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Temporal shearing interferometry is proposed to measure the temporal phase distribution of nanosecond laser pulses. In the proposed scheme, the pulse to be measured is divided into two pulses with a delay of hundreds of picoseconds in between, arbitrary one of the two pulses is added to by an appropriate amount of frequency shift, then is combined with the remaining pulse, thereby obtaining the temporal shearing interferogram that is recorded by a normal photodiode. The temporal phase distribution is calculated by an adaptive algorithm based on Fourier transform, and further the precise spectra of the measured pulse can also be calculated according to the Fourier relation between time domain and spectral domain. Based on the systematic analysis of the principle of the technology, the proposed technology is verified by numerical simulation. And the influence of the variable parameters including noise, relative delay, relative intensity on the measured error are systematically analyzed in the simulation. And the results show that the proposed nanosecond temporal phase diagnostic technique has a good performance when the signal noise ratio of the interferogram is above 15 dB, the relative delay of the pulses is between 0.5% and 28% and the relative intensity is above 0.1%. The proposed method is verified experimentally in a nanosecond laser system with central wavelength of 640 nm and pulse width of 20 ns. And the calculated spectra obtained from the temporal shearing interferogram match well with the spectra measured by a scanning Fabry-Perot interferometer. This proposed technique does not use any nonlinear optical effects, thus it can be applied to the diagnostic of nanosecond laser pulse centered at any wavelength. Hence, it provides a simple experimental setup for implementing the higher-accuracy diagnostic of the temporal phase distribution of nanosecond laser pulses.
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Keywords:
- nanosecond lase pulse /
- temporal phase /
- self-referencing /
- temporal shearing
[1] Zhu J 2019 High Power Laser Sci. Eng. 7 12
Google Scholar
[2] Zhu J, Xie X, Sun M, Kang J, Yang Q, Guo A, Zhu H, Zhu P, Gao Q, Liang X, Cui Z, Yang S, Zhang C, Lin Z 2018 High Power Laser Sci. Eng. 6 e29
Google Scholar
[3] Amirov R K, Asinovskii E I, Markovets V V 1981 High Temp. 19 37
Google Scholar
[4] Wang Y, Chen A, Zhang D, Wang Q, Li S, Jiang Y, Jin M 2020 Phys. Plasmas 27 023507
Google Scholar
[5] Mannion O M, Igumenshchev I V, Anderson K S, Betti R, Campbell E M, Cao D, Forrest C J, Johnson M G, Glebov V Y, Goncharov V N, Gopalaswamy V, Ivancic S T, Jacobs-Perkins D W, Kalb A, Knauer J P, Kwiatkowski J, Lees A, Marshall F J, Michalko M, Mohamed Z L, Patel D, Rinderknecht H G, Shah R C, Stoeckl C, Theobald W, Woo K M, Regan S P 2021 Phys. Plasmas 28 042701
Google Scholar
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Google Scholar
[7] Glenzer S H, Redmer R 2009 Rev. Mod. Phys. 81 1625
Google Scholar
[8] Kim H Y, Golkowski M, Harid V 2021 Eur. Phys. J. D 75 134
Google Scholar
[9] Jourdain N, Chaulagain U, Havlik M, Kramer D, Kumar D, Majerova I, Tikhonchuk V T, Korn G, Weber S 2021 Matter Radiat. Extrem. 6 015401
Google Scholar
[10] Delong K W, Trebino R, Hunter J, White W E 1994 J. Opt. Soc. Am. B 11 2206
Google Scholar
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Google Scholar
[12] Jafari R, Trebino R 2020 IEEE J. Quantum Electron. 56 8600108
Google Scholar
[13] Iaconis C, Walmsley I A 1998 Opt. Lett. 23 792
Google Scholar
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Google Scholar
[15] 何铁英 2004 硕士学位论文 (天津: 天津大学)
He T Y 2004 M. S. Thesis (Tianjin: Tianjin University) (in Chinese)
[16] Pedatzur O, Trabattoni A, Leshem B, Shalmoni H, Castrovilli M C, Galli M, Lucchini M, Mansson E, Frassetto F, Poletto L, Nadler B, Raz O, Nisoli M, Calegari F, Oron D, Dudovich N 2019 Nat. Photonics 13 91
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 (a)自参考时域剪切纳秒相位测量技术原理; (b)重建过程
Figure 1. (a) Schematic diagram of temporal self-referencing technique for the diagnostics of a nanosecond laser pulse; (b) reconstruction procedure.
图 2 基于自参考时域剪切的纳秒相位测量技术的仿真结果. 每列表示不同强度分布脉冲的重建结果, 每一列中第一幅图是合束后的时域剪切干涉图; 第二幅中蓝色实线表示脉冲的时间强度分布, 绿色实线为原相位分布, 红色虚线为重建的相位分布; 第三幅中蓝色实线为计算所得的光谱分布, 红色虚线为原光谱分布
Figure 2. Simulation results of phase retrieval of nanosecond laser pulses based on temporal shearing interferometry. Each column represents reconstructed results. In each column, the first plot represents the recorded temporal interferogram; the second plot presents the original temporal intensity distribution (blue solid line), original temporal phase distribution (green solid line) and reconstructed temporal phase distribution (red dashed line); the third shows the original spectral intensity distribution (blue solid line) versus reconstructed spectral intensity distribution (red dashed line).
