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Herriott multi-pass block material stretcher and grism compressor in chirped-pulse amplification

Zhang Peng Teng Hao Yang Hao Lü Ren-Chong Wang Ke-Jian Zhu Jiang-Feng Wei Zhi-Yi

Zhang Peng, Teng Hao, Yang Hao, Lü Ren-Chong, Wang Ke-Jian, Zhu Jiang-Feng, Wei Zhi-Yi. Herriott multi-pass block material stretcher and grism compressor in chirped-pulse amplification. Acta Phys. Sin., 2022, 71(11): 114202. doi: 10.7498/aps.71.20212381
Citation: Zhang Peng, Teng Hao, Yang Hao, Lü Ren-Chong, Wang Ke-Jian, Zhu Jiang-Feng, Wei Zhi-Yi. Herriott multi-pass block material stretcher and grism compressor in chirped-pulse amplification. Acta Phys. Sin., 2022, 71(11): 114202. doi: 10.7498/aps.71.20212381

Herriott multi-pass block material stretcher and grism compressor in chirped-pulse amplification

Zhang Peng, Teng Hao, Yang Hao, Lü Ren-Chong, Wang Ke-Jian, Zhu Jiang-Feng, Wei Zhi-Yi
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  • We report a femtosecond chirped-pulse amplification (CPA) system based on block material stretcher and grism compression. An optical material block is employed in Herriott multi-reflection configuration as a pulse stretcher, and a transmission grating is combined with dispersion prism to form grism as a compressor which can provide the negative second and third-order dispersion. By optimizing the prism vertex angle and grating line density, the grism can completely compensate for the third-order material dispersion. We obtain shorter compressed pulses. In the experiment, the stretched pulses are amplified by regenerative amplifier, which amplifies the 800 nm seed pulse to 2.30 W under the 11.4 W, 527 nm, 1 kHz pumping conditions, and the spectral width of the amplified pulse is 26.7 nm. The amplified pulses are compressed to 39.6 fs, which is close to the Fourier transform limit of 35.2 fs. The design of the system simplifies the structure of the conventional chirped pulse amplification system, reduces the space size of the optical path, and improves the operational stability of the laser system. With the block material stretcher and grism compressor, the whole CPA laser system is very compact and can be used as a reliable light source for subsequent amplification as well as ultrafast phenomenon studies.
      PACS:
      42.60.-v(Laser optical systems: design and operation)
      42.65.Re(Ultrafast processes; optical pulse generation and pulse compression)
      42.55.Rz(Doped-insulator lasers and other solid state lasers)
      42.55.-f(Lasers)
      Corresponding author: Teng Hao, hteng@iphy.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12034020, 11774277) and the Synergic Extreme Condition User Facility, China

    1985年, Strickland 和Mourou[1]发明的啁啾脉冲放大技术打破了超快激光能量放大的限制与瓶颈, 超快超强激光进入了高速发展阶段. 在过去的几十年里, 啁啾脉冲放大技术的发展使得超快超强激光脉冲的峰值功率不断提高, 峰值功率可达太瓦(1012 W, TW), 甚至拍瓦(1015 W, PW)量级的激光系统[2]不断涌现, 这使得超快超强激光逐渐成为前沿基础科学的重要研究工具, 已经成功应用于如原子分子运动规律[3]、实验室天体物理[4]、激光加速器[5]、自由电子激光器[6]等研究领域.

    在啁啾脉冲放大系统中, 首先是将脉冲宽度为飞秒量级的种子脉冲通过展宽器在时域上进行展宽, 然后注入到放大器中进行能量放大, 最后由压缩器提供与展宽器相反的色散进行补偿以获得与傅里叶变换极限相近的脉冲宽度, 所以色散的精确补偿是获得窄脉冲的首要条件, 也是评判飞秒放大系统成功的关键指标. 系统中的色散主要来自展宽器、压缩器以及材料, 但关键的是展宽器与压缩器之间的色散匹配. 在理想情况下, 压缩器的负色散完全补偿展宽器的正色散, 但由于放大过程中有大量的材料色散引入, 特别是高阶色散的引入, 所以展宽器与压缩器的设计要全面考虑系统中所有的色散, 包括高阶色散的影响.

