin Sui Zhan

Low-coherece laser based lens array beam smoothing techique

Gao Yan-Qi, Zhao Xiao-Hui, Jia Guo, Li Fu-Jian, Cui Yong, Rao Da-Xing, Ji Lai-Lin, Liu Dong, Feng Wei, Huang Xiu-Guang, Ma Wei-Xin, Sui Zhan
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  • The experimental study of laser-driven material state equation puts forward extremely high requirements for the uniformity and stability of the target spot intensity distribution, and these two characteristics greatly determine the accuracy and repeatability of the experimental results. In this paper, a beam smoothing scheme combining diffraction-weakened lens array (LA) with induced spatial incoherent (ISI) technique based on low-coherence laser is proposed to solve the problems, that is, the uniformity and stability of the target spot intensity distribution in the material state equation experiments driven with narrow-band coherent laser. The super-Gaussian soft aperture used in our scheme can improve the intensity fluctuation caused by the hard-edge diffraction of the lens elements, and the temporal smoothing technique, ISI, can reduce the interference effect between the lens array elements. The speckle patterns of target spot, which are caused by interference between beamlets and determine the high nonuniformity, will randomly reconstruct after each coherent time. The high-frequency components are further smoothed by the time-average effect. In broadband high-power laser devices, ISI can be combined with LA by making the lens elements with different thickness values. This scheme can enhance the focal spot uniformity and improve the tolerance of the system to the wavefront phase distortion. The influence of wavefront phase distortion on target surface uniformity and stability are analyzed. The simulation results show that this smoothing scheme significantly reduces the target spot nonuniformity, improves the tolerance of random wavefront phase distortion, and presents a uniform and stable target spot intensity distribution. The nonuniformity of target spot will be reduced to about 10% after 10 ps, and about 3% after 100 ps. In addition, statistical analysis shows that the peak-to-valley value and the nonuniformity of the target spot intensity distribution are strongly correlated with the gradient of root-mean-square of the wavefront phase distortion. Using this method, the tolerance range of the wavefront phase distortion can be given according to the requirements of the experiments, which has reference value for designing and optimizing the laser driver parameters in the state equation experiment.
      Corresponding author: Zhao Xiao-Hui, xhzhao_silp@163.com
    [1]

    Lin Y, Kessler T, Lawrence G 1996 Opt. Lett. 21 1703

    [2]

    Kato Y, Mima K, Miyanaga N, Arinaga S, Kitagawa Y, Nakatsuka M, Yamanaka C 1984 Phys. Rev. Lett. 53 1057

    [3]

    Deng X M, Liang X C, Chen Z Z, Yu W Y, Ma R Y 1986 Appl. Opt. 25 3377

    [4]

    江秀娟, 李菁辉, 朱俭, 林尊琪 2015 物理学报 64 054201

    Jiang X J, Li J H, Zhu J, Lin Z Q 2015 Acta Phys. Sin. 64 054201

    [5]

    周冰洁, 钟哲强, 张彬 2012 物理学报 61 214002

    Zhou B J, Zhong Z Q, Zhang B 2012 Acta Phys. Sin. 61 214002

    [6]

    Skupsky S, Short R, Kessler T, Craxton R, Letzring S, Soures J 1989 J. Appl. Phys. 66 3456

    [7]

    Skupsky S, Craxton R, Skupsky S, Craxton R S 1999 Phys. Plasmas 6 2157

    [8]

    Miyaji G, Miyanaga N, Urushihara S, Suzuki K, Matsuoka S, Nakatsuka M 2002 Opt. Lett. 27 725

    [9]

    Obenschain S, Grun J, Herbst M, Kearney K, Manka C, McLean E, Mostovych A, Stamper A, Whitlock R, Bodner S, Gardner J, Lehmberg R 1986 Phys. Rev. Lett. 56 2807

    [10]

    Obenschain S, BodnerS, Colombant D, Gerber K, Lehmberg R, McLean E, Mostovych A, Pronko M, Pawley C, Schmitt A, Sethian J, Serlin V, Stamper J, Sullivan C 1996 Phys. Plasmas 3 5

