纯四次孤子光纤激光器研究进展

罗民; 张泽贤; 陈乃妙; 刘萌; 罗爱平; 徐文成; 罗智超

doi:10.7498/aps.72.20230868

摘要

纯四次孤子光纤激光器是一种新型的超短脉冲激光器, 能够在四阶色散和自相位调制效应平衡下保持脉冲形状稳定传输. 相比于二阶色散主导下的常规孤子激光器, 纯四次孤子激光器输出的锁模脉冲能量可以高出1—2个数量级, 这将为研制高能量、高峰值功率的光纤激光器提供新思路. 本文系统地回顾了近年来在光纤激光器等非线性光学系统中纯四次孤子的产生以及传输特性, 并探讨了纯四次孤子中已观察到的一些特殊瞬态动力学现象. 同时, 介绍了笔者所在课题组在该研究方向上的最新成果. 最后, 本文对纯四次孤子光纤激光器的应用前景以及发展趋势进行展望, 为相关领域未来的研究提供有价值的参考. 这些结果将有助于更全面认识纯四次孤子光纤激光器的基本物理特性.

关键词:

Abstract

The pure-quartic soliton fiber laser is an innovative ultra-short pulse laser that can maintain a stable pulse shape through a balance between fourth-order dispersion effect and self-phase modulation effect. Comparing with traditional soliton laser that is dominated by second-order dispersion, the mode-locked pulse energy of pure-quartic soliton laser can be 1–2 orders of magnitude higher. This provides researchers with new ideas for developing high-energy and high-peak-power fiber lasers. Here, the generation and transmission characteristics of pure-quartic solitons in nonlinear optical systems such as fiber lasers in recent years are systematically reviewed. It also explores some special transient dynamic phenomena. Furthermore, in this article, the latest achievements of our research group in this area are also presented. Finally, the application prospect and development trend of pure-quartic soliton fiber lasers are prospected. These results will contribute to a more comprehensive understanding of the basic physical properties of pure-quartic soliton fiber lasers.

Keywords:

作者及机构信息

华南师范大学信息光电子科技学院, 广州　510631

通信作者: 罗智超, zcluo@scnu.edu.cn

基金项目: 国家自然科学基金 (批准号: 11874018, 11974006, 61805084, 61875058)和广东省自然科学基金 (批准号: 2022A1515011760, 2021A1515012315)资助的课题.

Authors and contacts

School of Information and Optoelectronic Science and Engineering, South China Normal University, Guangzhou 510631, China

Corresponding author: Luo Zhi-Chao, zcluo@scnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11874018, 11974006, 61805084, 61875058) and the Natural Science Foundation of Guangdong Province, China (Grant Nos. 2022A1515011760, 2021A1515012315).

