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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.
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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
Figure 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 $的空间分布
Figure 2. Imaging resolution and time delay calibration: (a) Image of the USAF 1951 resolution target, where the imaging system resolves down to the Group 7 Element 1 (128 lp/mm) in the horizontal direction; (b) spatial distribution of transmitted light intensity variation (∆I) measured via the polarization gating (PG) method; (c) time delay calibration using PG, where the 9 curves represents 9 different measurements of ∆I vs. space with delay increment of 33.3 fs.
图 3 石英片厚度对延时零点标定精度的影响, 即探测光和泵浦光在融石片不同厚度的地方具有不同的延时
Figure 3. Effect of quartz plate thickness on the accuracy of the delay zero point. Probe light and pump light experience different delays at different thicknesses of the quartz plate.
图 4 样品平面与标定平面不重合时带来的延时误差, 其中O点是利用偏振门方案标定的延时零点, A点是透射相机“认为”的样品上的延时零点, B点是反射相机“认为”的样品上的延时零点
Figure 4. Delay error introduced when sample plane and calibration plane do not coincide. Point O is the delay zero point calibrated using the polarization gate method, Point A is the delay zero point on the sample perceived by the transmission camera, Point B is the delay zero point on the sample perceived by the reflection camera.
图 5 突变结构的成像模拟 (a)一个瞬时突变结构(real)经过成像系统后的像(imaged)带有衍射振荡结构; (b) 5—20 fs缓变结构的像
Figure 5. Imaging simulation of abrupt structures: (a) An instantaneous abrupt structure (real) after passing through the imaging system, the image (imaged) exhibits a diffractive oscillatory structure; (b) images of 5, 10, 12, 15 and 20 fs gradually varying structures.
表 1 单发测量温稠密交流电导率演化的误差分析
Table 1. Error analysis of conductivity evolution in single-shot measurements of warm dense matter.
系统物理量 误差来源 依赖关系 典型值 系统时间分辨率$ \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{f}}{\mathrm{s}}; {\tau }_{2}=5{\mathrm{f}}{\mathrm{s}} $
$ \chi =2.1{\mathrm{ }}{\mathrm{f}}{\mathrm{s}}/\text{μm} $,
$ \Delta x=4\text{μm} $
$ \Delta \tau =13.8{\mathrm{f}}{\mathrm{s}} $探测光脉宽$ {\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}\left[{\mathrm{f}}{\mathrm{s}}\right]\approx 0.42 L\left[\text{μm}\right] $ $ L=30\text{ μm} $
$ \Delta {\tau }_{0}=12.7\;{\mathrm{f}}{\mathrm{s}} $透射延时零点定位误差$ \Delta {\tau }_{0 T} $ 成像定位精度$ d $ $ {\Delta \tau }_{0 T}\left[{\mathrm{f}}{\mathrm{s}}\right]\approx -0.72 d\left[\text{μm}\right] $, $ d=35\text{ μm} $
$ \Delta {\tau }_{0 T}=25.2{\mathrm{f}}{\mathrm{s}} $反射延时零点定位误差$ \Delta {\tau }_{0 R} $ $ {\Delta \tau }_{0 R}\left[{\mathrm{f}}{\mathrm{s}}\right]\approx 0.038 d\left[\text{μm}\right] $ $ d=35\text{ μm} $
$ \Delta {\tau }_{0 T}=1.33{\mathrm{f}}{\mathrm{s}} $动力学突变的时间分辨率$ \Delta {\tau }_{{\mathrm{f}}} $ 成像系统数值孔径$ {\mathrm{N}}{\mathrm{A}} $ $ \Delta {\tau }_{{\mathrm{f}}}\propto \dfrac{1}{{\mathrm{N}}{\mathrm{A}}} $ $ {\mathrm{N}}{\mathrm{A}}=0.1 $
$ \Delta {\tau }_{{\mathrm{f}}} > 20{\mathrm{f}}{\mathrm{s}} $
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