    [11]

    Rothenberg J 2000 J. Appl. Phys. 87 3654

    [12]

    Wang Y C, Wang F, Zhang Y, Huang X X, Hu D X, Zheng W G, Zhu R H, Deng X W 2017 Appl. Opt. 56 8087

    [13]

    Zhong Z Q, Hou P C, Zhang B 2015 Opt. Lett. 40 5850

    [14]

    Weng X F, Li T F, Zhong Z Q, Zhang B 2017 Appl. Opt. 56 8902

    [15]

    Haynam C, Wegner P, Auerbach J, Bowers M, Dixit S, Erbert G, Heestand G, Henesian M, Hermann M, Jancaitis K, Manes K, Marshall C, Mehta N, Menapace J, Moses E, Murray J, Nostrand M, Orth C, Patterson R, Sacks R, Shaw M, Spaeth M, Sutton S, Williams W, Widmayer C, White R, Yang S, Wonterghem B 2007 Appl. Opt. 46 3276

    [16]

    Jiang X J, Li J H, Li H G, Li Y, Lin Z Q 2011 Appl. Opt. 50 5213

    [17]

    江秀娟, 李菁辉, 李华刚, 周申蕾, 李扬, 林尊琪 2012 物理学报 61 124202

    Jiang X J, Li J H, Li H G, Zhou S L, Li Y, Lin Z Q 2012 Acta Phys. Sin. 61 124202

    [18]

    Zhou S L, Lin Z Q, Jiang X J 2007 Opt. Commun. 272 186

    [19]

    陈泽尊, 向春, 邓锡铭 1985 中国激光 13 65

    Chen Z Z, Xiang C, Deng X M 1985 Chin. J. Las. 13 65

    [20]

    Regan S, Marozas J, Kelly J, Boehly T, Donaldson W, Jaanimagi P, Keck R, Kessler T, Meyerhofer D, Seka W 2000 J. Opt. Soc. Am. B 17 1483

  • 图 1  阵列透镜及束匀滑装置示意图

    Figure 1.  Diagram of lens array and the beam smoothing scheme.

    图 2  阵列透镜匀滑靶面光强分布

    Figure 2.  Intensity distribution of target spot after lens array smoothing.

    图 3  (a), (b)相邻发次状态方程的实验结果; (c)曲线为对应突出靶后界面的时间分布曲线

    Figure 3.  (a) and (b) Are the adjacent experimental results of state equation, and the curves in (c) are the time distributions of back of the target.

    图 5  滤波后不同波前误差对应靶面强度分布的对比

    Figure 5.  Comparison of the target intensity distribution corresponding to the different wavefronts after filtering.

    图 4  波前畸变造成的焦斑分布不均匀性及差异性 上排为波前相位理想分布及波前畸变, 下排为对应的焦斑强度分布

    Figure 4.  The nonuniformity and difference of the focal spot distributions caused by wavefront distortion. The upper row is the ideal distribution of the wavefront phase and the wavefront distortion, and the lower row is the focal spot intensity distribution, respectively.

    图 6  仅采用阵列透镜匀滑时, 焦斑光强分布与波前相位畸变统计特性之间的关系

    Figure 6.  Relationship of the statistical characteristics of target intensity distributions and that of the wavefront phase distortions, with only the lens array used for smoothing.

    图 7  焦斑不均匀度随匀滑时间的变化关系的理论与模拟结果对比

    Figure 7.  The relationship of target spot nonuniformity versus smoothing time: theory and simulation results.

    图 8  不同波前误差, 消衍射阵列透镜联合ISI束匀滑方案焦斑光强分布对比

    Figure 8.  The target spots smoothed by diffraction-weakened LA and ISI with different wavefront distortion.

    图 9  消衍射阵列透镜联合ISI束匀滑后, 焦斑光强分布与波前相位畸变统计特性之间的关系

    Figure 9.  Relationship of the statistical characteristics of target intensity distributions and that of the wavefront phase distortions, with diffraction-weakened LA and ISI used for smoothing.