文章全文

参考文献

[1]	Cundiff S T, Ye J 2003 Rev. Mod. Phys. 75 325 Google Scholar
[2]	Yi X, Yang Q F, Yang K Y, Suh M G, Vahala K 2015 Optica 2 1078 Google Scholar
[3]	Okhotnikov O, Grudinin A, Pessa M 2004 New J. Phys. 6 177 Google Scholar
[4]	Wise F W, Chong A, Renninger W H 2008 Laser Photon. Rev. 2 58 Google Scholar
[5]	Grelu P, Akhmediev N 2012 Nat. Photonics 6 84 Google Scholar
[6]	Xu C, Wise F W 2013 Nat. Photonics 7 875 Google Scholar
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[8]	Mollenauer L F, Stolen R H, Gordon J P 1980 Phys. Rev. Lett. 45 1095 Google Scholar
[9]	Agrawal G P 2007 Nonlinear Fiber Optics (4th Ed.) (Academic Press
[10]	Fermann M E, Hartl I 2013 Nat. Photonics 7 868 Google Scholar
[11]	Dennis M L, Duling I N 1994 IEEE J. Quantum Elect. 30 1469 Google Scholar
[12]	Nelson L E, Jones D J, Tamura K, Haus H A, Ippen E P 1997 Appl. Phys. B 65 277 Google Scholar
[13]	Shabat A, Zakharov V 1972 Sov. Phys. JETP 34 62
[14]	Renninger W H, Chong A, Wise F W 2010 J. Opt. Soc. Am. B 27 1978 Google Scholar
[15]	Tamura K, Ippen E P, Haus H A, Nelson L E 1993 Opt. Lett. 18 1080 Google Scholar
[16]	Chong A, Buckley J, Renninger W, Wise F 2006 Opt. Express 14 10095 Google Scholar
[17]	Blow K J, Doran N J, Wood D 1988 J. Opt. Soc. Am. B 5 381 Google Scholar
[18]	Karlsson M, Höök A 1994 Opt. Commun. 104 303 Google Scholar
[19]	Christov I P, Murnane M M, Kapteyn H C, Zhou J, Huang C P 1994 Opt. Lett. 19 1465 Google Scholar
[20]	Piché M, Cormier J F, Zhu X 1996 Opt. Lett. 21 845 Google Scholar
[21]	Roy S, Biancalana F 2013 Phys. Rev. A 87 025801 Google Scholar
[22]	Blanco-Redondo A, de Sterke C M, Sipe J E, Krauss T F, Eggleton B J, Husko C 2016 Nat. Commun. 7 10427 Google Scholar
[23]	Runge A F J, Hudson D D, Tam K K K, de Sterke C M, Blanco-Redondo A 2020 Nat. Photonics 14 492 Google Scholar
[24]	de Sterke C M, Runge A F J, Hudson D D, Blanco-Redondo A 2021 APL Photonics 6 091101 Google Scholar
[25]	Runge A F J, Alexander T J, Newton J, Alavandi P A, de Sterke C M 2020 Opt. Lett. 45 3365 Google Scholar
[26]	Qian Z C, Liu M, Luo A P, Xu W C, Luo Z C 2022 Opt. Express 30 22066 Google Scholar
[27]	Soto-Crespo J M, Akhmediev N, Ankiewicz A 2000 Phys. Rev. Lett. 85 2937 Google Scholar
[28]	Akhmediev N, Soto-Crespo J M, Town G 2001 Phys. Rev. E 63 056602 Google Scholar
[29]	Zhao L M, Tang D Y, Lin F, Zhao B 2004 Opt. Express 12 4573 Google Scholar
[30]	Liu M, Wei Z W, Li H, Li T J, Luo A P, Xu W C, Luo Z C 2020 Laser Photonics Rev. 14 1900317 Google Scholar
[31]	Akhmediev N, Soto-Crespo J M 2003 Phys. Lett. A 317 287 Google Scholar
[32]	Liu M, Luo A P, Yan Y R, Hu S, Liu Y C, Cui H, Luo Z C, Xu W C 2016 Opt. Lett. 41 1181 Google Scholar
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[35]	Aossey D W, Skinner S R, Cooney J L, Williams J E, Gavin M T, Andersen D R, Lonngren K E 1992 Phys. Rev. A 45 2606 Google Scholar
[36]	Liu M, Li T J, Luo A P, Xu W C, Luo Z C 2020 Laser Photon. Rev. 14 1900317 Google Scholar
[37]	Wai P K A, Chen H H, Lee Y C 1990 Phys. Rev. A 41 426 Google Scholar
[38]	Kodama Y, Romagnoli M, Wabnitz S, Midrio M 1994 Opt. Lett. 19 165 Google Scholar
[39]	Höök A, Karlsson M 1993 Opt. Lett. 18 1388 Google Scholar
[40]	Karpman V I 1996 Phys. Rev. E 53 R1336 Google Scholar
[41]	Roy S, Bhadra S K, Agrawal G P 2009 Opt. Commun. 282 3798 Google Scholar
[42]	Blanco-Redondo A, Eades D, Li J, Lefrancois S, Krauss T F, Eggleton B J, Husko C 2014 Optica 1 299 Google Scholar
[43]	Blanco-Redondo A, Husko C, Eades D, Zhang Y, Li J, Krauss T F, Eggleton B J 2014 Nat. Commun. 5 3160 Google Scholar
[44]	Hasegawa A, Tappert F 1973 Appl. Phys. Lett. 23 142 Google Scholar
[45]	Lo C W, Stefani A, de Sterke C M, Blanco-Redondo A 2018 Opt. Express 26 7786 Google Scholar
[46]	Tam K K K, Alexander T J, Blanco-Redondo A, de Sterke C M 2019 Opt. Lett. 44 3306 Google Scholar
[47]	Kelly S M J 1992 Electron. Lett. 28 806 Google Scholar
[48]	Runge A F J, Qiang Y L, Alexander T J, Rafat M Z, Hudson D D, Blanco-Redondo A, de Sterke C M 2021 Phys. Rev. Res. 3 013166 Google Scholar
[49]	Widjaja J, Kobakhidze E, Cartwright T R, Lourdesamy J P, Runge A F J, Alexander T J, de Sterke C M 2021 Phys. Rev. A 104 043526 Google Scholar
[50]	Zhang Z X, Luo M, Chen J X, Liu M, Luo A P, Xu W C, Luo Z C 2022 Opt. Lett. 47 1750 Google Scholar
[51]	Soto-Crespo J M, Grapinet M, Grelu P, Akhmediev N 2004 Phys. Rev. E 70 066612 Google Scholar
[52]	Liu K W, Yao S Y, Yang C X 2021 Opt. Lett. 46 993 Google Scholar

