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基于空间啁啾的单发泵浦-探测技术是探究物质在强激光泵浦下达到温稠密态过程中电子非平衡动力学的重要手段, 其时间分辨率已达到百飞秒量级. 本文详细阐述了温稠密物质交流电导率的空间啁啾单发测量原理及高时间分辨实验装置, 并对影响系统时间分辨率的关键因素进行深入剖析. 分析表明, 基于超短泵浦-探测脉冲, 该系统可实现13.8 fs的时间分辨率. 然而, 在实际实验中, 延时零点的精确标定、成像系统的景深限制以及低通滤波效应等因素, 均会对系统的时间分辨能力产生显著影响. 本研究不仅为提升温稠密物质交流电导率单发测量的时间精度提供了理论依据和实践指导, 而且为探索强场条件下材料的超快动力学过程奠定了坚实的技术基础.The spatial chirp based single-shot pump-probe technique represents a pivotal technology for studying electron non-equilibrium dynamics in warm dense matter created with intense laser pulses. Notably, its time resolution can reach tens of femtoseconds. In this work, we introduce the single-shot measurement technique of ac conductivity of warm dense matter, as well as a detailed account of the experimental setup. In addition, the main factors limiting the time resolution of the system are discussed in depth. We show the system can achieve a resolution of 13.8 femtoseconds. Nevertheless, during practical application, several aspects, namely the calibration of the zero-delay, the depth of field of the imaging system, and the low-pass filtering effect inherent in the imaging system, will exert a substantial influence on the time-resolution. This research has important reference for enhancing the time accuracy of single-shot measurement of ac conductivity of warm dense matter. Moreover, it serves as a potent tool for the in-depth study of the ultrafast dynamic processes of materials under strong-field conditions.
[1] 陈其峰, 顾云军, 郑君, 李江涛, 李治国, 权伟龙, 付志坚, 李成军 2017 科学通报 62 812
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[8] Wu D, Yu W, Sheng Z M, Fritzsche S, He X T 2020 Phys. Rev. E 101 051202
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[16] Ng A, Sterne P, Hansen S, Recoules V, Chen Z, Tsui Y Y, Wilson B 2016 Phys. Rev. E 94 03321
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[20] Widmann K, Ao T, Foord M E, Price D F, Ellis A D, Springer P T, Ng A 2004 Phys. Rev. Lett. 92 125002
Google Scholar
[21] Ping Y, Hanson D, Koslow I, Ogitsu T, Prendergast D, Schwegler E, Collins G, Ng A 2006 Phys. Rev. Lett. 96 255003
Google Scholar
[22] Chen Z, Holst B, Kirkwood S E, Sametoglu V, Reid M, Tsui Y Y, Recoules V, Ng A 2013 Phys. Rev. Lett. 110 135001
Google Scholar
[23] Chen Z, Sametoglu V, Tsui Y Y, Ao T, Ng A 2012 Phys. Rev. Lett. 108 165001
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图 1 WDM交流电导率时间演化的单发测量原理 (a) 实验系统示意图, 其中CM1和CM2为两个柱面镜, RCam和Tcam分别为反射光成像相机和透射光成像相机; (b) 空间啁啾把不同延时映射在不同空间位置上的原理
Fig. 1. Single-shot measurement principle for time-dependent AC conductivity evolution in WDM: (a) Schematic of the experimental system, where CM1 and CM2 are two cylindrical mirrors, and RCam and Tcam are the reflection light imaging camera and transmission light imaging camera, respectively; (b) principle of spatial chirp which maps different time delays to different spatial positions.
图 2 成像分辨率与延时标定 (a) USAF 1951分辨率板的像, 成像系统在水平方向能分辨至第7组第1个元素 (128 lp/mm); (b) 在偏振选通法(PG)中测得的透射光光强变化($ \Delta I $)随空间的分布; (c) 利用PG标定延时, 图中9条曲线代表9个间隔为33.3 fs的不同延时点测得的$ \Delta I $的空间分布
Fig. 2. Imaging resolution and time delay calibration: (a) Image of the USAF 1951 resolution target, where the imaging system resolves down to the Group 7 Element 1 (128 lp/mm) in the horizontal direction; (b) spatial distribution of transmitted light intensity variation (∆I ) measured via the polarization gating (PG) method; (c) time delay calibration using PG, where the 9 curves represents 9 different measurements of ∆I vs. space with delay increment of 33.3 fs.