    自啁啾脉冲放大技术发明以来, 已经发展了多种展宽与压缩技术方案. 在展宽器设计中, 其中一类时域展宽方案是基于镀金膜反射式衍射光栅的展宽器, 如Martinez型展宽器[7]、Öffner型展宽器[8]等. Martinez展宽器和Öffner展宽器的色散量都源于物光栅与像光栅的等效距离, 但此类结构的展宽器, 其衍射光栅都放置在偏离球面镜的球心处, 在偏离球心的位置产生一个与物光栅对应的像光栅. 由于物点、像点在光轴上的分离, 所以物光栅与像光栅之间存在不同程度的像差, 这种像差必然包含在色散项中[9]. 此类展宽器结构都存在一些缺点: 1) 与之匹配的光栅对压缩器并不能完全补偿高阶色散, 系统中残存冗余的高阶色散; 3) 由于采用了镀金膜反射式的衍射光栅, 其表面平整度较低, 经过展宽器后的脉冲引入了光谱相位噪声, 会降低压缩后的脉冲对比度; 3) 此类展宽器体积庞大, 不易调节, 稳定性较差. 另一类时域展宽器是基于材料色散的展宽器, 如利用光纤引入的正色散进行展宽[10]. 同样基于材料色散的展宽器还有块材料展宽器[11], 它是利用具有高折射率的块状玻璃材料, 通过通光长度的积累, 将短脉冲展宽成所需的长脉冲. 以SF57玻璃为例, 它能够提供的二阶色散为223.58 fs2/mm, 通光长度为50 cm的该材料能将10 fs的脉冲展宽至31 ps, 该系统中材料引入的群速色散及三阶色散均为正值, 但放大后的脉冲一般都采用双光栅的Treacy结构[12]进行脉冲压缩, 由于它只能提供负的二阶色散和正的三阶色散, 虽然通过优化两个光栅之间的距离以及角度, 可以完全补偿二阶色散, 但无法匹配三阶色散, 不能实现很好的压缩效果.

    因此, 本文发展了一种基于Herriott型多通结构的块材料展宽器. 与传统块材料展宽器利用大块玻璃材料单次通过实现时域展宽不同, 该结构将一小块玻璃材料置于Herriott型多次反射腔中, 激光脉冲通过反射的形式多次穿过块状材料引入材料色散. 这种结构不存在像差带来的色散影响, 同时具有缩小光路体积、色散量可调、节约成本的优点. 根据CPA系统引入的材料色散, 设计了与之匹配的棱栅对压缩器(grism)[13], 它可以同时提供负的二阶色散与三阶色散, 实现了接近傅里叶变换极限的压缩脉冲输出, 证明了基于Herriott型多通结构的块材料展宽与棱栅对色散补偿的啁啾脉冲放大方案是可行的.

    图1是基于Herriott型多通结构的块材料展宽器示意图, 该展宽器采用具有高折射率的H-ZF52A材料作为色散介质, 实验中将H-ZF52A材料加工成圆柱体, 口径为1 in, 通光厚度为20 mm. 将玻璃块置于由两块凹面反射镜组成的多次反射腔的束腰位置, 多条光束形成的包络为双曲面, 其截面为圆, 精细调节凹面反射镜之间的距离, 使两个凹面反射镜上的光斑个数为25, 表明此时种子光25次通过块状材料, 对应的总透射长度为500 mm, 从而实现时域展宽.

    图 1 基于Herriott型多通结构的块材料展宽器示意图\r\nFig. 1. Schematic diagram of block material stretcher based on Herriott.
    图 1  基于Herriott型多通结构的块材料展宽器示意图
    Fig. 1.  Schematic diagram of block material stretcher based on Herriott.

    通过对H-ZF52A材料的折射率方程求各阶偏导数, 得到其引入的各阶色散值. 图2表示在不同波长下, 每毫米的H-ZF52A材料引入的二阶色散量与三阶色散量.

    图 2 H-ZF52A材料引入的二、三阶色散分布曲线\r\nFig. 2. Second and third order dispersion introduced by H-ZF52A material.
    图 2  H-ZF52A材料引入的二、三阶色散分布曲线
    Fig. 2.  Second and third order dispersion introduced by H-ZF52A material.

