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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.
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Keywords:
- beam smoothing /
- high-power laser driver /
- lens array /
- introduced
[1] Lin Y, Kessler T, Lawrence G 1996 Opt. Lett. 21 1703
Google Scholar
[2] Kato Y, Mima K, Miyanaga N, Arinaga S, Kitagawa Y, Nakatsuka M, Yamanaka C 1984 Phys. Rev. Lett. 53 1057
Google Scholar
[3] Deng X M, Liang X C, Chen Z Z, Yu W Y, Ma R Y 1986 Appl. Opt. 25 3377
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Google Scholar
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Google Scholar
[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
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Google Scholar
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Google Scholar
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Google Scholar
[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
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
Jiang X J, Li J H, Li H G, Zhou S L, Li Y, Lin Z Q 2012 Acta Phys. Sin. 61 124202
Google Scholar
[18] Zhou S L, Lin Z Q, Jiang X J 2007 Opt. Commun. 272 186
Google Scholar
[19] 陈泽尊, 向春, 邓锡铭 1985 中国激光 13 65
Google Scholar
Chen Z Z, Xiang C, Deng X M 1985 Chin. J. Las. 13 65
Google Scholar
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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 $) 1 10 100 1000 Inf $ \sigma ({\phi _0})$ 0.9716 0.3423 0.0956 0.0303 0.0060 $ \sigma ({\phi _1})$ 1.0267 0.3209 0.1012 0.0332 0.0118 $ \sigma ({\phi _2})$ 0.9374 0.3042 0.0989 0.0345 0.0158 
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[1] Lin Y, Kessler T, Lawrence G 1996 Opt. Lett. 21 1703
Google Scholar
[2] Kato Y, Mima K, Miyanaga N, Arinaga S, Kitagawa Y, Nakatsuka M, Yamanaka C 1984 Phys. Rev. Lett. 53 1057
Google Scholar
[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
Google Scholar
Jiang X J, Li J H, Zhu J, Lin Z Q 2015 Acta Phys. Sin. 64 054201
Google Scholar
[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
Google Scholar
[7] Skupsky S, Craxton R, Skupsky S, Craxton R S 1999 Phys. Plasmas 6 2157
Google Scholar
[8] Miyaji G, Miyanaga N, Urushihara S, Suzuki K, Matsuoka S, Nakatsuka M 2002 Opt. Lett. 27 725
Google Scholar
[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
Google Scholar
[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
Google Scholar
[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
Google Scholar
[13] Zhong Z Q, Hou P C, Zhang B 2015 Opt. Lett. 40 5850
Google Scholar
[14] Weng X F, Li T F, Zhong Z Q, Zhang B 2017 Appl. Opt. 56 8902
Google Scholar
[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
Google Scholar
[16] Jiang X J, Li J H, Li H G, Li Y, Lin Z Q 2011 Appl. Opt. 50 5213
Google Scholar
[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
Google Scholar
Jiang X J, Li J H, Li H G, Zhou S L, Li Y, Lin Z Q 2012 Acta Phys. Sin. 61 124202
Google Scholar
[18] Zhou S L, Lin Z Q, Jiang X J 2007 Opt. Commun. 272 186
Google Scholar
[19] 陈泽尊, 向春, 邓锡铭 1985 中国激光 13 65
Google Scholar
Chen Z Z, Xiang C, Deng X M 1985 Chin. J. Las. 13 65
Google Scholar
[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
Google Scholar
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