    表 1  不同波前相位畸变, 焦斑不均匀度随匀滑时间的变化

    Table 1.  The nonuniformity of target at different smoothing time with different wavefront distortion.

    T($\tau $)1101001000Inf
    $ \sigma ({\phi _0})$0.97160.34230.09560.03030.0060
    $ \sigma ({\phi _1})$1.02670.32090.10120.03320.0118
    $ \sigma ({\phi _2})$0.93740.30420.09890.03450.0158
    DownLoad: CSV
  • [1]

    Lin Y, Kessler T, Lawrence G 1996 Opt. Lett. 21 1703

    [2]

    Kato Y, Mima K, Miyanaga N, Arinaga S, Kitagawa Y, Nakatsuka M, Yamanaka C 1984 Phys. Rev. Lett. 53 1057

    [3]

    Deng X M, Liang X C, Chen Z Z, Yu W Y, Ma R Y 1986 Appl. Opt. 25 3377

    [4]

    江秀娟, 李菁辉, 朱俭, 林尊琪 2015 物理学报 64 054201

    Jiang X J, Li J H, Zhu J, Lin Z Q 2015 Acta Phys. Sin. 64 054201

    [5]

    周冰洁, 钟哲强, 张彬 2012 物理学报 61 214002

    Zhou B J, Zhong Z Q, Zhang B 2012 Acta Phys. Sin. 61 214002

    [6]

    Skupsky S, Short R, Kessler T, Craxton R, Letzring S, Soures J 1989 J. Appl. Phys. 66 3456

    [7]

    Skupsky S, Craxton R, Skupsky S, Craxton R S 1999 Phys. Plasmas 6 2157

    [8]

    Miyaji G, Miyanaga N, Urushihara S, Suzuki K, Matsuoka S, Nakatsuka M 2002 Opt. Lett. 27 725

    [9]

    Obenschain S, Grun J, Herbst M, Kearney K, Manka C, McLean E, Mostovych A, Stamper A, Whitlock R, Bodner S, Gardner J, Lehmberg R 1986 Phys. Rev. Lett. 56 2807

    [10]

    Obenschain S, BodnerS, Colombant D, Gerber K, Lehmberg R, McLean E, Mostovych A, Pronko M, Pawley C, Schmitt A, Sethian J, Serlin V, Stamper J, Sullivan C 1996 Phys. Plasmas 3 5

    [11]

    Rothenberg J 2000 J. Appl. Phys. 87 3654

    [12]

    Wang Y C, Wang F, Zhang Y, Huang X X, Hu D X, Zheng W G, Zhu R H, Deng X W 2017 Appl. Opt. 56 8087

    [13]

    Zhong Z Q, Hou P C, Zhang B 2015 Opt. Lett. 40 5850

    [14]

    Weng X F, Li T F, Zhong Z Q, Zhang B 2017 Appl. Opt. 56 8902

    [15]

    Haynam C, Wegner P, Auerbach J, Bowers M, Dixit S, Erbert G, Heestand G, Henesian M, Hermann M, Jancaitis K, Manes K, Marshall C, Mehta N, Menapace J, Moses E, Murray J, Nostrand M, Orth C, Patterson R, Sacks R, Shaw M, Spaeth M, Sutton S, Williams W, Widmayer C, White R, Yang S, Wonterghem B 2007 Appl. Opt. 46 3276

    [16]

    Jiang X J, Li J H, Li H G, Li Y, Lin Z Q 2011 Appl. Opt. 50 5213

    [17]

    江秀娟, 李菁辉, 李华刚, 周申蕾, 李扬, 林尊琪 2012 物理学报 61 124202

    Jiang X J, Li J H, Li H G, Zhou S L, Li Y, Lin Z Q 2012 Acta Phys. Sin. 61 124202

    [18]

    Zhou S L, Lin Z Q, Jiang X J 2007 Opt. Commun. 272 186

    [19]