    对于中心波长为800 nm的钛宝石激光器, 长度为1 mm的H-ZF52A材料引入的二阶色散量为220.40 fs2, 三阶色散量为145.04 fs3, 其中三阶色散量与二阶色散的比值为0.658 fs. 实验中, 设计其总通光长度为500 mm, 引入的二阶色散量为1.1 × 105 fs2, 该色散量能将20 fs的激光脉冲展宽至15.5 ps. 除了材料的色散特性, 在设计时还应考虑材料的吸收损耗与表面反射损耗. H-ZF52A材料的吸收系数为0.02002 mm–1, 500 mm的通光长度对应的吸收损耗为9.5%. 在750—850 nm范围内, 材料镀膜后的反射率小于0.2%. 为减少反射损耗, 实验中选定块状材料的厚度为20 mm. 实现500 mm的通光长度仅需透射块状材料25次, 同时选取曲率半径R = 300 mm的两块凹面镜作为腔镜. 为满足腔型的稳定性条件, 选取腔长L = 500 mm. 在该参数下, 腔内本征模光斑在凹面反射镜上的光斑半径为413 μm, 束腰处光斑半径为169 μm. 该设计可以保证在损耗较小的情况下尽可能缩小光路体积, 实现光路小型化.

    在设计脉冲压缩装置时要考虑其与脉冲展宽器色散特性的匹配, 只有两者引入的色散实现精确互补, 压缩后的脉宽才有可能接近傅里叶变换极限脉宽. 基于上述分析, 设计了图3所示的棱栅对(grism)压缩器[14-18]. 该装置由两块透射光栅、两块色散棱镜和爬低镜构成, 两块光栅平行放置且光栅表面均平行于相邻的棱镜入射面, 两块棱镜反向平行放置, 棱镜P2、光栅G2与光栅G1、棱镜P1在空间上具有旋转对称的关系. 在长条状光斑出射方向安装爬低镜, 光线爬低后原路返回再次通过棱栅对压缩器, 同时便于在空间上分离出射光和入射光.

    图 3 棱栅对压缩器示意图(RM, 反射镜; P, 棱镜; G, 光栅)\r\nFig. 3. Schematic diagram of grism compressor (RM, mirror; P, prism; G, grating).
    图 3  棱栅对压缩器示意图(RM, 反射镜; P, 棱镜; G, 光栅)
    Fig. 3.  Schematic diagram of grism compressor (RM, mirror; P, prism; G, grating).

    为获得最大的光栅衍射效率、提高脉冲压缩效率, 以中心波长的Littrow角入射透射光栅G1. 该压缩器的设计变量包括: 光栅G1与棱镜P1之间的距离h1, 光栅G2与棱镜P2之间的距离h2, 棱镜P1与棱镜P2之间的距离L, 棱镜P1与棱镜P2的顶角大小α, 棱镜P1与棱镜P2的材质(折射率), 入射角θ1, 透射光栅的光栅常数, 棱镜P1与棱镜P2的顶点之间的距离O1O2. 在模拟过程中发现h1, h2的改变对棱栅对提供的色散值几乎没有影响[19]. 因此, 在给定光栅刻线密度和棱镜材质的情况下, 仅需调整α, L, O1O2这三个参数就可以调整Grism提供的色散. 图4是模拟的Grism内部的光线追迹图.

    图 4 棱栅对内部光线追迹图\r\nFig. 4. Internal ray tracing of grism.
    图 4  棱栅对内部光线追迹图
    Fig. 4.  Internal ray tracing of grism.

    此外, 在CPA系统中, 压缩器的色散补偿还需考虑放大器中引入的材料色散. 放大器中涉及的材料色散器件有钛宝石晶体、普克尔盒晶体、格兰棱镜、透镜以及石英窗口等, 种子光在再生腔内总共被放大20次, 引入的材料色散如表1所列.