施引文献

图 1 纯四次孤子概念及其及实验证明^[22]　(a) 纯四次孤子原理图; (b) 频率分辨电开关; (c) 扫描电子显微镜下的样品图像; (d) 光子晶体波导的色散测量

Fig. 1. Concept of pure-quartic solitons and their experimental demonstration^[22]: (a) Schematic of pure-quartic solitons; (b) frequency-resolved electrical gating; (c) scanning electron microscopy image of the sample; (d) measured dispersion of the photonic crystal waveguides.

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图 2 不同输入功率下的频域和时域结果(红色虚线为实验结果, 蓝色实线为模拟结果)^[22]

Fig. 2. Frequency domain and time domain results at different input powers (the red dashed line is the experimental result, and the solid blue line is the simulation result)^[22].

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图 3 纯四次孤子输出特性　(a) 线性坐标下的时域脉冲; (b) 对数坐标下的时域脉冲; (c) 线性坐标下的频域光谱; (d) 对数坐标下的频域光谱(红色为常规孤子光谱)^[46]

Fig. 3. Output characteristics of pure-quartic solitons: (a) Time domain pulses at linear coordinates; (b) time domain pulses at logarithmic coordinates; (c) frequency domain spectrum in linear coordinates; (d) frequency domain spectrum in logarithmic coordinates (red is the spectrum of traditional soliton)^[46].

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图 4 纯四次孤子光纤激光器原理示意图　(a) 实验装置图; (b) 二阶色散相位; (c)四阶色散相位^[23]

Fig. 4. Schematic diagram of pure-quartic fiber soliton laser: (a) Experimental setup; (b) second-order dispersion phases; (c) fourth-order dispersion phases^[23].

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图 5 实验和模拟上的光谱和时域曲线　(a)—(d) 传统孤子; (e)—(h) 纯四次孤子^[23]

Fig. 5. Experimental (exp.) and simulated (sim.) spectra and time-domain curves: (a)–(d) Conventional solitons; (e)–(h) pure-quartic solitons^[23].

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图 6 自相似纯四次孤子激光器　(a) 模拟结构图; (b)时域曲线; (c) 频域曲线^[25]

Fig. 6. Self-similar pure-quartic soliton laser: (a) Simulation structure diagram; (b) time domain curves; (c) frequency domain curves^[25]

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图 7 耗散纯四次孤子^[26]　(a) 线性与对数坐标下的光谱; (b) 脉冲和啁啾; (c), (d) 1000圈下的频域和时域演化

Fig. 7. Dissipative pure-quartic solitons^[26]: (a) Spectrum with log and linear coordinates; (b) pulse and chirp; (c), (d) evolution of frequency domain and time domain with 1000 roundtrips.

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图 8 非对称“M”型耗散纯四次孤子^[26]　(a) 线性与对数坐标下的光谱; (b) 脉冲(蓝色)和啁啾(红色); (c), (d) 1000圈下的频域和时域演化

Fig. 8. Asymmetric “M” type dissipative pure-quartic solitons^[26]: (a) Spectrum with log and linear coordinates; (b) pulse (blue) and chirp (red); (c), (d) evolution of frequency domain and time domain with 1000 roundtrips.

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图 9 纯高阶色散孤子六次色散(上行)、八次色散(中行)和十次色散(下行)的频域和时域测量　(a)—(c) 测量光谱(蓝色)和计算光谱(红色虚线); (d)—(f) 频谱图; (g)—(i) 时域强度(蓝色)、相位(橙色)以及相应的计算时域形状(红色虚线)^[48]

Fig. 9. Spectral and temporal measurements of pure high-order dispersion solitons sextic (top row), octic (middle row), and decic (bottom row) dispersion: (a)–(c) Measured (blue) and calculated (red-dashed) spectrum; (d)–(f) spectrograms; (g)–(i) temporal intensity (blue), phase (orange), and corresponding calculated temporal shapes (red-dashed)^[48].

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图 10 纯四次孤子在不同初始相位差条件下碰撞动力学^[49]

Fig. 10. Collision dynamics of pure-quartic solitons with different initial phase differences^[49].