    陈泽尊, 向春, 邓锡铭 1985 中国激光 13 65

    Chen Z Z, Xiang C, Deng X M 1985 Chin. J. Las. 13 65

    [20]

    Regan S, Marozas J, Kelly J, Boehly T, Donaldson W, Jaanimagi P, Keck R, Kessler T, Meyerhofer D, Seka W 2000 J. Opt. Soc. Am. B 17 1483

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  • Received Date:  05 December 2018
  • Accepted Date:  14 February 2019
  • Available Online:  23 March 2019
  • Published Online:  01 April 2019

Low-coherece laser based lens array beam smoothing techique

    Corresponding author: Zhao Xiao-Hui, xhzhao_silp@163.com
  • 1. Shanghai Institute of Laser Plasma, China Academy of Engineering Physics, Shanghai 201800, China
  • 2. Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiaotong University, Shanghai 200240, China
  • 3. National Laboratory on High Power Laser and Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

Abstract: The experimental study of laser-driven material state equation puts forward extremely high requirements for the uniformity and stability of the target spot intensity distribution, and these two characteristics greatly determine the accuracy and repeatability of the experimental results. In this paper, a beam smoothing scheme combining diffraction-weakened lens array (LA) with induced spatial incoherent (ISI) technique based on low-coherence laser is proposed to solve the problems, that is, the uniformity and stability of the target spot intensity distribution in the material state equation experiments driven with narrow-band coherent laser. The super-Gaussian soft aperture used in our scheme can improve the intensity fluctuation caused by the hard-edge diffraction of the lens elements, and the temporal smoothing technique, ISI, can reduce the interference effect between the lens array elements. The speckle patterns of target spot, which are caused by interference between beamlets and determine the high nonuniformity, will randomly reconstruct after each coherent time. The high-frequency components are further smoothed by the time-average effect. In broadband high-power laser devices, ISI can be combined with LA by making the lens elements with different thickness values. This scheme can enhance the focal spot uniformity and improve the tolerance of the system to the wavefront phase distortion. The influence of wavefront phase distortion on target surface uniformity and stability are analyzed. The simulation results show that this smoothing scheme significantly reduces the target spot nonuniformity, improves the tolerance of random wavefront phase distortion, and presents a uniform and stable target spot intensity distribution. The nonuniformity of target spot will be reduced to about 10% after 10 ps, and about 3% after 100 ps. In addition, statistical analysis shows that the peak-to-valley value and the nonuniformity of the target spot intensity distribution are strongly correlated with the gradient of root-mean-square of the wavefront phase distortion. Using this method, the tolerance range of the wavefront phase distortion can be given according to the requirements of the experiments, which has reference value for designing and optimizing the laser driver parameters in the state equation experiment.

    • 基于高功率激光驱动器的相关物理实验研究, 例如材料状态方程的研究, 惯性约束核聚变(inertial confinement fusion, ICF)等均需要实现对靶面的均匀辐照, 束匀滑技术是实现靶面光强调控的核心技术手段. 随着物理研究的深入和驱动器实验条件的大幅提升, 基于高功率激光驱动器实验研究的研究对象呈现出了多样化的特点, 同时, 相关实验对装置靶面光强的均匀性和稳定性等都提出了越来越高的要求. 为此, 人们发展了多种束匀滑技术, 按照其特点主要可分为空间束匀滑技术、时间束匀滑技术和偏振匀滑技术等. 空间束匀滑技术是利用干涉或衍射的方法对焦斑进行空间整形, 例如连续相位板[1](continuous phase plate, CPP)、随机相位板[2](random phase plate, RPP)、阵列透镜[3,4](lens array, LA)等; 时间束匀滑技术通过空间整形产生的散斑随时间扫动来达到平滑的目的[5], 例如光谱色散匀滑[6-8](smoothing by spectral dispersion, SSD)、诱导空间非相干技术[9,10] (induced spatial incoherence, ISI)等; 偏振匀滑技术[11,12](polarization smoothing, PS)是将入射光分为偏振垂直的两束在远场进行叠加, 进一步消除焦斑小尺度不均匀性. 除此之外, 研究人员仍在不断探索新型束匀滑技术, 例如利用克尔效应实现径向匀滑[13,14](radial smoothing, RS). 国内外高功率激光装置通常采用多种匀滑技术联用的方案, 例如美国国家点火装置采用的是SSD结合CPP与PS的束匀滑方案[15].