图 3 石英片厚度对延时零点标定精度的影响, 即探测光和泵浦光在融石片不同厚度的地方具有不同的延时
Fig. 3. Effect of quartz plate thickness on the accuracy of the delay zero point. Probe light and pump light experience different delays at different thicknesses of the quartz plate.
图 4 样品平面与标定平面不重合时带来的延时误差, 其中O点是利用偏振门方案标定的延时零点, A点是透射相机“认为”的样品上的延时零点, B点是反射相机“认为”的样品上的延时零点
Fig. 4. Delay error introduced when sample plane and calibration plane do not coincide. Point O is the delay zero point calibrated using the polarization gate method, Point A is the delay zero point on the sample perceived by the transmission camera, Point B is the delay zero point on the sample perceived by the reflection camera.
图 5 突变结构的成像模拟 (a)一个瞬时突变结构(real)经过成像系统后的像(imaged)带有衍射振荡结构; (b) 5—20 fs缓变结构的像
Fig. 5. Imaging simulation of abrupt structures: (a) An instantaneous abrupt structure (real) after passing through the imaging system, the image (imaged) exhibits a diffractive oscillatory structure; (b) images of 5, 10, 12, 15 and 20 fs gradually varying structures.
表 1 单发测量温稠密交流电导率演化的误差分析
Table 1. Error analysis of conductivity evolution in single-shot measurements of warm dense matter.
系统物理量 误差来源 依赖关系 典型值 系统时间分辨率$ \Delta \tau $ 泵浦光脉宽$ {\tau }_{1} $ $ \Delta \tau =\sqrt{{\tau }_{1}^{2}+{\tau }_{2}^{2}+{\left(\chi {{\Delta }}x\right)}^{2}} $ $ {\tau }_{1}=9.7\;{\mathrm{fs}}; {\tau }_{2}=5\;{\mathrm{fs}} $
$ \chi =2.1\;{\mathrm{fs/μm}}, $
$ \Delta x=4\;\text{μm},\; \Delta \tau =13.8\;{\mathrm{fs}} $探测光脉宽$ {\tau }_{2} $ 成像系统分辨率$ \Delta x $ 延时零点标定误差$ \Delta {\tau }_{0} $ 融石英片厚度$ L $ $ \Delta {\tau }_{0}[{\mathrm{fs}}]\approx 0.42 L\;[\text{μm}] $ $ L=30\text{ μm},\; \Delta {\tau }_{0}=12.7\;{\mathrm{fs}} $ 透射延时零点定位误差$ \Delta {\tau }_{\rm 0T} $ 成像定位精度$ d $ $ {\Delta \tau }_{\rm 0T}\left[{\mathrm{fs}}\right]\approx -0.72 d\left[\text{μm}\right] $, $ d=35\text{ μm}, \; \Delta {\tau }_{\rm 0T}=25.2\;{\mathrm{fs}} $ 反射延时零点定位误差$ \Delta {\tau }_{\rm 0R} $ $ {\Delta \tau }_{\rm 0R} \left[{\mathrm{fs}}\right]\approx 0.038 d\left[\text{μm}\right] $ $ d=35\text{ μm} ,\; \Delta {\tau }_{\rm 0T}=1.33\;{\mathrm{fs}} $ 动力学突变的时间分辨率$ \Delta {\tau }_{{\mathrm{f}}} $ 成像系统数值孔径$ NA $ $ \Delta {\tau }_{{\mathrm{f}}}\propto {1}/{{{NA}}} $ $ {{NA}}=0.1 ,\; \Delta {\tau }_{{\mathrm{f}}} > 20\;{\mathrm{fs}} $ 
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[1] 陈其峰, 顾云军, 郑君, 李江涛, 李治国, 权伟龙, 付志坚, 李成军 2017 科学通报 62 812
Google Scholar
Chen Q F, Gu Y J, Zheng J, Li J T, Li Z G, Quan W L, Fu Z J, Li C J 2017 Chin. Sci. Bull. 62 812
Google Scholar
