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Pi Yihan, Wang Chunze, Song Youjian, Hu Minglie. Ultra-low timing jitter femtosecond laser technology (Invited)[J]. Infrared and Laser Engineering, 2020, 49(12): 20201058. doi: 10.3788/IRLA20201058
Citation: Pi Yihan, Wang Chunze, Song Youjian, Hu Minglie. Ultra-low timing jitter femtosecond laser technology (Invited)[J]. Infrared and Laser Engineering, 2020, 49(12): 20201058. doi: 10.3788/IRLA20201058

Ultra-low timing jitter femtosecond laser technology (Invited)

doi: 10.3788/IRLA20201058
  • Received Date: 2020-09-18
  • Rev Recd Date: 2020-10-11
  • Available Online: 2021-01-14
  • Publish Date: 2020-12-25
  • The time jitter of a femtosecond laser is the short-term deviation of the optical pulse position relative to its ideal equally spaced pulse position. Femtosecond lasers emit uniformly spaced ultrashort pulse train. The quantum-noise-limited timing jitter can be as low as few tens of attoseconds in millisecond time scale. This unique property and its advanced applications constitute a new branch of ultrafast research, "Attosecond precision ultrafast photonics". In this paper, the recent advances in femtosecond laser timing jitter research, high-precision timing jitter characterization methods, and the ultralow timing jitter that can be achieved by different kinds of femtosecond laser sources were reviewed. Finally, the application of low-jitter femtosecond lasers in the fields of synchronization of large-scale scientific instruments, high-speed analog-to-digital conversion, absolute ranging technology and coherent beam combination are introduced.
  • [1] Ahmed H Zewail. Femtochemistry: atomic-scale dynamics of the chemical bond [J]. The Journal of Physical Chemistry A, 2000, 104(24): 5660-5694.
    [2] Xin Zhu, Christine L Kalcic, Nelson Winkler, et al. Applications of femtochemistry to proteomic and metabolomic analysis [J]. The Journal of Physical Chemistry A, 2010, 114(38): 10380-10387.
    [3] Hrvoje Petek. Single-molecule femtochemistry: molecular imaging at the space-time limit [J]. Acs Nano, 2014, 8(1): 5-13.
    [4] Ulf Saalmann, Jan-Michael Rost. Ionization of clusters in intense laser pulses through collective electron dynamics [J]. Physical Review Letters, 2003, 91(22): 223401.
    [5] Psikal J, Tikhonchuk V T, Limpouch J, et al. Ion acceleration by femtosecond laser pulses in small multispecies targets [J]. Physics of Plasmas, 2008, 15(5): 053102.
    [6] Rafael R Gattass, Eric Mazur. Femtosecond laser micromachining in transparent materials [J]. Nature Photonics, 2008, 2(4): 219-225.
    [7] Anatol Khilo, Steven J Spector, Matthew E Grein, et al. Photonic ADC: overcoming the bottleneck of electronic jitter [J]. Optics Express, 2012, 20(4): 4454-4469.
    [8] Schulz S, Grguras I, Behrens C, et al. Femtosecond all-optical synchronization of an X-ray free-electron laser [J]. Nature Communication, 2015, 6: 5938.
    [9] Matthew Walbran, Alexander Gliserin, Kwangyun Jung, et al. 5-femtosecond laserelectron synchronization for pump-probe crystallography and diffraction [J]. Physical Review Applied, 2015, 4: 044013.
    [10] Bartels A, Diddams S A, Oates C W, et al. Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references [J]. Optics Letters, 2005, 30(6): 667-669.
    [11] Cox J A, Putnam W P, Sell A, et al. Pulse synthesis in the single-cycle regime from independent mode-locked lasers using attosecond-precision feedback [J]. Optics Letters, 2012, 37(17): 3579-3581.
    [12] Paolo Ghelfi, Francesco Laghezza, Filippo Scotti, et al. A fully photonics-based coherent radar system [J]. Nature, 2014, 507: 341-345.
    [13] Ming Xin, Kemal Şafak, Franz X Kärtner. Ultra-precise timing and synchronization for large-scale scientific instruments [J]. Optica, 2018, 5(12): 1564-1578.
    [14] Kim J, Kärtner F X. Attosecond-precision ultrafast photonics [J]. Laser and Photonics Reviews, 2010, 4(3): 432-456.
    [15] Donald Barrett Sullivan, David W Allan, David A Howe, et al.. Characterization of Clocks and Oscillators [M]. US: Department of Commerce, National Institute of Standards and Technology, 1990.
    [16] Montress G K, Parker T E, Loboda M J. Residual phase noise measurements of VHF, UHF, and microwave components [C]//Proceedings of the 43rd Annual Symposium on IEEE, 1989, 41(5): 664-679.
    [17] D vonder Linde. Characterization of the noise in continuously operating mode-locked lasers [J]. Applied Physics B, 1986, 39: 201-217.
    [18] Ouyang Chunmei, Shum Ping, Wang Honghai, et al. Observation of timing jitter reduction induced by spectral filtering in a fiber laser mode locked with a carbon nanotube-based saturable absorber [J]. Optics Letters, 2010, 35(14): 2320-2322.
    [19] Scott R P, Langrock C, Kolner B H. High-dynamic-range laser amplitude and phase noise measurement techniques [C]// IEEE Journal of Selected Topics in Quantum Electronics, 2001, 7(4): 641-655.
    [20] Youjian Song, Chur Kim, Kwangyun Jung, et al. Timing jitter optimization of mode-locked Yb-fiber lasers toward the attosecond regime [J]. Optics Express, 2011, 19(15): 14518-14525.
    [21] Xu Shaofu, Zou Xiuting, Ma Bowen, et al. Deep-learning-powered photonic analog-to-digital conversion [J]. Light: Science & Applications, 2019, 8: 66.
    [22] Andrew J Benedick, James G Fujimoto, Franz X. Kartner. Optical flywheels with attosecond jitter [J]. Nature Photonics, 2012, 6(2): 97-100.
    [23] Peng Qin, Youjian Song, Hyoji Kim, et al. Reduction of timing jitter and intensity noise in normal-dispersion passively mode-locked fiber lasers by narrow band-pass filtering [J]. Optics Express, 2014, 22(23): 28276-28283.
