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电光频率梳是一种单频激光器经相位调制构造的光学频率梳, 具有重复频率高、灵活可调等特点, 通过精确的色散控制, 电光频率梳在时域上可以输出超短脉冲激光序列, 其时间抖动特性对于开展精密测量等应用十分重要. 本文提出一种基于双光梳异步光学采样原理测量电光频率梳时间抖动的方案. 建立了时间抖动测量的理论模型并进行数值模拟. 搭建了一台重复频率为10 GHz、脉冲宽度为2.6 ps的电光频率梳, 并开展了时间抖动的测量实验. 测量的直方图分析表明, 电光频率梳的周期抖动为3.86 fs. 测量装置主体为光纤结构, 且不需要高速光电探测器, 有望对电光频率梳、微环频率梳等新型高重频光学频率梳时间抖动的测量与优化起到关键作用.
Electro-optic frequency combs (EOCs) are optical frequency combs constructed by phase modulation of single frequency lasers. The electro-optic modulated optical frequency combs have shown their unique advantages in many application fields due to their high repetition frequencies, high stabilities and other advantages, especially in precision measurement applications. Through accurate dispersion control, the electro-optical frequency combs can output ultra-short pulse laser sequences in the time domain, and their timing jitter characteristic is very important for precision measurement and other applications. This work presents a scheme to measure the timing jitter of the electro-optic combs directly in the time domain based on the principle of dual-comb asynchronous optical sampling method(ASOPS), which relies on temporal cross-correlation between the high repetition rate electro-optic combs and a low repetition rate passively mode-locked fiber laser. The ASOPS process allows timing jitter measurement in a magnified time scale where the timing jitter at a femtosecond level can be received and visualized by standard low speed electronics. We build a theoretical model for timing jitter measurement, conduct a numerical study to verify the model, and also construct an experimental system to characterize the period jitter of a 10-GHz electro-optic comb. Firstly, the theoretical model for measuring timing jitter is established. In this work, the basic theory of measuring the timing jitter is discussed by analyzing the histogram directly in time domain through using the obtained ASOPS signal. Subsequently, numerical simulations are conducted to simulate the ASOPS process after establishing a sequence of Gaussian pulse train with quantum limited timing jitter. Another pulse train without timing jitter serves as a local oscillator. Through the square law optical detection after sum-frequency generation between LO and LUT, the ASOPS process can be realized and periodic jitter can be obtained directly through histogram statistical analysis. The simulation result is consistent with the theoretical result very well. Finally, an EOC system with cascaded modulators at a repetition rate of 10 GHz is designed and built, and a timing jitter measurement system is designed and built with an all-fiber configuration. The period jitter of 10-GHz EOC is measured by using a 161-MHz mode-locked fiber laser as local oscillator. Histogram analysis shows that the period jitter of the EOC is 3.86 fs. This measurement technique does not require to use the intricate electrical phase-locked circuits or a high-speed photodetector to receive ultrashort pulses of EOC. Like the eye map analysis method commonly used in telecommunication, the histogram analysis can be used to determine the timing jitter approaching the quantum limit. This approach is easy to set up and operate, and it is anticipated to become a standard method of measuring period jitter of ultrashort pulse with high repetition frequency in a laboratory setting. It will be particularly useful for measuring timing jitters of the sources of novel high repetition rate optical frequency combs, such as micro-resonators and electro-optic frequency combs. -
Keywords:
- electro-optic frequency combs /
- timing jitter /
- asynchronous optical sampling /
- phase noise
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图 1 ASOPS法测量时域抖动原理图
Fig. 1. Principle diagram of time domain jitter measurement by ASOPS method.
图 2 模拟中带有抖动的ASOPS信号的叠加结果
Fig. 2. The superposition of ASOPS signals with jitter in the simulation.
图 3 ASOPS法测量待测电光频率梳系统时域抖动实验装置图 (a)待测的电光频率梳系统示意图, PS, 移相器; PC, 偏振控制器; Amp, 功率放大器; IM, 强度调制器; PM, 相位调制器; DC bias, 直流偏压; SMF, 单模光纤; (b)电光频率梳时间抖动测量实验装置图, OFC, 光纤锁模光频梳; EOC, 电光频率梳; BPF, 带通滤波器; Coupler, 保偏光纤耦合器; LPF, 低通滤波器; OC, 光学环形器
Fig. 3. Timing jitter test device of electro-optic combs system to be measured by ASOPS method: (a) Schematic diagram of the EOC system to be tested, PS, phase shifter; PC, polarization controller; Amp, power amplifier; IM, intensity modulator; PM, phase modulator; DC bias, DC bias; SMF, single mode fiber; (b) the timming jitter measurement experimental device diagram of electro-optic combs, OFC, optical fiber mode-locked optical frequency combs; EOC, electro-optic frequency combs; BPF, bandpass filter; Coupler, polarization-maintaining fiber coupler; LPF, low pass filter; OC, optical circulator.
图 4 电光频率梳输出的光谱脉冲和ASOPS采集信号示意图 (a)电光频率梳的输出光谱; (b)电光频率梳经单模光纤压缩后的输出脉冲的自相关曲线及其高斯拟合曲线; (c)采集的ASOPS信号示意图; (d)由采集的脉冲对得到的直方图统计结果
Fig. 4. Schematic diagram of spectral pulse output and ASOPS acquisition signal of electro-optic combs: (a) The output spectrum of the electro-optic combs; (b) the autocorrelation curve and Gaussian fitting curve of the output pulse after electro-optic combs compression by single-mode fiber are obtained; (c) schematic diagram of collected ASOPS signals; (d) the statistical results of the histogram obtained from the collected pulses.
图 5 时间抖动的PSD曲线及累计时间抖动曲线示意图
Fig. 5. PSD curve of timing jitter and schematic diagram of cumulative timing jitter curve.