      在激光加载状态方程实验中, 靶面光强的不均匀和不稳定将导致冲击波速度空间分布的不均匀和较差的实验重复性, 进而影响实验数据的置信度. 本文对导致靶面光强分布不均匀和重复性较差的主要因素进行了分析, 提出了基于宽带低相干激光, 利用消衍射阵列透镜[16-18]联合诱导非相干技术的束匀滑方案. 在具备宽带低相干光束特性的高功率激光装置中, 通过使阵列透镜的各子透镜具有不同的厚度, 可以将ISI与阵列透镜匀滑技术结合起来. 数值模拟结果表明, 该方法可以获得均匀、稳定的光强分布, 并能够明显降低靶面不均匀性, 提高对装置波前误差的包容度. 通过统计分析的方法, 进一步给出了满足实验条件的波前相位误差范围, 对光学系统的参数设计具有指导意义.

    2.   基于传统激光驱动器的状态方程实验现象分析
    • 由于不同的物理实验对焦斑的分布特性要求不同, 需采用不同的束匀滑手段. 目前, “神光Ⅱ”装置中材料状态方程的实验研究, 通常采用阵列透镜对远场焦斑进行整形和匀滑. 这是由于阵列透镜产生的焦斑具有更陡峭的边缘, 实验效果较好. 如图1所示, 阵列透镜B由一系列子透镜组成, 入射光通过后被分为一系列子束. 每一子束经主镜A聚焦后在主镜后焦面上形成各自的菲涅耳衍射分布. 不同子束的准近场衍射图样相互叠加, 从而实现焦斑匀滑. 实验中通常采用离焦的方法来进一步消除阵列透镜匀滑带来的焦斑“肩状”凸起.

      Figure 1.  Diagram of lens array and the beam smoothing scheme.

      根据实验参数可以对远场焦斑的强度空间分布进行数值模拟. 主透镜直径D = 0.38 m, 焦距fA = 1.575 m. 阵列透镜由边长为d1 = 50 mm, d2 = 35 mm的单元子透镜组成, 总口径D = 0.38 m, 每个单元子透镜的焦距fB = 78.75 m. 离焦量$ \Delta = 200\;{\text{μ}}{\rm{m}}$. 入射光为n阶高斯平顶光束, 束腰半径为w, 其电场复振幅分布可写作:

      其中, $ \phi \left( {x,y} \right)$是波前相位. 假设近场波前为理想平面, 即$ \phi \left( {x,y} \right)=0$, 且n = 7, w = 0.31 m, 根据理论模拟焦斑光强分布$ I \left( {x,y} \right)$,如图2所示, 经过阵列透镜及主镜聚焦后, 形成了尺寸约为$ 1000\;{\text{μ}}{\rm{m}} \times 700\;{\text{μ}}{\rm{m}}$的矩形焦斑. 其中, 高频的强度起伏可以通过等离子体热传导部分匀滑抹平.

      Figure 2.  Intensity distribution of target spot after lens array smoothing.