    [24] Wei Chen, Youjian Song, Kwangyun Jung, et al. Few-femtosecond timing jitter from a picosecond all-polarization-maintaining Yb-fiber laser [J]. Optics Express, 2016, 24(2): 1347-1357.
    [25] Hou D, Lee C-C, Yang Z, et al. Timing jitter characterization of mode-locked lasers with <1 zs/√Hz resolution using a simple optical heterodyne technique [J]. Optics Letters, 2015, 40(13): 2985-2988.
    [26] Tae Keun Kim, Youjian Song, Kwangyun Jung, et al. Sub-100-as timing jitter optical pulse trains from mode-locked Er-fiber lasers [J]. Optics Letters, 2011, 36(22): 4443-4445.
    [27] Kwangyun Jung, Jungwon Kim. All-fibre photonic signal generator for attosecond timing and ultralow-noise microwave [J]. Scientific Reports, 2015, 5: 16250.
    [28] Tian Haochen, Yang Wenkai, Dohyeon Kwon, et al. Optical frequency comb noise spectra analysis using an asymmetric fiber delay line interferometer [J]. Optics Express, 2020, 28(7): 9232-9243.
    [29] Bartels A, Cerna R, Kistner C, et al. Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling [J]. Review of Scientific Instruments, 2007, 78(3): 035107.
    [30] Shi Haosen, Song Youjian, Yu JiaHe, et al. Quantum-limited timing jitter characterization of mode-locked lasers by asynchronous optical sampling [J]. Optics Express, 2017, 25(1): 10-19.
    [31] Li Duo, Umit Demirbas, Andrew Benedick, et al. Attosecond timing jitter pulse trains from semiconductor saturable absorber mode-locked Cr:LiSAF lasers [J]. Optics Express, 2012, 20(21): 23422-23435.
    [32] Portuondo-Campa E, Paschotta R, Lecomte S. Sub-100 attosecond timing jitter from low-noise passively mode-locked solid-state laser at telecom wavelength [J]. Optics Letters, 2013, 38(15): 2650-2653.
    [33] Jungwon Kim, Jeff Chen, Jonathan Cox, et al. Attosecond-resolution timing jitter characterization of free-running mode-locked lasers [J]. Optics Letters, 2007, 32(24): 3519-3521.
    [34] Kuse N, Jiang J, Lee C-C, et al. All polarization-maintaining Er fiber-based optical frequency combs with nonlinear amplifying loop mirror [J]. Optics Express, 2016, 24(3): 3095-3102.
    [35] Jian Chen, Jason W Sickler, Peter Fendel, et al. Generation of low-timing-jitter femtosecond pulse trains with 2 GHz repetition rate via external repetition rate multiplication [J]. Optics Letters, 2008, 33(9): 959-961.
    [36] Heewon Yang, Hyoji Kim, Junho Shin, et al. Gigahertz repetition rate, sub-femtosecond timing jitter optical pulse train directly generated from a mode-locked Yb:KYW laser [J]. Optics Letters, 2014, 39(1): 56-59.
    [37] Wang Yan, Tian Haochen, Ma Yuxuan, et al. Timing jitter of high-repetition-rate mode-locked fiber lasers [J]. Optics Letters, 2018, 43(18): 4382-4385.
    [38] Wang Yan, Tian Haochen, Hou Dong, et al. Timing jitter reduction through relative intensity noise suppression in high-repetition-rate mode-locked fiber lasers [J]. Optics Express, 2019, 27(8): 11273-11280.
    [39] Jiazheng Song, Hushan Wang, Xinning Huang, et al. Compact low-noise passively mode-locked Er-doped femtosecond all-fiber laser with 2.68 GHz fundamental repetition rate [J]. Applied Optics, 2019, 58(7): 1733-1738.
    [40] Lianping Hou, Mohsin Haji, Jehan Akbar, et al. Low divergence angle and low jitter 40 GHz AlGaInAs/InP 1.55 μm mode-locked lasers [J]. Optics Letters, 2011, 36(6): 966-968.
    [41] Haroon Asghar, Wei Wei, Pramod Kumar, et al. Stabilization of self-mode-locked quantum dash lasers by symmetric dual-loop optical feedback [J]. Optics Express, 2018, 26(4): 4581-4592.
    [42] Liu Songtao, Tin Komljenovic, Sudharsanan Srinivasan, et al. Characterization of a fully integrated heterogeneous silicon/III-V colliding pulse mode-locked laser with on-chip feedback [J]. Optics Express, 2018, 26(8): 9714-9723.
    [43] Dongin Jeong, Dohyeon Kwon, Igju Jeon, et al. Ultralow jitter silica microcomb [J]. Optica, 2020, 7(9): 1108-1111.
    [44] Pang M, He W, Jiang X, et al. All-optical bit storage in a fibre laser by optomechanically bound states of solitons [J]. Nature Photonics, 2016, 10: 454-458.
    [45] Shi Haosen, Song Youjian, Wang Chingyue, et al. Observation of subfemtosecond fluctuations of the pulse separation in a soliton molecule [J]. Optics Letters, 2018, 43(7): 1623-1626.
    [46] Kim Jungwon, Song Youjian. Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications [J]. Advances in Optics and Photonics, 2016, 8(3): 465-540.
    [47] Jian Chen, Jason W Sickler, Erich P Ippen. High repetition rate, low jitter, low intensity noise, fundamentally mode-locked 167 fs soliton Er-fiber laser [J]. Optics Letters, 2007, 32(11): 1566-1568.
    [48] Jian Chen, Jason Sickler, Hyunil Byun, et al. Fundamentally mode-locked 3 GHz femtosecond erbium fiber laser [C]// Ultrafast Phenomena XVI: Proceedings of the 16th International Conference, 2009: 732–734.
    [49] Li Xing, Zou Weiwen, Wu Kan, et al., Timing-jitter reduction by use of a spectral filter in a broadband femtosecond fiber laser [C]//IEEE Photonics Technology Letters, 2010,27(8): 911-914.
    [50] Hyunil Byun, Michelle Y Sander, Ali Motamedi, et al. Compact, stable 1 GHz femtosecond Er-doped fiber lasers [J]. Applied Optics, 2010, 49(29): 5577-5582.
    [51] Chur Kim, Sangho Bae, Khanh Kieu, et al. Sub-femtosecond timing jitter, all-fiber, CNT-mode-locked Er-laser at telecom wavelength [J]. Optics Express, 2013, 21(22): 26533-26541.
    [52] Kan Wu, Xiaoyan Zhang, Jun Wang, et al. 463-MHz fundamental mode-locked fiber laser based on few-layer MoS2 saturable absorber [J]. Optics Letters, 2015, 40(7): 1374-1377.
    [53] Kwangyun Jung, Jungwon Kim. Characterization of timing jitter spectra in free-running mode-locked lasers with 340 dB dynamic range over 10 decades of Fourier frequency [J]. Optics Letters, 2015, 40(3): 316-319.