    表 1  kHz钛宝石放大器引入的材料色散
    Table 1.  Material dispersion introduced by kHz Ti: sapphire amplifier.
    材料色散长度/mmGDD/(fs2·mm–1)TOD/(fs3·mm–1)GDD/fs2TOD/fs3
    钛宝石晶体40058.0442.132321616852
    真空窗口6036.1627.502169.61650
    普克尔盒40027.3648.661094419464
    格兰棱镜60036.1627.502169616500
    总色散量58025.654466
    下载: 导出CSV 
    | 显示表格

    在考虑放大器和展宽器中材料色散基础上, 选用1250 线/mm的透射光栅和顶角为30°的色散棱镜组合成的棱栅对来实现压缩[20,21]. 表2代表啁啾脉冲放大系统中各个部分引入的色散值. 数值模拟表明, 通过优化棱栅对之间的距离和角度, 可以实现对展宽器与放大器引入的二阶色散与三阶色散较好的补偿, 理论上可以实现接近傅里叶变换极限脉宽的脉冲输出.

    表 2  啁啾脉冲放大系统各部分引入的色散
    Table 2.  Dispersion introduced by each part of chirped pulse amplification system.
    材料色散GDD/fs2TOD/fs3
    块材料展宽器+110200+72520
    再生放大器+58025.6+54466
    棱栅对压缩器–168225.6–126717
    总色散0+269
    下载: 导出CSV 
    | 显示表格

    为验证上述设计, 设计了采用Herriott型多通结构块材料展宽与棱栅对色散补偿的啁啾脉冲放大系统, 如图5所示. 该系统由钛宝石飞秒振荡器、Herriott型多通结构块材料展宽器、钛宝石再生放大器、棱栅对压缩器等四部分组成.

    图 5 基于Herriott型多通结构的块材料展宽与棱栅对色散补偿的啁啾脉冲放大系统(ISO, 隔离器; M, 反射镜; CM, 凹面反射镜; GP, 格兰棱镜; G, 光栅; PC, 普克尔盒; P, 棱镜)\r\nFig. 5. Schematic of the CPA system based on Herriott multi-pass block material stretcher and grism compressor (ISO, Isolator; M, mirror; CM, concave mirror; GP, Glan prism; G, grating; PC, Pockels cell; P, prism).
    图 5  基于Herriott型多通结构的块材料展宽与棱栅对色散补偿的啁啾脉冲放大系统(ISO, 隔离器; M, 反射镜; CM, 凹面反射镜; GP, 格兰棱镜; G, 光栅; PC, 普克尔盒; P, 棱镜)
    Fig. 5.  Schematic of the CPA system based on Herriott multi-pass block material stretcher and grism compressor (ISO, Isolator; M, mirror; CM, concave mirror; GP, Glan prism; G, grating; PC, Pockels cell; P, prism).

    在该系统中, 种子源采用的是克尔透镜锁模的钛宝石飞秒振荡器, 锁模后可稳定输出平均功率为320 mW、重复频率85.5 MHz, 脉冲宽度小于20 fs的飞秒激光脉冲, 光谱半高全宽约100 nm. 图6(a)为钛宝石振荡器的锁模光谱, 图6(b)为锁模脉冲序列.

    图 6 (a) 钛宝石振荡器的锁模光谱; (b) 锁模脉冲序列\r\nFig. 6. (a) Mode-locking spectrum of Ti: sapphire oscillator; (b) mode-locking pulse.
    图 6  (a) 钛宝石振荡器的锁模光谱; (b) 锁模脉冲序列
    Fig. 6.  (a) Mode-locking spectrum of Ti: sapphire oscillator; (b) mode-locking pulse.

    将种子光注入到基于Herriott型多通结构的块材料展宽器中, 得到图7所示的光谱图, 可见展宽器输出的光谱与振荡器输出光谱基本保持一致. 相比于Martinez型等基于反射式衍射光栅的展宽器, 此类展宽器避免了由于器件切光导致的光谱缺失问题. 入射的种子光功率为320 mW, 时域展宽后功率为287 mW, 透光效率达89.69%.

    图 7 块材料展宽器输出光谱图\r\nFig. 7. Output spectrum of block material stretcher.
    图 7  块材料展宽器输出光谱图
    Fig. 7.  Output spectrum of block material stretcher.