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图 11 纯四次孤子的脉动状态^[50]　(a) 时域的演化(插图为纯四次孤子中心部分(绿色)和振荡尾(白色)的能量演化); (b)光谱域的演化

Fig. 11. Pulsation state of pure-quartic solitons^[50]: (a) Evolution of the time domain(energy evolution of the pure quadruple soliton center (green) and oscillating tail (white)); (b) evolution of the spectral domain.

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图 12 (a) 具有不同饱和能量值的纯四次孤子的归一化峰值强度演化; (b), (c) 不同饱和能量下脉冲的两个典型分布^[50]

Fig. 12. (a) Normalized peak intensity evolution of pure-quartic solitons with different saturation energy values; (b), (c) two typical pulse distributions under different saturated energies^[50].

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图 13 (a) 拉曼效应下纯四次孤子的峰值功率(黑点)与泵浦功率(红色虚线)的关系(呼吸状态由灰色区域显示); (b) 稳定状态(泵浦功率为1 W, 6 W)和 (c) 呼吸状态(泵浦功率为4 W)的时域脉冲及其相应相位(红线); (d) 4 W泵浦功率下拉曼纯四次孤子呼吸的典型频谱; (e) 呼吸状态谱能量演化(白色虚线表示不同段的光谱能量峰值)^[52]

Fig. 13. (a)The relationship between peak power (black dot) and pump power (red dashed line) of Raman pure-quartic solitons (the breathing state is shown by the gray area); (b) time domain pulses in stable state (pump powers are 1 W and 6 W) and (c) breathing state (pump power is 4 W) and corresponding phases (red line); (d) typical breathing spectrum of Raman pure-quartic solitons at pump power of 4 W; (e) energy evolution of the breathing spectrum (the white dotted lines indicate the spectral energy peaks in different segments)^[52].