    [54] Junho Shin, Kwangyun Jung, Youjian Song, et al. Characterization and analysis of timing jitter in normal-dispersion mode-locked Er-fiber lasers with intra-cavity filtering [J]. Optics Express, 2015, 23(17): 22898-22906.
    [55] Dohyun Kim, Dohyeon Kwon, Bongwan Lee, et al. Polarization-maintaining nonlinear-amplifying-loop-mirror mode-locked fiber laser based on a 3 × 3 coupler [J]. Optics Letters, 2019, 44(5): 1068-1071.
    [56] Bao Chengying, Yang Changxi. Harmonic mode-locking in a Tm-doped fiber laser: characterization of its timing jitter and ultralong starting dynamics [J]. Optics Communications, 2015, 356: 463-467.
    [57] Ahmet E Akosman, Michelle Y Sander. Low noise, mode-locked 253 MHz Tm/Ho fiber laser with core pumping at 790 nm [C]//IEEE Photonics Technology Letters, 2016, 28(17): 1878-1881.
    [58] Cheng Huihui, Wang Wenlong, Zhou Yi, et al. High-repetition-rate ultrafast fiber lasers [J]. Optics Express, 2018, 26(13): 16411-16421.
    [59] Kristina Bagnell, Anthony Klee, Peter J Delfyett, et al. Demonstration of a highly stable 10 GHz optical frequency comb with low timing jitter from a SCOWA-based harmonically mode-locked nested cavity laser [J]. Optics Letters, 2018, 43(10): 2396-2399.
    [60] Emma P, Akre R, Arthur J, et al. First lasing and operation of an ångstrom-wavelength free-electron laser [J]. Nature Photonics, 2010, 4: 641-647.
    [61] Altarelli M. The European X-ray free-electron laser facility in Hamburg [J]. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2011, 269(24): 2845-2849.
    [62] Christopher J Milne. Thomas Schietinger, Masamitsu Aiba, et al. The Swiss X-ray free electron laser [J]. Applied Sciences, 2017, 7(7): 720.
    [63] Huang Zhirong, Ingolf Lindau. SACLA hard-X-ray compact FEL [J]. Nature Photonics, 2012, 6: 505-506.
    [64] Zhao Zhentang, Wang Dong, Gu Qiang, et al. SXFEL: a soft X-ray free electron laser in China [J]. Synchrotron Radiation News, 2017, 3(6): 29-33.
    [65] Zhao Zhentang, Wang Dong, Yin Lixin, et al. Shanghai soft X-ray freeelectron laser facility [J]. Chinese Journal of Lasers, 2019, 46(1): 0100004.
    [66] Eduard Prat, Sven Reiche. Simple method to generate terawatt-attosecond X-ray free-electron-laser pulses [J]. Physical Review Letters, 2015, 114(24): 244801.
    [67] Calegari F, Ayuso D, Trabattoni A, et al. Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses [J]. Science, 2014, 346(6207): 336-339.
    [68] Öström H, Öberg H, Xin H, et al. Probing the transition state region in catalytic CO oxidation on Ru [J]. Science, 2015, 347(6225): 978-982.
    [69] Şafak K, Cheng H P H, Dai A, et al. Single-mode fiber based pulsed-optical timing link with few-femtosecond precision in SwissFEL [C]//Conference on Lasers and Electro-Optics, 2019: JTh2A.100.
    [70] Ming Xin, Kemal Şafak, Michael Y Peng. One-femtosecond, long-term stable remote laser synchronization over a 3.5-km fiber link [J]. Optics Express, 2014, 22(12): 14904-14912.
    [71] George C Valley. Photonic analog-to-digital converters [J]. Optics Express, 2007, 15(5): 1955-1982.
    [72] Jungwon Kim, Matthew J Park, Michael H Perrott, et al. Photonic subsampling analog-to-digital conversion of microwave signals at 40-GHz with higher than 7-ENOB resolution [J]. Optics Express, 2008, 16(21): 16509-16515.
    [73] Jonghan Jin. Dimensional metrology using the optical comb of a mode-locked laser [J]. Measurement Science and Technology, 2016, 27(2): 022001.
    [74] Coddington I, Swann W C, Nenadovic L. Rapid and precise absolute distance measurements at long range [J]. Nature Photonics, 2009, 3: 351-356.
    [75] Zhang Hongyuan, Wei Haoyun, Wu Xuejian, et al. Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling [J]. Optics Express, 2014, 22(6): 6597-6604.
    [76] Shi Haosen, Song Youjian, Liang Fei, et al. Effect of timing jitter on time-of-flight distance measurements using dual femtosecond lasers [J]. Optics Express, 2015, 23(11): 14057-14069.
    [77] Ma Yanxing, Wang Xiaolin, Leng Jinyong, et al. Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique [J]. Optics Letters, 2011, 36(6): 951-953.
    [78] Liu Zejin, Ma Pengfei, Su Rongtao, et al. High-power coherent beam polarization combination of fiber lasers: progress and prospect [Invited] [J]. Journal of the Optical Society of America B, 2017, 34(3): A7-A14.
    [79] Robert K Shelton, Long-Sheng Ma, Henry C Kapteyn, et al. Phase-coherent optical pulse synthesis from separate femtosecond lasers [J]. Science, 2001, 17: 1286-1289.
    [80] Cristian Manzoni, Oliver D Mücke, Giovanni Cirmi, et al. Coherent pulse synthesis: towards sub‐cycle optical waveforms [J]. Laser & Photonics Reviews, 2012, 9: 129-171.
    [81] Cox J A, Putnam W P, Sell A, et al. Pulse synthesis in the single-cycle regime from independent mode-locked lasers using attosecond-precision feedback [J]. Optical Letters, 2012, 37(17): 3579-3581.
    [82] Tian Haochen, Song Youjian, Meng Fei, et al. Long-term stable coherent beam combination of independent femtosecond Yb-fiber lasers [J]. Optical Letters, 2016, 41(22): 5142-5145.
    [83] Ge Aichen, Liu Bowen, Chen Wei, et al. Generation of few-cycle laser pulses by coherent synthesis based on a femtosecond Yb-doped fiber laser amplification system [J]. Chinese Optics Letters, 2019, 17(4): 041403.
    [84] Trocha P, Karpov M, Ganin D, et al. Ultrafast optical ranging using microresonator soliton frequency combs [J]. Science, 2018, 359(6378): 887-891.
    [85] Myoung-Gyun Suh, Kerry J Vahala. Soliton microcomb range measurement [J]. Science, 2018, 359(6378): 884-887.
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Ultra-low timing jitter femtosecond laser technology (Invited)

