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With the unveiling of molecular and atomic dynamics, scientists crave finer and faster tools to communicate with the microworld. Attosecond pump-probe enjoys its reputation as the fastest camera, hinting ultrafast movements in the delay graph. To employ this camera, the stability and delay control should have very great accuracy comparable to the camera resolution. It is also of significant importance for stabilizing the carrier envelope phase (CEP) in few-cycle laser field. When dealing with a huge quantity of data, conventional Fourier transform algorism is challenging in high-speed control. Here we put forward the efficient calculation method, fast Fourier transform (FFT) algorism in Mach-Zehnder interferometer for arm length locking and f-2f for CEP locking. In the interferometer locking, 532 nm continuous wave laser is used in the Mach-Zehnder interferometer, and the phase of the FFT term corresponding to the delay between the two arms of the interferometer serves as a feedback signal on piezo transducer (PZT) in the delay line to reduce the change of the arm length. In the CEP control experiment, data to be analyzed are the f-2f spectrum interference fringes recorded by the spectrometer. The CEP values are obtained from the first order of FFT module output of the integrated spectrum interference fringes, and a labview program examines the relative phase drift and sends a feedback voltage signal to the PZT through the proportion integration differentiation module to compensate slow CEP drift after the chirped pulse amplification system by changing the insert length of a prism pair. The results show that the root mean square (RMS) of the arm length difference is 1.24 nm (4.1 attosecond for light to travel) per meter in the interferometer locking over 12 h, and the RMS of CEP is 227 mrad under 3 ms integration time in the CEP locking over 20 min. These results are able to meet the requirement of the accuracy for attosecond pulse generation and attosecond pump-probe experiments. We also use FFT to stabilize the CEP and relative time simultaneously in the waveform synthesis for 8 h (Huang P, Fang S, Gao Y, Zhao K, Hou X, Wei Z 2019 Appl. Phys. Lett. 115 031102), the phase-locking system results in a CEP stability of 280 mrad and a relative time stability of 110 as at a repetition rate of 1 kHz. These results imply that the FFT is versatile and reliable in ultrafast control.
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[4] Zhao K, Zhang Q, Chini M, Wu Y, Wang X W, Chang Z 2012 Opt. Lett. 37 3891
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Google Scholar
[7] Itatani J, Quéré F, Yudin G, Ivanov M, Krausz F, Corkum P 2002 Phys. Rev. Lett. 88 173903
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Google Scholar
[9] Dörner R, Mergel V, Jagutzki O, Spielberger L, Ullrich J, Moshammer R, Schmidt-Bögcking H 2000 Phys. Rep. 330 95
Google Scholar
[10] Luu T, Garg M, Kruchinin S, Moulet A, Hassan M, Goulielmakis E 2015 Nature 521 498
Google Scholar
[11] Goulielmakis E, Loh Z, Wirth A, Santra R, Rohringe N, Yakovlev V, Zherebtsov S, Pfeifer T, Azzeer A, Kling M, Leone S, Krausz F 2010 Nature 466 739
Google Scholar
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Google Scholar
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[14] Chini M, Wang X, Cheng Y, Wu Y, Zhao K, Zhang Q, Cunningham E, Wang Y, Zang H, Chang Z 2012 25 th IEEE Photonics Conference Burlingame, CA, USA, September 23–27, 2012 p622
[15] Kaldun A, Blättermann A, Stooß V, Donsa S, Wei H, Pazourek R, Nagele S, Ott C, Lin C, Burgdörfer J, Pfeifer T 2016 Science 354 738
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Google Scholar
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Google Scholar
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Google Scholar
[21] Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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[27] 张伟 2013 博士学位论文 (北京: 中国科学院大学)
Zhang W 2013 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese)
[28] Huang P, Fang S, Gao Y, Zhao K, Hou X, Wei Z 2019 Appl. Phys. Lett. 115 031102
Google Scholar
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图 1 抽运探测实验示意图 (m1−m15, 平面高反镜; f1, 平凹透镜; f2, f3, 凸透镜)
Figure 1. Sketch of the pump-probe setup (m1−m15, flat mirror; f1, flat-concave lens; f2, f3, convex lens).
图 2 用532 nm连续激光干涉锁定光路示意图(M1, 凹透镜; M2, 凸透镜; BS, 分束片; M3−M10, 平面银镜; P, 偏振片;
${\rm{\lambda }}/2$ , 半波片; FL, 凸透镜; CW, 连续)Figure 2. Arm length stabilization of a Mach-Zehnder interferometer (M1, concave lens; M2, convex lens; M3−M10, plane mirrors; P, polarizer;
${\rm{\lambda }}/2$ , half wave plate; FL, focusing lens; CW, continuous wave).
图 3 用532 nm连续激光干涉锁定12 h的稳定性, 其中均方差为14.6 mrad, 插图为未锁定下的相对相位漂移
Figure 3. Interferometer locking stability over 12 hours. Inset is the relative phase drift when armlength is not locked.