    当泵浦功率为11.4 W时, 钛宝石再生放大器的输出功率为2.3 W, 光光转换效率为20.18%, 将放大后的脉冲以中心波长的Littrow角注入到棱栅对中. 将棱栅对中的第一组棱镜-光栅固定, 通过安装架微调光栅与棱镜的姿态. 第二组棱镜-光栅安装在同一个二维平移台上, 通过精细调节与第一组棱镜-光栅之间的间距以及第二块棱镜的插入量实现系统内色散的精确补偿.

    由于种子脉冲在再生放大器中放大时有较强的增益窄化效应, 放大器输出的光谱宽度仅为26.7 nm, 见图8(a). 图8(b)是使用商用脉宽测量装置Wizzler测得的压缩后的脉冲宽度. 压缩后脉冲宽度为39.6 fs, 非常接近傅里叶变换极限脉冲宽度35.2 fs, 说明棱栅对压缩器可以实现色散的精确补偿. 入射棱栅对压缩器的激光功率为2.30 W, 出射激光功率为1.81 W, 透光效率为78.69%.

    图 8 (a) 注入棱栅对前的光谱; (b) 棱栅对的脉冲压缩结果\r\nFig. 8. (a) Spectrum before injection into grism; (b) pulse compression results of grism.
    图 8  (a) 注入棱栅对前的光谱; (b) 棱栅对的脉冲压缩结果
    Fig. 8.  (a) Spectrum before injection into grism; (b) pulse compression results of grism.

    图9是采用Coherent公司的LabMax-TOP功率计测量的Grism压缩后的1 h输出功率稳定性, 输出功率均方根(RMS)差为0.36%.

    图 9 压缩后脉冲的功率稳定性\r\nFig. 9. Power stability of compressed pulse.
    图 9  压缩后脉冲的功率稳定性
    Fig. 9.  Power stability of compressed pulse.

    本文报道了一种基于块材料展宽-棱栅对压缩的飞秒激光放大系统, 采用基于Herriott型多通结构的块材料作为展宽器, 透射光栅与棱镜组成的棱栅对作为压缩器, 可以实现色散的精确补偿, 输出更窄的压缩脉冲. 在实验中, 该放大系统在11.4 W, 527 nm, 1 kHz的泵浦条件下, 将800 nm的种子脉冲放大至2.30 W, 放大后脉冲的光谱宽度为26.7 nm, 经过棱栅对压缩器的压缩将放大激光脉冲宽度压缩至39.6 fs, 非常接近傅里叶变换极限. 该系统的设计简化了传统啁啾脉冲放大系统的结构, 在一定程度上缩小了光路体积, 提高了激光器的运行稳定性, 可以用于太瓦或拍瓦激光系统的前端、载波包络相位锁定、超快现象等应用的研究.

    感谢郑加安博士的指导与讨论. 

    [1]

    Strickland D, Mourou G 1985 Opt. Commun. 55 447Google Scholar

    [2]

    Jeong T M, Yu T J, Lee S K, Sung J H, Lee J 2012 Opt. Lett. 20 10807

    [3]

    Schultze M, Bothschafter E M, Sommer A, et al. 2013 Nature 493 75Google Scholar

    [4]

    Remington B A, Drake R P, Takabe H, Arnett D 2000 Phys. Plasmas 7 1641Google Scholar

    [5]

    Clark E L, Krushelnick K, Zepf M, Beg F N, Tatarakis M, Machacek A, Santala M I K, Watts I, Noreys P A, Dangor A E 2000 Phys. Rev. Lett. 85 1654Google Scholar

    [6]

    Murnane M M, Kapteyn H C, Rosen M D, Falcone R W 1991 Science 251 531Google Scholar

    [7]

    宋晏蓉, 张志刚, 王清月 2003 物理学报 52 581Google Scholar

    Song Y R, Zhang Z G, Wang Q Y 2003 Acta Phys. Sin. 52 581Google Scholar

    [8]

    Cheriaux G, Rousseau P, Salin F, Chambaret J P, Dimauro L F 1996 Opt. Lett. 21 414Google Scholar

    [9]

    Du D T, Squier J, Kane S, Korn G, Mourou G, Bogusch C, Cotton C T 1995 Opt. Lett. 20 2114Google Scholar

    [10]