doi: 10.3788/IRLA20201058
  • Key Laboratory of Opto-electronic Information Science and Technology of Ministry of Education, School of Precision Instruments and Opto-electronics Engineering, Tianjin University, Tianjin 300072, China

Abstract: The time jitter of a femtosecond laser is the short-term deviation of the optical pulse position relative to its ideal equally spaced pulse position. Femtosecond lasers emit uniformly spaced ultrashort pulse train. The quantum-noise-limited timing jitter can be as low as few tens of attoseconds in millisecond time scale. This unique property and its advanced applications constitute a new branch of ultrafast research, "Attosecond precision ultrafast photonics". In this paper, the recent advances in femtosecond laser timing jitter research, high-precision timing jitter characterization methods, and the ultralow timing jitter that can be achieved by different kinds of femtosecond laser sources were reviewed. Finally, the application of low-jitter femtosecond lasers in the fields of synchronization of large-scale scientific instruments, high-speed analog-to-digital conversion, absolute ranging technology and coherent beam combination are introduced.

  • 飞秒激光器诞生以来,因具有超短脉冲宽度、超宽带相干光谱、超高峰值功率等特性,被广泛地应用在超快成像[1-3]、极端物理环境产生[4-5]、光与物质相互作用[6]等前沿领域。除了窄脉冲、宽光谱特点外,飞秒激光器的低定时抖动特性在其应用中也起到了十分重要的作用,尤其是为低噪声光学频率梳的构建奠定了基础,极大地推动了高精度绝对距离测量、精密光谱测量、精密光学频率测量等领域的发展。


    • 定时是指某件事情发生的特定时间点。通常电磁波脉冲的定时信息可以通过脉冲的时间重心(center of gravity, COG)来定义,其表达式为[13]

      式中:${{E}}\left({{t}}\right)$为脉冲的电场;${{t}}$为脉冲变化的时间。对于周期为${{T}}$的电磁波脉冲序列,均方根误差$\left\{{{{T}}}_{{n}}-{{n}}{{T}}|{{n}}= {1,2},3\cdots \right\}$称为定时抖动(Timing Jitter),用来描述脉冲的各个有效瞬时位置对其当时的理想位置的短期性随机偏离。


      Figure 1.  Timing jitter of mode-locked laser output (a) in time domain and (b) in frequency domain


      式中:$ {T}_{0} $为载波信号的周期;$ k $为玻耳兹曼常量;$ T $为绝对温度,$ {E}_{mode} $为腔内振荡模式的能量;$ {\tau }_{cav,RF} $为腔内能量的衰减时间常数。与微波信号源相对应的,飞秒激光器中以放大自发辐射噪声(ASE)直接耦合至双曲正割形脉冲的定时抖动的扩散系数可以写成如下形式[14]

      式中:$ {\tau }_{p} $为脉冲的半极大全宽;$ {E}_{p} $为单脉冲能量;$ hv $为单光子能量;${\tau }_{cav, \; ML}=\dfrac{{T}_{rt}}{2{g}_{s}}$为腔内损耗时间常数;$ {g}_{s} $为饱和增益。对于工作在室温下、载波频率为10 GHz的微波信号源来说,$ {T}_{0} $为100 $\rm{ps}$$kT\approx 0.025\;\rm{eV}$;对于工作在室温下、中心波长为1040 nm的飞秒激光器,$hv\approx 1.2\;\rm{eV}$$ {\tau }_{p} $约为100 $\rm{fs}$。若假设二者的腔内模式能量与脉冲能量和衰减时间常数乘积位于同一数量级,则微波信号源的扩散系数约为飞秒激光器的$ {10}^{5} $倍。不难看出,飞秒激光器的低定时抖动的优势主要来源于其极窄的脉冲宽度。这种现象可以解释为:在飞秒激光器腔内,脉冲能量集中在飞秒量级的超短脉冲内,单位时间内的光子密度得到了极大的提升;对于一定的自发辐射(ASE)噪声水平,脉冲光子密度的提高可以降低ASE噪声引起的脉冲时域分布的相对变化量,进而降低其对于脉冲时域位置的短期稳定性的干扰,使得脉冲的定时抖动保持在极低水平。