[2] Kang D, Dai J 2018 J. Phys. Condens. Matter 30 073002
Google Scholar
[3] Ichimaru S 1982 Rev. Mod. Phys. 54 1017
Google Scholar
[4] Koenig M, Benuzzi-Mounaix A, Ravasio A, Vinci T, Ozaki N, Lepape S, Batani D, Huser G, Hall T, Hicks D, MacKinnon A, Patel P, Park H S, Boehly T, Borghesi M, Kar S, Romagnani L 2005 Plasma Phys. Control. Fusion 47 B441
Google Scholar
[5] Falk K 2018 High Power Laser Sci. Eng. 6 e59
Google Scholar
[6] 康冬冬, 曾启昱, 张珅, 王小伟, 戴佳钰 2020 强激光与粒子束 32 092006
Google Scholar
Kang D D, Zeng Q Y, Zhang S, Wang X W, Dai J Y 2020 High Power Laser Part. Beams 32 092006
Google Scholar
[7] Lee R W, Moon S J, Chung H K, Rozmus W, Baldis H A, Gregori G, Cauble R C, Landen O L, Wark J S, Ng A, Rose S J, Lewis C L, Riley D, Gauthier J C, Audebert P 2003 J. Opt. Soc. Am. B 20 770
Google Scholar
[8] Wu D, Yu W, Sheng Z M, Fritzsche S, He X T 2020 Phys. Rev. E 101 051202
Google Scholar
[9] Fletcher L B, Lee H J, Döppner T, Galtier E, Nagler B, Heimann P, Fortmann C, LePape S, Ma T, Millot M, Pak A, Turnbull D, Chapman D A, Gericke D O, Vorberger J, White T, Gregori G, Wei M, Barbrel B, Falcone R W, Kao C C, Nuhn H, Welch J, Zastrau U, Neumayer P, Hastings J B, Glenzer S H 2015 Nat. Photonics 9 274
Google Scholar
[10] Graziani F, Moldabekov Z, Olson B, Bonitz M 2022 Contrib. Plasma Phys. 62 e202100170
Google Scholar
[11] Dornheim T, Böhme M, Kraus D, Döppner T, Preston T R, Moldabekov Z A, Vorberger J 2022 Nat. Commun. 13 7911
Google Scholar
[12] Mercadier L, Benediktovitch A, Krušič Š, Kas J J, Schlappa J, Agåker M, Carley R, Fazio G, Gerasimova N, Kim Y Y, Le Guyader L, Mercurio G, Parchenko S, Rehr J J, Rubensson J E, Serkez S, Stransky M, Teichmann M, Yin Z, Žitnik M, Scherz A, Ziaja B, Rohringer N 2024 Nat. Phys. 20 1564
Google Scholar
[13] Forsman A, Ng A, Chiu G, More R M 1998 Phys. Rev. E 58 R1248
Google Scholar
[14] Ping Y, Correa A A, Ogitsu T, Draeger E, Schwegler E, Ao T, Widmann K, Price D F, Lee E, Tam H, Springer P T, Hanson D, Koslow I, Prendergast D, Collins G, Ng A 2010 High Energy Density Phys. 6 246
Google Scholar
[15] Ofori-Okai B K, Descamps A, McBride E E, Mo M Z, Weinmann A, Seipp L E, Ali S J, Chen Z, Fletcher L B, Glenzer S H 2024 Phys. Plasmas 31 042711
Google Scholar
[16] Ng A, Sterne P, Hansen S, Recoules V, Chen Z, Tsui Y Y, Wilson B 2016 Phys. Rev. E 94 03321
Google Scholar
[17] 孙旭, 吴海忠, 王小伟, 吕治辉, 张栋文, 刘东晓, 范伟, 粟敬钦, 周维民, 谷渝秋, 赵增秀, 袁建民 2023 中国激光 50 1714013
Google Scholar