      在材料状态方程实验研究中, 激光与靶相互作用时, 不同空间位置产生的冲击波速度与激光光强密切相关. 在冲击波经历相同靶厚的情况下, 若激光光强在空间上存在不均匀性, 则冲击波速度的不同将会在突出靶后界面的时间上产生差异, 利用条纹相机可以诊断该过程(如图3所示). 为了获得置信度较高的实验结果, 实验上要求冲击波突出靶后界面时间的一维分布极差小于20 ps, 均方根(RMS)值小于1%; 除此之外, 冲击波突出靶后界面时间分布应具有较好的稳定性和可重复性. 图3给出了在相同实验条件下, 连续两发次实验的实验结果. 图3(c)为对实验图像进行数据寻边后的结果, 可以看出中间区域冲击波突出靶后界面时间分布的极差值大于50 ps, 不满足实验数据高精度的要求. 并且, 冲击波突出靶后界面时间分布的一致性存在较大偏差, 平整分布存在一定的随机性. 导致这一问题的原因很多, 例如靶的一致性、调靶和瞄靶的精度、光束焦斑的强度分布变化等. 经过对多轮实验数据的分析, 从检测结果和原始数据来看, 靶的精度、调靶和瞄靶的精度等都已达到了较好的程度, 焦斑强度空间分布的不均匀性和发次之间的不稳定性可能是导致上述现象的主要原因.

      Figure 3.  (a) and (b) Are the adjacent experimental results of state equation, and the curves in (c) are the time distributions of back of the target.

      数值分析和相关实验结果表明, 焦斑的不均匀性及不稳定性主要来源于近场波前畸变, 而近场强度的不稳定性影响相对较小. 经LA匀滑后焦斑的空间分布主要取决于LA本身的聚焦特性和入射光束的波面特性. 受限于光学元件的加工精度和装校变形, 大口径激光光束在驱动器链路的放大、传输、谐波转化和聚焦过程中, 不可避免地引入球差、彗差、像散等多种像差, 使得光束相位的空间分布偏离理想的平面分布而发生畸变, 最终影响聚焦后的焦斑强度分布. 另外, 由于发次间光束的准直误差、装置多发次运行过程中累积的波前热畸变、传输链路中空气的随机扰动等, 不同发次间光束的输出波前分布将存在一定差异, 这些变化将导致不同发次间的焦斑强度分布产生差异.

      针对图3实验结果所采用的激光驱动器参数条件, 在仅采用阵列透镜对焦斑进行匀滑时, 利用随机相位分布来模拟装置的输出波面特性, 给出了不同相位畸变所对应的焦斑强度变化, 如图4所示. 当波前相位存在畸变时, 焦斑顶部的不均匀性也受到了影响, 将影响状态方程实验中冲击波突出靶后界面的时间分布的均匀性. 另外, 对图4中焦斑进行滤波(模拟等离子体热传导匀滑过程)发现, 由于相位畸变的随机性, 不同发次间焦斑顶部区域的光强分布差异较大, 如图5所示. 这将导致不同发次之间冲击波突出靶后界面的时间分布差异变大.

      Figure 5.  Comparison of the target intensity distribution corresponding to the different wavefronts after filtering.

      Figure 4.  The nonuniformity and difference of the focal spot distributions caused by wavefront distortion. The upper row is the ideal distribution of the wavefront phase and the wavefront distortion, and the lower row is the focal spot intensity distribution, respectively.

      为了确定靶面均匀性与相位畸变特性的关系以及满足实验要求的波前相位畸变的控制范围, 我们还对滤波后的靶面均匀性与波前相位畸变进行了统计分析, 如图6所示. 其中, 波前相位分布特性用极差(peak-to-valley value, PV)以及均方根梯度(gradient root-mean square, GRMS)表征:

      Figure 6.  Relationship of the statistical characteristics of target intensity distributions and that of the wavefront phase distortions, with only the lens array used for smoothing.

      焦斑强度分布特性用极差(PV)以及RMS不均匀度($ {\sigma _{{\rm{RMS}}}}$)来表征:

      式中I为焦斑强度分布, $ \bar I$为平均值.