    • 锁模激光器的定时抖动在时域表现为脉冲实际位置对理想位置的偏移,在频域上则与重复频率的相位噪声相对应,如图1(b)所示。


      这种方法结构简单、技术成熟,在飞秒激光器定时抖动研究初期起到了至关重要的作用。但是随着研究的深入,这种方法的局限性逐渐显露:首先,飞秒激光器输出脉冲的脉冲宽度一般在百飞秒量级甚至更窄,对应着10太赫兹($ {\rm{T}}{\rm{H}}{\rm{z}},{10}^{12}\;{\rm{H}}{\rm{z}} $)以上的带宽,而目前商用的光电探测器的带宽往往在百吉赫兹($ {\rm{G}}{\rm{H}}{\rm{z}}, {10}^{9}\;{\rm{H}}{\rm{z}} $)以内,因此光电转换的过程会不可避免地引入低通滤波效应,损失掉飞秒激光器的高时间分辨率的优势。其次,飞秒激光器输出脉冲的定时抖动一般在飞秒或者亚飞秒量级,远比一般的微波信号源噪声水平低,因此测量过程对系统中的光电探测器、信号分析仪以及频率基准的自身噪声水平提出了更高的要求,精确测量的复杂程度和成本也大幅度增加。尤其是光电二极管的强度噪声向相位噪声的耦合系数较高,因此测量时的光电转换过程将会引入过高的相位噪声。

      从以上分析不难看出,直接使用光电探测器来测量飞秒激光器的定时抖动,测量的分辨率受到了微波器件的限制,测量的动态范围也相应降低。因此,早期的飞秒激光器定时抖动的测量结果一般在10 fs量级[16-19]

    • 为了进一步提高飞秒激光器定时抖动的测量分辨率,利用平衡光学互相关来测量定时抖动的方法被提出并逐渐普及。这种方法使用平衡光学互相关器来代替了光检测和混频器件。由于飞秒激光脉冲本身具有很高的定时鉴别灵敏度,可以确保BOC方法具有亚飞秒甚至阿秒级的时间分辨率。因此,可以实现超高的定时抖动测量灵敏度和宽动态范围[20-24]

      基于BOC的定时抖动测量系统如图2所示。为了解决飞秒激光器定时抖动低于微波器件本身底噪的问题,该方法采用了另一台与被测激光器具有相同或者更低定时抖动水平的飞秒激光器作为本振激光器。平衡互相关信号的产生基于两个正交偏振光在晶体中传输的群延迟差以及二类相位匹配的非线性和频效应。如图2所示,具有$ {\Delta t} $相对时间延迟的正交偏振的飞秒激光脉冲合束后入射至互相关器中。脉冲首先透过一面双色镜并聚焦至非线性晶体。两个正交偏振态的脉冲经过晶体时由于群速度失配会发生一个脉冲对另一个脉冲的赶超,在此过程中伴随和频信号的产生。非线性晶体之后放置另一面双色镜,使得和频信号透过双色镜,并由平衡探测二极管的一个端口探测。基频信号经双色镜反射再次聚焦至晶体,产生的和频信号由平衡探测二极管的另一个探测头探测。平衡探测器的输出电压值只与入射至互相关器的两个脉冲的时间间隔有关,而激光脉冲的强度波动引起的相关信号由平衡探测过程完全抵消。在不同的初始时间延迟$ {\Delta t} $下,两个基频光在非线性晶体中的重叠程度不同,将产生不同功率的和频信号,并由两个光电二极管转化为不同的电压值。典型的平衡探测器的输出的电压值随入射脉冲时间间隔$ {\Delta t} $的变化如图2的插图所示。

      Figure 2.  Balanced optical cross-correlation timing jitter measurement system




    • 另一种高分辨率的定时抖动测量方法是科罗拉多大学的侯东等人提出的基于光学外差探测的定时抖动测量技术[25]。该方法是通过将两台激光器输出的不同频率,如$\left(m{f}_{rep}+{f}_{ceo}\right)$$ \left(n{f}_{rep}+{f}_{ceo}\right) $处,分别做拍频,并将两个信号混频,这样可以消除两台激光器的相对载波-包络偏移频率的影响,进而得到只与两台激光器重复频率差有关的信号。实验证实,这种测量方法的本底噪声约为$2.8\times {10}^{-13}\;\rm{fs}^{2}/\rm{H}{z}$[25],比BOC方法获得的结果[26]低约10 dB,可作为BOC方法的替代方法之一。

    • 不论是平衡光学互相关法还是光学外差法,在测量激光器的定时抖动时都需要引入参考激光器。为了解决这一问题,韩国KAIST的J. Kim等人提出了一种基于非对称放置的光纤延迟线的干涉仪来测量激光器定时抖动的方法[27]。该方法使用公里级长的光纤延迟线对激光器输出的脉冲进行延迟,将延迟后的脉冲与激光器直接输出的脉冲进行比较,即可测得激光器的定时抖动。天津大学田昊辰等人在此基础上,搭建了一种基于非对称光纤延迟线干涉仪的复合测量平台[28]。该装置可以对飞秒激光频率梳的定时抖动、载波包络偏移频率噪声和梳齿线宽进行测量,降低了测量成本,更加实用。

    • 前述方法对定时抖动的表征主要通过测量激光器的定时抖动噪声功率谱密度来进行,它们能够精确地给出定时抖动的在频域的频率分布情况及噪声特性,方便与理论分析进行对照。但在光通信等实际使用领域中,常常使用“眼图”来表示信号在时域中的定时抖动的水平和分布,具有简单直观的优势。然而,由于飞秒脉冲宽度极窄,电子学的“眼图”分析方法不再适用。为了解决这一问题,天津大学的师浩森等人提出了一种基于异步光学采样[29-30]方法的定时抖动分析法,可以利用示波器等电子学设备对飞秒激光脉冲序列的亚飞秒的定时抖动进行“可视化”的实时分析。

      基于异步光学采样的定时抖动时域分析原理图如图3所示。系统包含一台待测激光器和一台本振激光器,重复频率分别为$ {f}_{r} $$ {f}_{r}-\Delta {f}_{r} $。对于无定时抖动的理想情况,如图3(a)中所示,由于两台激光器具有微小的重复频率差$ \Delta {f}_{r} $,因此在每个重复频率周期内,本振光脉冲会对待测光脉冲的不同位置进行采样并转化为电信号。在经历$N=\dfrac{{f}_{r}}{\Delta {f}_{r}}$个本振光脉冲后,可以完成对待测激光脉冲的一次采样,所用时间为${T}_{r}=\dfrac{1}{\Delta {f}_{r}}$。因此,异步光学采样法可以将飞秒量级的光脉冲在时域拉伸$ N $倍,转化为较慢变地、易测量的电脉冲,只需要确定放大倍数$ N $就可以实现亚飞秒甚至阿秒级的定时分辨率。