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map

[1]	Cundiff S T, Ye J 2003 Rev. Mod. Phys. 75 325 Google Scholar
[2]	Yi X, Yang Q F, Yang K Y, Suh M G, Vahala K 2015 Optica 2 1078 Google Scholar
[3]	Okhotnikov O, Grudinin A, Pessa M 2004 New J. Phys. 6 177 Google Scholar
[4]	Wise F W, Chong A, Renninger W H 2008 Laser Photon. Rev. 2 58 Google Scholar
[5]	Grelu P, Akhmediev N 2012 Nat. Photonics 6 84 Google Scholar
[6]	Xu C, Wise F W 2013 Nat. Photonics 7 875 Google Scholar
[7]	Wang K, Horton N G, Charan K, Xu C 2014 IEEE J. Sel. Top. Quant. 20 50 Google Scholar
[8]	Mollenauer L F, Stolen R H, Gordon J P 1980 Phys. Rev. Lett. 45 1095 Google Scholar
[9]	Agrawal G P 2007 Nonlinear Fiber Optics (4th Ed.) (Academic Press
[10]	Fermann M E, Hartl I 2013 Nat. Photonics 7 868 Google Scholar
[11]	Dennis M L, Duling I N 1994 IEEE J. Quantum Elect. 30 1469 Google Scholar
[12]	Nelson L E, Jones D J, Tamura K, Haus H A, Ippen E P 1997 Appl. Phys. B 65 277 Google Scholar
[13]	Shabat A, Zakharov V 1972 Sov. Phys. JETP 34 62
[14]	Renninger W H, Chong A, Wise F W 2010 J. Opt. Soc. Am. B 27 1978 Google Scholar
[15]	Tamura K, Ippen E P, Haus H A, Nelson L E 1993 Opt. Lett. 18 1080 Google Scholar
[16]	Chong A, Buckley J, Renninger W, Wise F 2006 Opt. Express 14 10095 Google Scholar
[17]	Blow K J, Doran N J, Wood D 1988 J. Opt. Soc. Am. B 5 381 Google Scholar
[18]	Karlsson M, Höök A 1994 Opt. Commun. 104 303 Google Scholar
[19]	Christov I P, Murnane M M, Kapteyn H C, Zhou J, Huang C P 1994 Opt. Lett. 19 1465 Google Scholar
[20]	Piché M, Cormier J F, Zhu X 1996 Opt. Lett. 21 845 Google Scholar
[21]	Roy S, Biancalana F 2013 Phys. Rev. A 87 025801 Google Scholar
[22]	Blanco-Redondo A, de Sterke C M, Sipe J E, Krauss T F, Eggleton B J, Husko C 2016 Nat. Commun. 7 10427 Google Scholar
[23]	Runge A F J, Hudson D D, Tam K K K, de Sterke C M, Blanco-Redondo A 2020 Nat. Photonics 14 492 Google Scholar
[24]	de Sterke C M, Runge A F J, Hudson D D, Blanco-Redondo A 2021 APL Photonics 6 091101 Google Scholar
[25]	Runge A F J, Alexander T J, Newton J, Alavandi P A, de Sterke C M 2020 Opt. Lett. 45 3365 Google Scholar
[26]	Qian Z C, Liu M, Luo A P, Xu W C, Luo Z C 2022 Opt. Express 30 22066 Google Scholar
[27]	Soto-Crespo J M, Akhmediev N, Ankiewicz A 2000 Phys. Rev. Lett. 85 2937 Google Scholar
[28]	Akhmediev N, Soto-Crespo J M, Town G 2001 Phys. Rev. E 63 056602 Google Scholar
[29]	Zhao L M, Tang D Y, Lin F, Zhao B 2004 Opt. Express 12 4573 Google Scholar
[30]	Liu M, Wei Z W, Li H, Li T J, Luo A P, Xu W C, Luo Z C 2020 Laser Photonics Rev. 14 1900317 Google Scholar
[31]	Akhmediev N, Soto-Crespo J M 2003 Phys. Lett. A 317 287 Google Scholar
[32]	Liu M, Luo A P, Yan Y R, Hu S, Liu Y C, Cui H, Luo Z C, Xu W C 2016 Opt. Lett. 41 1181 Google Scholar
[33]	Luo M, Zhang Z X, Liu M, Luo A P, Xu W C, Luo Z C 2022 Opt. Express 30 22143 Google Scholar
[34]	Luo M, Zhang Z X, Chen N M, Liu M, Luo A P, Xu W C, Luo Z C 2023 Adv. Phys. Res. 2 2200103 Google Scholar
[35]	Aossey D W, Skinner S R, Cooney J L, Williams J E, Gavin M T, Andersen D R, Lonngren K E 1992 Phys. Rev. A 45 2606 Google Scholar
[36]	Liu M, Li T J, Luo A P, Xu W C, Luo Z C 2020 Laser Photon. Rev. 14 1900317 Google Scholar
[37]	Wai P K A, Chen H H, Lee Y C 1990 Phys. Rev. A 41 426 Google Scholar
[38]	Kodama Y, Romagnoli M, Wabnitz S, Midrio M 1994 Opt. Lett. 19 165 Google Scholar
[39]	Höök A, Karlsson M 1993 Opt. Lett. 18 1388 Google Scholar
[40]	Karpman V I 1996 Phys. Rev. E 53 R1336 Google Scholar
[41]	Roy S, Bhadra S K, Agrawal G P 2009 Opt. Commun. 282 3798 Google Scholar
[42]	Blanco-Redondo A, Eades D, Li J, Lefrancois S, Krauss T F, Eggleton B J, Husko C 2014 Optica 1 299 Google Scholar
[43]	Blanco-Redondo A, Husko C, Eades D, Zhang Y, Li J, Krauss T F, Eggleton B J 2014 Nat. Commun. 5 3160 Google Scholar
[44]	Hasegawa A, Tappert F 1973 Appl. Phys. Lett. 23 142 Google Scholar
[45]	Lo C W, Stefani A, de Sterke C M, Blanco-Redondo A 2018 Opt. Express 26 7786 Google Scholar
[46]	Tam K K K, Alexander T J, Blanco-Redondo A, de Sterke C M 2019 Opt. Lett. 44 3306 Google Scholar
[47]	Kelly S M J 1992 Electron. Lett. 28 806 Google Scholar
[48]	Runge A F J, Qiang Y L, Alexander T J, Rafat M Z, Hudson D D, Blanco-Redondo A, de Sterke C M 2021 Phys. Rev. Res. 3 013166 Google Scholar
[49]	Widjaja J, Kobakhidze E, Cartwright T R, Lourdesamy J P, Runge A F J, Alexander T J, de Sterke C M 2021 Phys. Rev. A 104 043526 Google Scholar
[50]	Zhang Z X, Luo M, Chen J X, Liu M, Luo A P, Xu W C, Luo Z C 2022 Opt. Lett. 47 1750 Google Scholar
[51]	Soto-Crespo J M, Grapinet M, Grelu P, Akhmediev N 2004 Phys. Rev. E 70 066612 Google Scholar
[52]	Liu K W, Yao S Y, Yang C X 2021 Opt. Lett. 46 993 Google Scholar

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