      图6可知, 焦斑强度分布的PV值和不均匀度与激光束波前相位空间分布的GRMS相关性较高, 而波前相位PV值对应的焦斑光强分布的PV值与$ {\sigma _{{\rm{RMS}}}}$值都比较离散(这也符合PV值本身离散度较大的基本特征). 材料状态方程实验中, 为达到实验数据精度要求, 靶面光强PV值应小于5%, $ {\sigma _{{\rm{RMS}}}}$应小于1%. 根据拟合结果, 要使焦斑强度的PV值满足实验要求, 激光束波前相位畸变的GRMS值就应小于18 nm/cm; 而焦斑不均匀度在仅采用阵列透镜对焦斑进行匀滑的情况下, 无法达到实验要求, 需要对阵列透镜匀滑的方法进行改进, 常用的方式是将阵列透镜的光轴进行随机调整, 通过子束焦斑随机错位的方式缓解这一问题, 但这一措施存在很大的不确定性和不可控性.

    3.   消衍射阵列透镜联合诱导空间非相干束匀滑技术
    • 当采用阵列透镜进行焦斑匀滑时, 靶面上的光强分布实际是单个子透镜边界引起的衍射和各子透镜之间二维干涉的卷积[19]. 为了改善束匀滑的效果, 满足激光与靶相互作用时对光强分布均匀性的要求, 需要从以上两点入手. 首先, 改善子透镜边界硬边衍射引起的“肩状”效应及低频不均匀性, 从而降低滤波后焦斑光强分布的不均匀性; 另外, 引入时间束匀滑技术, 使各阵列透镜分割的各子束之间引入时间延迟, 当延迟时间超过子束的相干时间后, 子束在焦斑处的叠加将变为非相干叠加, 这将大幅改善焦斑分布的高频不均匀性, 同时降低波前相位畸变对焦斑分布的影响. 因此, 我们提出了消衍射阵列透镜联合诱导空间非相干技术的束匀滑方案, 以提高焦斑均匀性及装置对波前相位畸变的包容性.

      对于LA束匀滑方式而言, 子透镜硬边衍射导致的焦斑低频调制可以利用在子光束近场上增加软边光阑来消除, 其孔径函数可写作超高斯形式:

      其中, $ w_{x/y}^b$, $ n_{x/y}^b$分别为软边光阑x方向及y方向的束腰半径及阶数. 此时, 阵列透镜的透过率可以表示为

      ISI技术是将光束在空间上进行分割, 并使相邻子束之间产生时间延迟, 当延迟时间大于光束的相干时间$\tau $时, 空间上子束间便成为不相干光, 从而实现了光束整体的空间相干性的降低. 也就是说匀滑的焦斑是在同时实现了时间低相干和空间低相干之后获得的. 原则上, 子束切分越多, 空间相干性越差, 获得的匀滑效果越好. 但子束的数目又受到焦斑轮廓要求、总体器件厚度差、整体透过率、制造工艺难度等条件的限制, 不宜过高. 某一时刻(相干时间内), 各子束叠加形成具有散斑分布的远场焦斑. 经过相干时间$\tau $后, 散斑分布将发生重构, 使得时间积分后焦斑光强分布得到快速匀滑, 其不均匀度随匀滑时间的变化满足关系[20]:

      其中, $ {\sigma _0}$$ {\sigma _{{\rm{inf}}}}$分别为初始条件下及经过无限长时间后焦斑的不均匀度, T为匀滑时间, 其单位是相干时间.

      使阵列透镜的各子透镜具有不同的厚度l, 如图1所示, 可以将ISI与阵列透镜匀滑技术结合起来, 实现高质量的束匀滑. 传统Nd激光器由于输出带宽较窄(相干时间较长), ISI方法无法应用. 我们目前正在研制的千焦级低相干激光装置, 输出带宽约20 nm, 主要作用之一就是探索低相干激光的束匀滑技术. 模拟中我们采用倍频光特性作为模拟参数, 其波长为527 nm, 带宽为10 nm, 相干时间$\tau $ ≈ 95 fs. 阵列透镜相邻子透镜厚度差为$ 30\;{\text{μ}}{\rm{m}}$即可满足时间延迟的要求, 整个阵列透镜厚度差值最大处为1.89 mm.