      Figure 3.  Principle of time-domain timing jitter characterization method based on ASPOS, the ASOPS process (a) without LUT timing jitter (b) with LUT timing jitter


    • 随着飞秒激光器定时抖动理论的不断完善和测量精度的逐渐提升,关于低抖动的飞秒激光源的实验研究也逐渐展开。

      固体飞秒激光器由于输出脉冲具有极窄的脉冲宽度和极高的峰值功率,ASE直接耦合的定时抖动水平较低。目前为止,飞秒激光器低定时抖动的纪录是麻省理工大学的A. J. Benedick等人通过BOC方法在脉冲宽度为10 fs的钛宝石飞秒激光器内获得的13 as的残余定时抖动[22]。另外,在基于SESAM锁模的Cr:LiSAF激光器和Er:Yb-glass激光器中,也分别获得了30 as[31]和83 as[32]的定时抖动(积分带宽为[10 kHz-50 MHz])。然而,由于固体激光器往往对腔镜的空间耦合精度要求极高,且使用和维护成本较高,因此很难在实验室以外的环境大范围地推广应用。

      与固体激光器相比,光纤激光器的光-光转化效率更高,热效应不明显,结构紧凑,价格低廉,更具有实用化优势。近年来,光纤飞秒激光器的定时抖动性能被不断优化,已经可以接近固体飞秒激光器的参数,进一步提高了其实用价值。2007年,韩国KAIST的J. Kim等人首次利用BOC技术实现了对掺铒光纤激光器的高频抖动的测量,在[10 kHz,10 MHz]积分带宽内获得了5 fs的定时抖动[33]。之后,宋有建等人在实验中探索了腔内净色散与脉冲序列定时抖动的耦合机制,通过优化激光器的色散参数将掺镱和掺铒光纤激光的高频定时抖动分别降低至175 as[20]和76 as[26]。2014年,天津大学的秦鹏等人通过在腔内加入窄带滤波器,使得掺镱激光器在很宽的腔色散范围内均可获得较低的的定时抖动[23],降低了低抖动飞秒激光源设计的难度。由于上述激光器均为基于非线性偏振旋转(Nonlinear Polarization Evolution, NPE)锁模的飞秒激光器,因此对于环境扰动和光纤应力较为敏感。2016年,美国IMRA公司N. Kuse等人设计了的一种基于非线性放大环形镜(Nonlinear Amplifying Loop Mirror, NALM)锁模的全保偏9字腔激光器,可获得40 as的定时抖动[34]。其研究提高了激光器长期稳定性和可重复性,为低定时抖动光纤飞秒激光器的实用化奠定了基础。

      尽管上述工作在降低锁模固体飞秒激光器和光纤飞秒激光器的定时抖动方面取得了巨大进步,但是这些阿秒级定时抖动性能的激光器重复频率大多被限制在100 MHz。为了探究高重频飞秒激光器的定时抖动特性,麻省理工大学的J. Chen等人通过在200 MHz激光振荡器外加入自由空间Fabry-Perot腔作为重频倍增器,获得了重复频率为2 GHz,定时抖动为27 fs的脉冲[35]。韩国KAIST的H. Yang等人搭建了重复频率为1.13 GHz的Yb:KYW固体激光器,并测得其在[17.5 kHz,10 MHz]带宽内的定时抖动为0.7 fs[36]。北京大学的王燕等人测量了基于NPE锁模的掺Yb光纤激光器在重复频率为882 MHz时的定时抖动,在[30 kHz,5 MHz]的积分带宽内最低为10 fs[37], 并提出高重频的光纤飞秒激光器的定时抖动可以通过减小相对强度噪声与定时抖动的耦合来抑制[38]。西安光机所的张建国等人报道了一种2.68 GHz全光纤SESAM锁模光纤激光器,在[300 Hz,30 MHz]的积分带宽内测得的定时抖动为82.5 fs[39]。此外,半导体锁模激光器和微环谐振腔也是可以产生数十GHz高重频超短脉冲的可靠光源。但是,由于半导体锁模激光器的脉冲宽度通常在皮秒量级,很难实现飞秒量级以下的极低抖动[40-42]。2020年,韩国KAIST课题组的D. Jeong等人测量了一台22 GHz的硅基微环光疏的定时抖动,在[10 kHz, 3 MHz]积分带宽内获得了2.6 fs的定时抖动积分值[43],进一步证明了微环谐振腔作为高重频低抖动飞秒激光光源的应用潜力。

      除单脉冲运转状态之外,飞秒激光器还能工作在多脉冲的束缚态。德国马普所的庞盟等发现,利用光机械力可以束缚住激光器内多个孤子,并编程调控其间隔,孤子之间的抖动小于100 fs[44],这种稳定的多孤子状态能够在激光器内一直稳定运转,为全光存储提供了一种新的思路。天津大学的师浩森等人发现,激光器内,光孤子尾部相互作用产生的紧束缚态孤子对的定时抖动<1 fs[45],这种稳定的双孤子结构有可能为全光信息处理提供一种新型多级字母表编码单元(multi-alphabet coding unit)。