    Grüner-Nielsen L, Jakobsen D, Jespersen K G, Pálsdóttir B 2010 Opt. Express 18 3768Google Scholar

    [11]

    Hentschel M, Cheng Z, Krausz F, Spielmann C 2000 Appl. Phys. B 70 S161Google Scholar

    [12]

    Imeshev G, Hartl I, Fermann M E 2004 Opt. Lett. 29 679Google Scholar

    [13]

    Ricci A, Jullien A, Forget N, Crozatier V, Tournois P, Lopez-Martens R 2012 Opt. Lett. 37 1196Google Scholar

    [14]

    Forget N, Crozatier V, Tournois P 2012 Appl. Phys. B 109 121Google Scholar

    [15]

    秦爽, 宁笑楠, 陈九成 2019 光子学报 48 0914001Google Scholar

    Qin S, Ning X N, Chen J C 2019 Acta Photonica Sin. 48 0914001Google Scholar

    [16]

    郭淑艳, 叶蓬, 滕浩, 张伟, 李德华, 王兆华, 魏志义 2013 物理学报 62 094202Google Scholar

    Guo S Y, Ye P, Teng H, Zhang W, Li D H, Wang Z H, Wei Z Y 2013 Acta Phys. Sin. 62 094202Google Scholar

    [17]

    苏娟, 刘忠华, 魏涛 2015 激光与光电子学进展 52 060501Google Scholar

    Su J, Liu Z H, Wei T, Li J F 2015 Laser Optoelectron. Process 52 060501Google Scholar

    [18]

    Lefort C, Mansuryan T, Louradour F, Barthelemy A 2011 Opt. Lett. 36 292Google Scholar

    [19]

    Kuznetsova L, Wise F, Kane S, Squier J 2007 Advanced Solid-state Photonics January 1, 2007

    [20]

    Bagnoud V, Salin F 1998 IEEE J. Sel. Top. Quantum Electron. 4 445Google Scholar

    [21]

    Zheng J, Zacharias H 2009 Appl. Phys. B 96 445Google Scholar

  • 图 1  基于Herriott型多通结构的块材料展宽器示意图

    Figure 1.  Schematic diagram of block material stretcher based on Herriott.

    图 2  H-ZF52A材料引入的二、三阶色散分布曲线

    Figure 2.  Second and third order dispersion introduced by H-ZF52A material.

    图 3  棱栅对压缩器示意图(RM, 反射镜; P, 棱镜; G, 光栅)

    Figure 3.  Schematic diagram of grism compressor (RM, mirror; P, prism; G, grating).

    图 4  棱栅对内部光线追迹图

    Figure 4.  Internal ray tracing of grism.

    图 5  基于Herriott型多通结构的块材料展宽与棱栅对色散补偿的啁啾脉冲放大系统(ISO, 隔离器; M, 反射镜; CM, 凹面反射镜; GP, 格兰棱镜; G, 光栅; PC, 普克尔盒; P, 棱镜)

    Figure 5.  Schematic of the CPA system based on Herriott multi-pass block material stretcher and grism compressor (ISO, Isolator; M, mirror; CM, concave mirror; GP, Glan prism; G, grating; PC, Pockels cell; P, prism).

    图 6  (a) 钛宝石振荡器的锁模光谱; (b) 锁模脉冲序列

    Figure 6.  (a) Mode-locking spectrum of Ti: sapphire oscillator; (b) mode-locking pulse.

    图 7  块材料展宽器输出光谱图

    Figure 7.  Output spectrum of block material stretcher.

    图 8  (a) 注入棱栅对前的光谱; (b) 棱栅对的脉冲压缩结果

    Figure 8.  (a) Spectrum before injection into grism; (b) pulse compression results of grism.

    图 9  压缩后脉冲的功率稳定性

    Figure 9.  Power stability of compressed pulse.

    表 1  kHz钛宝石放大器引入的材料色散

    Table 1.  Material dispersion introduced by kHz Ti: sapphire amplifier.

    材料色散长度/mmGDD/(fs2·mm–1)TOD/(fs3·mm–1)GDD/fs2TOD/fs3
    钛宝石晶体40058.0442.132321616852
    真空窗口6036.1627.502169.61650
    普克尔盒40027.3648.661094419464
    格兰棱镜60036.1627.502169616500
    总色散量58025.654466
    DownLoad: CSV

    表 2  啁啾脉冲放大系统各部分引入的色散

    Table 2.  Dispersion introduced by each part of chirped pulse amplification system.