Sun X, Wu H Z, Wang X W, Lü Z H, Zhang D W, Liu D X, Fan W, Su J Q, Zhou W M, Gu Y Q, Zhao Z X, Yuan J M 2023 Chin. J. Lasers 50 1714013
Google Scholar
[18] Ofori-Okai B K, Descamps A, Lu J, Seipp L E, Weinmann A, Glenzer S H, Chen Z 2018 Rev. Sci. Instrum. 89 10D109
Google Scholar
[19] Ao T, Ping Y, Widmann K, Price D F, Lee E, Tam H, Springer P T, Ng A 2006 Phys. Rev. Lett. 96 055001
Google Scholar
[20] Widmann K, Ao T, Foord M E, Price D F, Ellis A D, Springer P T, Ng A 2004 Phys. Rev. Lett. 92 125002
Google Scholar
[21] Ping Y, Hanson D, Koslow I, Ogitsu T, Prendergast D, Schwegler E, Collins G, Ng A 2006 Phys. Rev. Lett. 96 255003
Google Scholar
[22] Chen Z, Holst B, Kirkwood S E, Sametoglu V, Reid M, Tsui Y Y, Recoules V, Ng A 2013 Phys. Rev. Lett. 110 135001
Google Scholar
[23] Chen Z, Sametoglu V, Tsui Y Y, Ao T, Ng A 2012 Phys. Rev. Lett. 108 165001
Google Scholar
[24] Dhar L, Fourkas J T, Nelson K A 1994 Opt. Lett. 19 643
Google Scholar
[25] Lindenberg A M, Larsson J, Sokolowski-Tinten K, Gaffney K J, Blome C, Synnergren O, Sheppard J, Caleman C, MacPhee A G, Weinstein D, Lowney D P, Allison T K, Matthews T, Falcone R W, Cavalieri A L, Fritz D M, Lee S H, Bucksbaum P H, Reis D A, Rudati J, Fuoss P H, Kao C C, Siddons D P, Pahl R, Als-Nielsen J, Duesterer S, Ischebeck R, Schlarb H, Schulte-Schrepping H, Tschentscher Th, Schneider J, Von Der Linde D, Hignette O, Sette F, Chapman H N, Lee R W, Hansen T N, Techert S, Wark J S, Bergh M, Huldt G, Van Der Spoel D, Timneanu N, Hajdu J, Akre R A, Bong E, Krejcik P, Arthur J, Brennan S, Luening K, Hastings J B 2005 Science 308 392
Google Scholar
[26] Chen Z, Hering P, Brown S B, Curry C, Tsui Y Y, Glenzer S H 2016 Rev. Sci. Instrum. 87 11E548
Google Scholar
[27] Liu Y Y, Zhao K, He P, Huang H D, Teng H, Wei Z Y 2017 Chin. Phys. Lett. 34 074204
Google Scholar
[28] Wang Y, Wang S, Rockwood A, Luther B M, Hollinger R, Curtis A, Calvi C, Menoni C S, Rocca J J 2017 Opt. Lett. 42 3828
Google Scholar
[29] Xiao F, Fan X H, Wang L, Zhang D W, Wu J H, Wang X W, Zhao Z X 2020 Chin. Phys. Lett. 37 114202
Google Scholar
[30] Chang H T, Zürch M, Kraus P M, Borja L J, Neumark D M, Leone S R 2016 Opt. Lett. 41 5365
Google Scholar
[31] Wang X W, Wang L, Xiao F, Zhang D W, Lue Z H, Yuan J M, Zhao Z X 2020 Chin. Phys. Lett. 37 023201
Google Scholar
[32] Born M, Wolf E 1999 Principles of Optics (Cambridge: Cambridge University Press
[33] Shillaber C P 1945 Photomicrography: In Theory and Practice (New York: Wiley
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