      Laser sourceIntegrated
      timing jitter
      Integrated Fourier
      frequency range
      ClassificationLaser cavity parameter
      fiber laser
      194-MHz NPR,soliton mode-
      locking regime (2007)[47]
      18 fs [1 kHz–10 MHz] PD MIT
      3-GHz SESAM,soliton mode-
      locking regime (2009)[48]
      19 fs [10 kHz–40 MHz] PD MIT
      200-MHz NPR with spectral filter,stretched-pulse mode-locking regime (2010)[49] 17.4 fs [1 kHz–10 MHz] PD Shanghai Jiao Tong University
      1-GHz SESAM,soliton mode-
      locking regime (2010)[50]
      22 fs [1 kHz–10 MHz] PD MIT
      80-MHz NPR,cavity dispersion
      $-0.002\;\rm{ps}^{2}$ (2011)[26]
      0.07 fs* [10 kHz–40 MHz] BOC KAIST
      80-MHz CNT-SA,cavity dispersion
      $-0.02\;\rm{ps}^{2}$ (2013)[51]
      0.5 fs [10 kHz–40 MHz] BOC KAIST
      463-MHz MoS2-SA,soliton mode-
      locking regime (2015)[52]
      33 fs [1 kHz–1 MHz] PD Shanghai Jiao Tong University
      80-MHz NPR,cavity dispersion
      $+0.002\;\rm{ps}^{2}$ (2015)[53]
      0.7 fs [10 kHz–10 MHz] BOC KAIST
      129-MHz NPR with spectral filter,cavity dispersion$+0.008\;\rm{ps}^{2}$ (2015)[54] 3.46 fs [10 kHz–10 MHz] BOC KAIST
      75-MHz NALM,cavity dispersion
      $-0.003\;\rm{ps}^{2}$,soliton molecule (2018)[45]
      0.83 fs [10 Hz–2 MHz] BOC Tianjin University
      36.56 MHz NALM,soliton mode-
      locking regime (2019)[55]
      7.3 fs [10 kHz–1 MHz] FDL KAIST
      2.68 GHz SESAM,cavity dispersion
      $\sim 50\;\rm{fs}^{2}$ (2019)[39]
      82.5 fs [300 Hz-30 MHz] PD Xi'an Institute of Optics and Precision Mechanics of CAS
      fiber Laser
      80-MHz NPR,stretched-pulse mode-
      locking regime (2011)[20]
      0.18 fs* [10 kHz–40 MHz] BOC KAIST
      80-MHz NPR,soliton laser (2011)[20] 1.8 fs [10 kHz–40 MHz] BOC KAIST
      80-MHz NPR,amplifier-similariton (2011)[20] 2.9 fs [10 kHz–40 MHz] BOC KAIST
      80-MHz, NPR with spectral filter,cavity dispersion $+0.008\;\rm{ps}^{2}$ (2014)[23] 0.57 fs [10 kHz–10 MHz] BOC Tianjin University
      10-MHz SESAM,all-PM,cavity dispersion $+0.46\;\rm{ps}^{2}$ (2016)[24] 5.9 fs [10 kHz–5 MHz] BOC Tianjin University
      880 MHz NPR,stretched-pulse mode-
      locking regime (2018)[37]
      10 fs [30 kHz–5 MHz] BOC Peking University
      fiber laser
      690-MHz harmonic mode-locking NPR,soliton mode-locking regime (2015)[56] 6 ps [100 Hz–1 MHz] PD Tsinghua University
      253 MHz SBR Tm/Ho fiber laser (2016)[57] 20 fs [100 Hz–2 MHz] PD Boston University
      1.5 GHz SESAM (2018)[58] 940 fs [10 Hz–1 MHz] PD South China University of Technology
      80-MHz KLM Ti:sapphire laser (2012)[22] 0.013 fs* [100 Hz–40 MHz] BOC MIT
      100-MHz SESAM Cr:LiSAF laser (2012)[31] 0.03 fs [10 kHz–50 MHz] BOC MIT
      100-MHz, SESAM, Er:Yb-glass laser (2013)[32] 0.083 fs [10 kHz–50 MHz] BOC CSEM
      500-MHz SESAM Er:Yb-glass laser (2015)[25] 0.016 fs [10 kHz–250 MHz] OH University of Colorado
      10 GHz SCOWA-based harmonically mode-locked nested cavity laser (2018)[59] 3.4 fs [10 Hz,100 MHz] PD University of Central Florida
      21 GHz InAs/InP quantum dash laser (2018)[41] 400 fs [10 kHz,100 MHz] PD University College Cork
      19 GHz integrated heterogeneous silicon/III-V colliding pulse mode-locked laser (2018)[42] 1.2 ps [100 kHz,100 MHz] PD University of California
      22 GHz silica microcomb (2020)[43] 2.6 fs* [10 kHz–3 MHz] FDL KAIST
      * indicates the measured lowest timing jitter of lasers in this category

      Table 1.  Representative progress of low timing jitter femtosecond laser

      Laser sourceIntegrated timing jitterIntegrated Fourier frequency rangeCompany
      Figure 9 fiber laser <2 fs [10 kHz–10 MHz] Menlo System
      Figure 9 Er- fiber laser[34] 0.04 fs [10 kHz–10 MHz] IMRA America
      MENHIR-1550 ≤30 fs [1 kHz–10 MHz] MenHir Photonics
      ORIGAMI 5-40 <30 fs [1 kHz–10 MHz] NKT Photonics

      Table 2.  Timing jitter of commercial femtosecond laser

    • 精密定时是许多分布式大科学装置的必备技术。极具代表性的一个应用是目前世界各地在建的下一代X射线自由电子激光器(XFEL),包括美国斯坦福的硬X射线自由电子激光器(LCLS)[60]、德国的European XFEL[61]、瑞士的SwissFEL[62]、日本的SACLA[63]以及我国上海软X射线自由电子激光装置(SXFEL)[64]和上海硬X射线自由电子激光装置(SHINE)[65]等等。这些科学装置的设计目标是产生高能阿秒X射线脉冲[66],进而可以实现亚原子量级的空间分辨率,用来观测物理、化学反应的过程[67-68]。为了产生阿秒量级的X射线脉冲,需要对X射线自由电子激光器内部的所有光源和子微波源进行飞秒甚至阿秒精度的定时同步[13]。SwissFEL的定时同步系统中,德国Cycle GmbH, Notkestr等人使用了800 m长的单模光纤搭建了光纤链路来对激光器进行定时同步,该系统在[20 µHz,1 MHz]下获得了2.6 fs的抖动积分值[69]。在European XFEL的设计中,德国CFEL的辛明等人利用平衡光学互相关技术在3.5公里长的保偏光纤链路中对两台激光器进行了远程同步,40小时内的定时抖动仅为2.5 fs[70]。由于飞秒激光器输出的脉冲序列具有极低的高频定时抖动,因此可作为低抖动的时钟信号源和种子光振荡器,在这种现代大科学装置的建设中发挥至关重要作用。