图 3 (a)不同强度分布的脉冲, 相位重建误差随信噪比变化的曲线图; (b)—(d)在图2(b) 所示的移频剪切图中分别添加信噪比(SNR)为10, 20, 40 dB的噪声下的重建结果, 其中的插图表示计算得到的光谱强度分布
Figure 3. (a) Reconstructed error between reconstructed and original signals as a function of the SNR for pulse with different intensity distribution; (b)–(d) reconstructed pulse distribution for SNR of 10, 20, 40 dB, respectively, and the computed spectra is presented in the inset.
图 4 (a) 不同强度分布的脉冲, 相位重建误差随相对延时变化的曲线图; (b) 不同强度分布的脉冲, 相位重建误差随相对强度变化的曲线图
Figure 4. (a) Reconstructed error between reconstructed and original signals as a function of relative delay for pulse with different intensity distribution; (b) reconstructed error between reconstructed and original signals as a function of relative intensity delay for pulse with different intensity distribution.
图 5 实验结果 (a) 实验记录的时间剪切干涉图; (b) 重建的时间相位分布(红色虚线)和示波器记录到的时间强度图(绿色实线); (c) 计算光谱强度分布(蓝色实线)和测得的光谱强度分布(红色虚线)
Figure 5. Experimental result: (a) Recorded temporal shearing interferogram; (b) reconstructed temporal phase distribution (red dashed line) and the temporal intensity distribution (green solid line) recorded by oscilloscope; (c) calculated (blue solid line) and measured (red dashed line) spectral intensity distribution.
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[1] Zhu J 2019 High Power Laser Sci. Eng. 7 12
Google Scholar
[2] Zhu J, Xie X, Sun M, Kang J, Yang Q, Guo A, Zhu H, Zhu P, Gao Q, Liang X, Cui Z, Yang S, Zhang C, Lin Z 2018 High Power Laser Sci. Eng. 6 e29
Google Scholar
[3] Amirov R K, Asinovskii E I, Markovets V V 1981 High Temp. 19 37
Google Scholar
[4] Wang Y, Chen A, Zhang D, Wang Q, Li S, Jiang Y, Jin M 2020 Phys. Plasmas 27 023507
Google Scholar
[5] Mannion O M, Igumenshchev I V, Anderson K S, Betti R, Campbell E M, Cao D, Forrest C J, Johnson M G, Glebov V Y, Goncharov V N, Gopalaswamy V, Ivancic S T, Jacobs-Perkins D W, Kalb A, Knauer J P, Kwiatkowski J, Lees A, Marshall F J, Michalko M, Mohamed Z L, Patel D, Rinderknecht H G, Shah R C, Stoeckl C, Theobald W, Woo K M, Regan S P 2021 Phys. Plasmas 28 042701
Google Scholar
[6] Zhang H, Yu T, Guo N, Xue H, Zhang W, Gao D, Ma X, Shen H, Wang Q 2021 Nucl. Instrum. Meth. B 493 1
Google Scholar
[7] Glenzer S H, Redmer R 2009 Rev. Mod. Phys. 81 1625
Google Scholar
[8] Kim H Y, Golkowski M, Harid V 2021 Eur. Phys. J. D 75 134
Google Scholar
[9] Jourdain N, Chaulagain U, Havlik M, Kramer D, Kumar D, Majerova I, Tikhonchuk V T, Korn G, Weber S 2021 Matter Radiat. Extrem. 6 015401
Google Scholar
[10] Delong K W, Trebino R, Hunter J, White W E 1994 J. Opt. Soc. Am. B 11 2206
Google Scholar
[11] Yang Z, Cao W, Chen X, Zhang J, Mo Y, Xu H, Mi K, Zhang Q, Lan P, Lu P 2020 Opt. Lett. 45 567
Google Scholar
[12] Jafari R, Trebino R 2020 IEEE J. Quantum Electron. 56 8600108
Google Scholar
[13] Iaconis C, Walmsley I A 1998 Opt. Lett. 23 792
Google Scholar
[14] Sheng H C, Zhi G Z, Lu C, Yu Q D, Qing Y W 2009 J. Optoelectron. Laser 20 1005
Google Scholar
[15] 何铁英 2004 硕士学位论文 (天津: 天津大学)
He T Y 2004 M. S. Thesis (Tianjin: Tianjin University) (in Chinese)
[16] Pedatzur O, Trabattoni A, Leshem B, Shalmoni H, Castrovilli M C, Galli M, Lucchini M, Mansson E, Frassetto F, Poletto L, Nadler B, Raz O, Nisoli M, Calegari F, Oron D, Dudovich N 2019 Nat. Photonics 13 91
Google Scholar
[17] Fee M S, Danzmann K, Chu S 1992 Phys. Rev. A 45 4911
Google Scholar
[18] Gangopadhyay S, Melikechi N, Eyler E E 1994 J. Opt. Soc. Am. B 11 2314
Google Scholar
[19] Bowlan P, Trebino R 2011 Opt. Express 19 1367
Google Scholar
[20] Dorrer C, Kang I 2008 J. Opt. Soc. Am. B 25 A1
Google Scholar
[21] Takeda M, Ina H, Kobayashi S 1982 J. Opt. Soc. Am. 72 156
Google Scholar
[22] Freischlad K R, Koliopoulos C L 1986 J. Opt. Soc. Am. A 3 1852
Google Scholar
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