    材料色散GDD/fs2TOD/fs3
    块材料展宽器+110200+72520
    再生放大器+58025.6+54466
    棱栅对压缩器–168225.6–126717
    总色散0+269
    DownLoad: CSV
  • [1]

    Strickland D, Mourou G 1985 Opt. Commun. 55 447Google Scholar

    [2]

    Jeong T M, Yu T J, Lee S K, Sung J H, Lee J 2012 Opt. Lett. 20 10807

    [3]

    Schultze M, Bothschafter E M, Sommer A, et al. 2013 Nature 493 75Google Scholar

    [4]

    Remington B A, Drake R P, Takabe H, Arnett D 2000 Phys. Plasmas 7 1641Google Scholar

    [5]

    Clark E L, Krushelnick K, Zepf M, Beg F N, Tatarakis M, Machacek A, Santala M I K, Watts I, Noreys P A, Dangor A E 2000 Phys. Rev. Lett. 85 1654Google Scholar

    [6]

    Murnane M M, Kapteyn H C, Rosen M D, Falcone R W 1991 Science 251 531Google Scholar

    [7]

    宋晏蓉, 张志刚, 王清月 2003 物理学报 52 581Google Scholar

    Song Y R, Zhang Z G, Wang Q Y 2003 Acta Phys. Sin. 52 581Google Scholar

    [8]

    Cheriaux G, Rousseau P, Salin F, Chambaret J P, Dimauro L F 1996 Opt. Lett. 21 414Google Scholar

    [9]

    Du D T, Squier J, Kane S, Korn G, Mourou G, Bogusch C, Cotton C T 1995 Opt. Lett. 20 2114Google Scholar

    [10]

    Grüner-Nielsen L, Jakobsen D, Jespersen K G, Pálsdóttir B 2010 Opt. Express 18 3768Google Scholar

    [11]

    Hentschel M, Cheng Z, Krausz F, Spielmann C 2000 Appl. Phys. B 70 S161Google Scholar

    [12]

    Imeshev G, Hartl I, Fermann M E 2004 Opt. Lett. 29 679Google Scholar

    [13]

    Ricci A, Jullien A, Forget N, Crozatier V, Tournois P, Lopez-Martens R 2012 Opt. Lett. 37 1196Google Scholar

    [14]

    Forget N, Crozatier V, Tournois P 2012 Appl. Phys. B 109 121Google Scholar

    [15]

    秦爽, 宁笑楠, 陈九成 2019 光子学报 48 0914001Google Scholar

    Qin S, Ning X N, Chen J C 2019 Acta Photonica Sin. 48 0914001Google Scholar

    [16]

    郭淑艳, 叶蓬, 滕浩, 张伟, 李德华, 王兆华, 魏志义 2013 物理学报 62 094202Google Scholar

    Guo S Y, Ye P, Teng H, Zhang W, Li D H, Wang Z H, Wei Z Y 2013 Acta Phys. Sin. 62 094202Google Scholar

    [17]

    苏娟, 刘忠华, 魏涛 2015 激光与光电子学进展 52 060501Google Scholar

    Su J, Liu Z H, Wei T, Li J F 2015 Laser Optoelectron. Process 52 060501Google Scholar

    [18]

    Lefort C, Mansuryan T, Louradour F, Barthelemy A 2011 Opt. Lett. 36 292Google Scholar

    [19]

    Kuznetsova L, Wise F, Kane S, Squier J 2007 Advanced Solid-state Photonics January 1, 2007

    [20]

    Bagnoud V, Salin F 1998 IEEE J. Sel. Top. Quantum Electron. 4 445Google Scholar

    [21]

    Zheng J, Zacharias H 2009 Appl. Phys. B 96 445Google Scholar

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  • Abstract views:  6160
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Publishing process
  • Received Date:  24 December 2021
  • Accepted Date:  15 February 2022
  • Available Online:  04 March 2022
  • Published Online:  05 June 2022

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