    • 低定时抖动的信号源在信息处理领域同样具有重要的作用。模拟信号到数字信号的高速、高精度转换,是现代信息处理最基础的环节。然而,现阶段常见的模数转换系统(Analog-Digital Converter, ADC)大多基于微波器件。尽管微波器件在理论和技术上都较为成熟,但是受到其高频定时抖动的限制,在较高的采样频率下,模数转换系统能够实现的有效采样位数十分有限[71]。由于现代芯片级时钟电路最低只可以达到100 fs的定时抖动,因此无法在10 GHz的采样频率下实现6位以上的有效采样位数。

      为了兼顾高采样频率和高有效采样位数,必须降低采样信号源的定时抖动水平。飞秒激光器的高频定时抖动往往在飞秒甚至阿秒量级,将其作为采样信号进行模数转换,可以实现在高采样率下获得更高的有效采样位数。麻省理工大学的J. Kim等人通过将商用的掺镱飞秒激光器输出的超短脉冲序列用作采样信号,使用电光强度调制器对40 GHz的射频载波信号进行了采样实验。由于采样信号具有较低的定时抖动(在[10 kHz,2 MHz]的频率带宽内的定时抖动小于5 fs),该系统在2 MHz的探测带宽内的信噪比为44.3 dB,有效采样位数达到了7.06位[72]。上海交通大学的邹卫文等人构建的深度学习供电的光子模数转换(DL-PADC)体系结构中,使用了CALMAR公司的PSL-10-TT主动锁模激光器(实验测得定时抖动为26.5 fs)作为光子前端,来提供采样光脉冲序列和精确的量化时钟。在使用DL-PADC对23 GHz的载波信号进行采样时,有效采样位数可达9.24位。[21]

    • 近年来,空间合成孔径、地形地貌测量以及大型工件制造等前沿应用的出现,对距离测量的精度、动态范围和更新速率等指标提出了更高的要求。而随着光纤飞秒激光器的发展,低成本、高集成化、低抖动的特性进一步推动了其在高精度绝对距离测量领域的应用,飞秒激光频率梳合成波长干涉测距、多波长干涉测距、飞行时间测距、光谱色散测距等测量方法被相继提出[73]。尤其是基于两台具有一定重复频率差的低噪声飞秒激光器实现的双光梳绝对距离测量技术[74-75]更是以其高更新速率、高精度和大量程的优势得到了广泛关注。


    • 光束合成可以分为非相干合成和相干合成两大类。与非相干合成的强度叠加不同,相干合成中各路激光要实现稳定的干涉,进行振幅叠加。该技术能够克服单台光纤激光器功率限制以获得高输出功率,同时解决亮度、热管理等问题,保持良好的光束质量,是高功率激光技术的一个重要研究方向。早期的相干合成研究主要针对连续激光。国防科技大学马阎星等人通过主动相位控制对9路百瓦级光纤放大器进行相干合成,实现了1.08 kW的输出功率[77]。2017年,国防科技大学的刘泽金等人通过4路光纤激光的相干偏振合成,实现了5.02 kW的高功率输出[78]


      2001年,NIST的Sheldon等人首次证明了两台飞秒激光器相干脉冲合成的可能性[79]。然而,该技术的实现面临着巨大的挑战。一个必要的前提是两台飞秒激光器的相对定时抖动和载波-包络相位抖动必须稳定至数十阿秒,达到原子时间尺度[80]。因此,直到平衡互相关技术的产生和发展,才使得飞秒激光的相干合成成为可能。2012年,J. A Cox等人通过将钛宝石激光器和掺铒光纤激光器产生的超连续谱的相干合成,实现二者之间的剩余相对定时抖动为2.2 fs,得到了超过一个倍频程的光谱和脉冲宽度为3.7 fs的近单周期时域脉冲[81]。2016年,天津大学的田昊辰等人通过优化激光腔的量子噪声,对两台独立的掺镱光纤飞秒激光器进行相干合束,如图4所示,实现了长达1小时的稳定运转,克服了此前飞秒激光相干合成维持时间短、难以实用化的缺点,为单周期脉冲合成、光学任意波形产生及飞秒频率梳的远程分布等应用带来了突破[82]。2019年,天津大学的葛爱晨等人搭建的掺镱光纤飞秒激光器的相干合成系统,两个脉冲之间的相对定时抖动小于光周期的十分之一,在放大后利用光子晶体光纤进行非线性脉冲压缩,获得了8 fs的时域脉冲[83]

      Figure 4.  Coherent synthesis system based on femtosecond fiber laser. (a) Scheme; (b) long term stable spectral interferogram

    • 与常用的微波信号源以及其他类型的脉冲激光器相比,飞秒激光器输出的超短脉冲序列在时域上具有极低的定时抖动;在频域上,则提供了一个处于射频频率且相位噪声极低的重复频率信号源。飞秒激光器的输出脉冲序列同时携带了低抖动的光频信号和射频信号,可以实现与现有的光学、射频系统的低成本对接。

      随着飞秒激光器在低抖动方面的优势日益明显,关于其定时抖动的研究也逐渐开展:不仅定时抖动的理论体系逐渐完善,相关的测量手段也在不断进步,这些都为低抖动飞秒激光器的开发奠定了坚实的基础。与此同时,随着低抖动飞秒激光器的推广应用,一些全新的方法和技术也为其定时抖动水平的进一步优化提供了新的思路。比如,近期快速兴起的基于微腔孤子的光学频率梳[84-85],由于其具有极高的重复频率(通常在10 GHz~100 GHz以上)、较低的定时抖动水平[43]同时兼具易于微型光子集成、发展为芯片系统的潜力,无疑是未来激光雷达、精密测距、高速ADC领域的理想低抖动飞秒光源之一。


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