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[1] Jones D J, Diddams S A, Ranka J K, Stentz A, Windeler R S, Hall J L, Cundiff S T 2000 Science 288 635
Google Scholar
[2] Hansch T W 2006 Rev. Mod. Phys. 78 1297
Google Scholar
[3] Giorgetta F R, Swann W C, Sinclair L C, Baumann E, Coddington I, Newbury N R 2013 Nat. Photonics 7 435
[4] 刘亭洋, 张福民, 吴翰钟, 李建双, 石永强, 石永强, 曲兴华 2016 62 020601
Google Scholar
Liu T Y, Zhang F M, Wu H Z, Li J S, Shi Y Q, Qu X H 2016 Acta Phys. Sin. 62 020601
Google Scholar
[5] Liang X, Wu T F, Lin J R, Yang L H, Zhu J G 2023 Nanomanuf. Metrol. 6 61
[6] Ma Q Y, Yu H Y 2023 Nanomanuf. Metrol. 6 36
Google Scholar
[7] 石俊凯, 纪荣祎, 黎尧, 刘娅, 周维虎 2017 66 134203
Google Scholar
Shi J K, Ji R W, Li Y, Liu Y, Zhou W H, 2017 Acta Phys. Sin. 66 134203
Google Scholar
[8] Cui Y D, Zhang Y S, Huang L, Zhang A G, Liu Z M, Kuang C F, Tao C N, Chen D R, Liu X, Malomed B A 2023 Phys. Rev. Lett. 130 153801
Google Scholar
[9] Martín-Mateos P, Jerez B, Acedo P 2015 Opt. Express 23 21149
Google Scholar
[10] Zhang X, Yin K, Zhang J H, Li Y M, Yang J, Zheng X, Jiang T 2020 Asia Communications and Photonics Conference (ACP), Chengdu, China, November 2–5, 2019 p1056
[11] Xu G, Gelash A, Chabchoub A, Zakharov V, Kibler B 2019 Phys. Rev. Lett. 122 84101
Google Scholar
[12] Durán V, Andrekson P A, Torres-Company V 2016 Opt. Lett. 41 4190
Google Scholar
[13] 赵显宇, 曲兴华, 陈嘉伟, 郑继辉, 王金栋, 张福民 2020 69 090601
Google Scholar
Zhao X Y, Qu X H, Chen J W, Zheng J H, Wang J D, Zhang F M 2020 Acta Phys. Sin. 69 090601
Google Scholar
[14] Zhuang R, Ni K, Wu G H, Hao T, Lu L Z, Li Y, Zhou Q 2023 Laser Photonics Rev. 17 2200353.1
[15] Kim J, Song Y J 2016 Adv. Opt Photonics 8 465
Google Scholar
[16] Song Y J, Kim C, Jung K, Kim H, Kim J 2011 Opt. Express 19 14518
Google Scholar
[17] Hou D, Lee C C, Yang Z, Schibli T R 2015 Opt. Lett. 40 2985
Google Scholar
[18] Carlson D R, Hickstein D D, Zhang W, Metcalf A J, Quinlan F, Diddams S A, Papp S B 2018 Science. 361 1358
Google Scholar
[19] Cai Y J, Sohanpal R, Luo Y, Heidt A M, Liu Z X 2023 APL Photonics 8 110802
Google Scholar
[20] Watts R T, Murdoch S G, Barry L P 2016 IEEE Photonics J. 8 1
[21] Ishizawa A, Nishikawa T, Goto T, Hitachi K, Sogawa T, Gotoh H 2016 Sci. Rep. 6 24621
Google Scholar
[22] Kim J, Richardson D J, Slavik R 2017 Opt. Lett. 42 1536
Google Scholar
[23] Ishizawa A, Nishikawa T, Mizutori A, Takara H, Takada A, Sogawa T, Koga M 2013 Opt. Express 21 29186
Google Scholar
[24] Lundberg L, Mazur M, Fulop A, Torres-commpany V, Karlsson M, Andrekson P A 2018 Conference on Lasers and Electro-Optics, San Jose, May 13–18, 2018 p2369
[25] Sakamoto T, Kawanishi T, Tsuchiya M 2008 Opt. Lett. 33 890
Google Scholar
[26] Metcalf A J, Quinlan F, Fortier T M, Diddams S A, Weiner A M 2015 Electron. Lett. 51 1596
Google Scholar
[27] Xiao S J, Hollberg L, Newbury N R, Diddams S A 2008 Opt. Express 16 8498
Google Scholar
[28] Peng H F, Lei P, Xie X P, Chen Z Y 2021 Opt. Express 29 42435
Google Scholar
[29] Peng H F, Xu Y C, Guo R, Du H Y, Chen J B, Chen Z Y 2018 Asia Communications and Photonics Conference, Hangzhou, China, October 26–29, 2018 p364
[30] Peng H F, Guo R, Du H Y, Xu Y C, Zhang C, Chen J B, Chen Z Y 2018 International Conference on Information Optics and Photonics , Beijing, China, July 8–11, 2018 p1269
[31] He Z W, Li L Z, Zhang J J, Yao J P 2021 Opt. Express 29 33491
Google Scholar
[32] Zhai K P, Wang W T, Zhu S, Wen H S, Zhu N H 2023 IEEE Photonics J. 15 1
[33] Bao C Y, Suh M G, Shen B Q, Safak K, Dai A, Wang H M, Wu L, Yuan Z Q, Yang Q F, Matsko A B, Kaertner F X, Vahala K J 2021 Nat. Phys. 17 462
Google Scholar
[34] Shi H S, Song Y J, Yu J H, Li R M, Hu M L, Wang C Y 2017 Opt. Express 25 10
Google Scholar
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