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
Fund Project:Project supported by the Science Challenge Project,China (Grant No. TZ2016005), and the National Natural Science Foundation of China (Grant Nos. 11604317, 11604318, 11804321).
Received Date:05 December 2018
Accepted Date:14 February 2019
Available Online:23 March 2019
Published Online:05 April 2019
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. Keywords:beam smoothing/ high-power laser driver/ lens array/ introduced
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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. 图 1 阵列透镜及束匀滑装置示意图 Figure1. 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. 图 2 阵列透镜匀滑靶面光强分布 Figure2. 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. 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 Figure3. (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. 图 5 滤波后不同波前误差对应靶面强度分布的对比 Figure5. 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 Figure4. 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: 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 Figure6. Relationship of the statistical characteristics of target intensity distributions and that of the wavefront phase distortions, with only the lens array 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 Table1.The nonuniformity of target at different smoothing time with different wavefront distortion.
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 Figure7. 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. 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 Figure8. The target spots smoothed by diffraction-weakened LA and ISI with different wavefront distortion.