图 4 在同一脉冲包络下不同CEP值所对应的实际电场(CEP对少周期脉冲电场实际形状影响显著)
Figure 4. Actual electric field of a few cycle laser pulse under different CEP values, which affect the electric field significantly.
图 5 f-2f装置光路图(采用共线设计以避免延时变化)
Figure 5. f-2f setup diagram, where collinear design is applied to avoid delay variation.
图 6 f-2f锁定CEP20分钟的效果(均方差为227 mrad)
Figure 6. CEP offset over 20 minutes when CEP is locked using f-2f.
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[1] Bloembergen N 1999 Rev. Mod. Phys. 71 283
Google Scholar
[2] Auston D 1988 Top. Appl. Phys. 60 183
[3] Drescher M, Hentschel M, Kienberger R, Tempea G, Spielmann C, Reider G, Corkum P, Krausz F 2001 Science 291 5510
[4] Zhao K, Zhang Q, Chini M, Wu Y, Wang X W, Chang Z 2012 Opt. Lett. 37 3891
Google Scholar
[5] Li J, Ren X, Yin Y, Zhao K, Chew A, Cheng Y, Cunningham E, Wang Y, Hu S, Wu Y, Chini M, Chang Z 2017 Nat. Commun. 8 186
[6] Gaumnitz T, Jain A, Pertot Y, Huppert M, Jordan I, Ardana-Lamas F, Wörner H 2017 Opt. Express 25 27506
Google Scholar
[7] Itatani J, Quéré F, Yudin G, Ivanov M, Krausz F, Corkum P 2002 Phys. Rev. Lett. 88 173903
[8] Eppink A, Parker D 1997 Rev. Sci. Instrum. 68 3477
Google Scholar
[9] Dörner R, Mergel V, Jagutzki O, Spielberger L, Ullrich J, Moshammer R, Schmidt-Bögcking H 2000 Phys. Rep. 330 95
Google Scholar
[10] Luu T, Garg M, Kruchinin S, Moulet A, Hassan M, Goulielmakis E 2015 Nature 521 498
Google Scholar
[11] Goulielmakis E, Loh Z, Wirth A, Santra R, Rohringe N, Yakovlev V, Zherebtsov S, Pfeifer T, Azzeer A, Kling M, Leone S, Krausz F 2010 Nature 466 739
Google Scholar
[12] Jones D, Diddams S, Ranka J, Stentz A, Windeler S, Hall J, Cundiff S 2000 Science 288 635
Google Scholar
[13] Schibli T, Kim J, Kuzucu O, Gopinath J, Tandon S, Petrich G, Kolodziejski L, Fujimoto J, Ippen E, Kaertner F 2003 Opt. Lett. 28 947
[14] Chini M, Wang X, Cheng Y, Wu Y, Zhao K, Zhang Q, Cunningham E, Wang Y, Zang H, Chang Z 2012 25 th IEEE Photonics Conference Burlingame, CA, USA, September 23–27, 2012 p622
[15] Kaldun A, Blättermann A, Stooß V, Donsa S, Wei H, Pazourek R, Nagele S, Ott C, Lin C, Burgdörfer J, Pfeifer T 2016 Science 354 738
[16] Ishii N, Xia P, Kanai T, Itatani J 2019 Opt. Express 27 11447
Google Scholar
[17] Cooley J, Tukey J 1965 Math. Comp. 19 297
Google Scholar
[18] Seres E, Seres J, Serrat C, Namba S 2016 Phys. Rev. B 94 165125
Google Scholar
[19] Feng X, Gilbertson S, Mashiko H, Wang H, Khan S, Chini M, Wu Y, Zhao K, Chang Z 2009 Phys. Rev. Lett. 103 183901
Google Scholar
[20] Pertot Y, Schmidt C, Matthews M, Chauvet A, Huppert M, Svoboda V, Conta A, Tehlar A, Baykusheva D, Wolf J, Wörner H 2017 Science 355 264
Google Scholar
[21] Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163
Google Scholar
[22] Rathje T, Johnson N, Moller M, Sussmann F, Adolph D, Kubel M, Kienberger R, Kling M, Paulus G, Sayler A 2012 J. Phys. B 45 074003
[23] Yu Z, Han H, Xie Y, Teng H, Wang Z, Wei Z 2016 Chin. Phys. B 25 044205
Google Scholar
[24] Wittmann T, Horvath B, Helml W, Schatzel M, Gu X, Cavalieri A, Paulus G, Kienberger R 2009 Nat. Phys. 5 5
Google Scholar
[25] Xu L, Spielmann C, Poppe A, Brabec T, Krausz F, Hansch T 1996 Opt. Lett. 21 24
Google Scholar
[26] Kakehata M, Takada H, Kobayashi Y, Torizuka K, Fujihira Y, Homma T, Takahashi H 2001 Opt. Lett. 26 1436
[27] 张伟 2013 博士学位论文 (北京: 中国科学院大学)
Zhang W 2013 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese)
[28] Huang P, Fang S, Gao Y, Zhao K, Hou X, Wei Z 2019 Appl. Phys. Lett. 115 031102
Google Scholar
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