      我们对消衍射阵列透镜联合ISI匀滑方案进行了数值模拟, 当软边光阑参数选择$ w_x^b$ = 45 mm, $ w_y^b$ = 31.5 mm, $ n_x^b$ = 5, $ n_y^b$ = 4时可获得较好的匀滑效果. 在不同波前畸变的条件下, 焦斑不均匀度随时间的变化如表1所列. 匀滑时间为10 ps时, 焦斑不均匀性可以降低到约10%, 而100 ps的匀滑时间可以将焦斑不均匀性降低到约3%. 对于不同的波前相位分布, 焦斑不均匀性随时间的变化均满足(1)式, 如图7所示. 其中, 理论曲线根据理想波面, 即$ \phi \left( {x,y} \right) = 0$的模拟结果进行计算. 波前相位畸变造成的焦斑不均匀性变化也随匀滑时间的增加而降低, 这说明系统对波前畸变的容差特性得到了改善.

      T($\tau $)1101001000Inf
      $ \sigma ({\phi _0})$0.97160.34230.09560.03030.0060
      $ \sigma ({\phi _1})$1.02670.32090.10120.03320.0118
      $ \sigma ({\phi _2})$0.93740.30420.09890.03450.0158

      Table 1.  The nonuniformity of target at different smoothing time with different wavefront distortion.

      Figure 7.  The relationship of target spot nonuniformity versus smoothing time: theory and simulation results.

      对于匀滑时间足够长的情况, 各子束之间可认为是完全不相干的. 因此, 靶面光强相当于各子束光强的直接叠加, 与子束在靶面上的衍射分布一致, 如图8所示. 由于阵列透镜中软边光阑的使用消除了硬边衍射造成的强度起伏, 降低了靶面光强分布不均匀性的低频成分.

      Figure 8.  The target spots smoothed by diffraction-weakened LA and ISI with different wavefront distortion.

    4.   模拟结果分析
    • 我们对经过消衍射阵列透镜联合ISI束匀滑后的焦斑光强分布与波前相位畸变统计特性之间的关系进行了模拟, 如图9所示. 与单独使用阵列透镜相比, 在波前相位PV值与GRMS值相同的条件下, 焦斑强度的PV值与$ {\sigma _{{\rm{RMS}}}}$整体下降. 与之前结论相同, 焦斑强度分布PV值和$ {\sigma _{{\rm{RMS}}}}$与波前相位GRMS值相关性较高. 根据物理实验对焦斑均匀性的要求, 即PV < 1%, $ {\sigma _{{\rm{RMS}}}}$ < 5%, 可以推断, 需要控制波前相位的GRMS值小于26 nm/cm. 而单独使用阵列透镜匀滑, 焦斑不均匀性无法达到要求, 且焦斑强度PV值要求波前相位畸变GRMS值小于18 nm/cm. 由此可见, 消衍射阵列透镜联合ISI的束匀滑方案提升了焦斑强度分布均匀性及对波前相位畸变的容差性, 可以满足实验对焦斑分布的要求.

      Figure 9.  Relationship of the statistical characteristics of target intensity distributions and that of the wavefront phase distortions, with diffraction-weakened LA and ISI used for smoothing.

    5.   结 论
    • 材料状态方程实验中, 近场波前相位畸变对突出靶后界面时间分布与焦斑强度分布相关, 均匀、稳定的焦斑分布有利于提升状态方程数据的精度与置信度. 本文通过分析波前相位畸变对焦斑均匀性的影响, 提出了消衍射阵列透镜联合空间诱导非相干的束匀滑方案. 该方案通过改善子透镜硬边衍射引起的强度起伏及各子透镜间的干涉效应, 改善了焦斑均匀性, 并提高了系统对波前行为畸变的容差性. 对焦斑光强分布与波前相位畸变统计特性之间的关系进行分析显示, 焦斑强度分布极差与不均匀性与波前相位畸变均方根梯度相关性较强. 根据统计结果以及实验对焦斑强度分布的要求, 可以给出波前相位畸变的容差范围, 这对激光驱动器的参数设计与优化具有指导意义.

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