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Dissipative solitons (DSs) usually play an important role in understanding the intricate phenomena in various nonlinear systems. As a special regime in the dissipative system, noise-like pulses (NLPs) can have typical characteristics of ultra-broad and smooth spectrum, high pulse energy and low temporal coherence, making them a good candidate for many applications, including supercontinuum generation, industrial micromachining and optical metrology. In this paper, a noteworthy observation concerning the dynamics on coexistence of the multiple solitons and NLPs operation in a net-normal-dispersion passively mode-locked fiber laser based on nonlinear amplifying loop mirror (NALM) is reported. In the experiment, the stable DSs can be easily obtained at a proper pump power. When appropriately increasing the pump power and changing the polarization state, the DS operation can change to the NLP regime. When the fiber laser operates in an NLP state, the single soliton bunch contains multiple pulses with different temporal spacings. And the temporal interval between the adjacent pulses is in a range of several hundred picoseconds, which decreases from left to right with time changing, indicating that there are long-distance interactions among these multiple pulses and they gradually become stronger and stronger. Besides, the pulse number of single soliton bunches on the NLP operation increases almost linearly with pump power increasing. At a maximum pump power, there are eight pulses inside the single soliton bunch. With the increase of pump power, the average output power and pulse energy of these multiple solitons in the NLP state increase. The maximum average output power and pulse energy are 12.3 mW and 1.65 nJ, respectively. In addition, the real-time dynamic evolution of these multiple solitons in the NLP state is investigated by using the time-stretch dispersive Fourier-transform method. The results show that all the pulses in NLP regime actually consist of chaotic noise waves with stochastic intensities. We believe that this paper will be of significance in studying ultrafast fiber lasers and nonlinear optics. Moreover, we hope that these findings will be helpful in understanding the physical mechanism of NLPs and paving the way for exploring other complex soliton dynamics.
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图 1 光纤激光器实验装置图
Figure 1. Experimental setup of the fiber laser.
图 2 耗散孤子的输出特性 (a)光谱; (b)脉冲序列; (c)射频谱; (d)映射光谱
Figure 2. Output characteristics of dissipative solitons: (a) Optical spectrum; (b) pulse trains; (c) radio-frequency spectrum; (d) shot-to-shot spectra.
图 3 (a)光谱; (b)脉冲序列; (c)射频谱; (d)自相关; (e)基于高速示波器记录的脉冲序列; (f)图(e)中红色虚线框的细节
Figure 3. (a) Optical spectrum; (b) pulse trains; (c) radio-frequency spectrum; (d) autocorrelation curve; (e) temporal trains based on high-speed oscilloscope; (f) close-ups of red dotted section in (e).
图 4 (a)抽运功率为300 mW的三维时序; (b)抽运功率为500 mW的三维时序; (c)不同抽运功率时单个孤子簇中脉冲的数目
Figure 4. (a) Three-dimensional pulse trains at pump power of 300 mW; (b) three-dimensional pulse trains at pump power of 500 mW; (c) total amount of single soliton bunch at different pump powers.
图 5 (a)不同抽运功率的光谱演化过程; (b)输出功率随抽运功率的变化
Figure 5. (a) Optical spectra and (b) output power at different pump powers.
图 6 共存脉冲的平均光谱 (a)和映射光谱(b)
Figure 6. (a) Average spectrum and (b) shot-to-shot spectra at pump power of coexisting pulses.
图 7 脉冲能量变化曲线(黑色曲线: 共存脉冲; 红色曲线: 耗散孤子)
Figure 7. Energy evolution of consecutive roundtrips (black line: coexisting pulses; red line: dissipative solitons).
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[1] Fermann M E, Hartl I 2013 Nat. Photonics 7 868
Google Scholar
[2] Shi W, Fang Q, Zhu X, Norwood R A, Peyghambarian N 2014 Appl. Opt. 53 6554
Google Scholar
[3] Phillips K C, Gandhi H H, Mazur E, Sundaram S K 2015 Adv. Opt. Photon. 7 684
Google Scholar
[4] 马金栋, 吴浩煜, 路桥, 马挺, 时雷, 孙青, 毛庆和 2018 物理学报 67 094207
Google Scholar
Ma J D, Wu H Y, Lu Q, Ma T, Shi L, Sun Q, Mao Q H 2018 Acta Phys. Sin. 67 094207
Google Scholar
[5] Chang G, Wei Z 2020 iScience 23 101101
Google Scholar
[6] 俞强, 郭琨, 陈捷, 王涛, 汪进, 史鑫尧, 吴坚, 张凯, 周朴 2020 物理学报 69 184208
Google Scholar
Yu Q, Guo K, Chen J, Wang T, Wang J, Shi X Y, Wu J, Zhang K, Zhou P 2020 Acta Phys. Sin. 69 184208
Google Scholar
[7] Grelu P, Akhmediev N 2012 Nat. Photonics 6 84
Google Scholar
[8] Sulimany K, Lib O, Masri G, Klein A, Fridman M, Grelu P, Gat O, Steinberg H 2018 Phys. Rev. Lett. 121 133902
Google Scholar
[9] Wei Z W, Liu M, Ming S X, Cui H, Luo A P, Xu W C, Luo Z C 2020 Opt. Lett. 45 531
Google Scholar
[10] Peng J, Boscolo S, Zhao Z, Zeng H 2019 Sci. Adv. 5 eaax1110
Google Scholar
[11] 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
[12] Liu J, Li X, Zhang S, Liu L, Yan D, Wang C 2021 Opt. Express 29 30494
Google Scholar
[13] Lauterio-Cruz J P, Hernandez-Garcia J C, Pottiez O, Estudillo-Ayala J M, Kuzin E A, Rojas-Laguna R, Santiago-Hernandez H, Jauregui-Vazquez D 2016 Opt. Express 24 13778
Google Scholar
[14] Özgören K, Öktem B, Yilmaz S, Ilday F Ö, Eken K 2011 Opt. Express 19 17647
Google Scholar
[15] Keren S, Brand E, Levi Y, Levit B, Horowitz M 2002 Opt. Lett. 27 125
Google Scholar
[16] Sobon G, Sotor J, Przewolka A, Pasternak I, Strupinski W, Abramski K 2016 Opt. Express 24 20359
Google Scholar
[17] Jeong Y, Vazquez Zuniga L A, Lee S, Kwon Y 2014 Opt. Fiber Technol. 20 575
Google Scholar
[18] 陈家旺, 赵鹭明 2017 激光与光电子学进展 54 110002
Google Scholar
Chen J W, Zhao L M 2017 Laser Optoelectron. Prog. 54 110002
Google Scholar
[19] 窦志远, 张斌, 刘帅林, 侯静 2020 物理学报 69 164202
Google Scholar
Dou Z Y, Zhang B, Liu S L, Hou J 2020 Acta Phys. Sin. 69 164202
Google Scholar
[20] Tang D Y, Zhao L M, Zhao B, Liu A Q 2005 Phys. Rev. A 72 043816
Google Scholar
[21] Liu X, Wang L, Li X, Sun H, Lin A, Lu K, Wang Y, Zhao W 2009 Opt. Express 17 8506
Google Scholar
[22] Sobon G, Krzempek K, Kaczmarek P, Abramski K M, Nikodem M 2011 Opt. Commun. 284 4203
Google Scholar
[23] Wang Y, Mao D, Gan X, Han L, Ma C, Xi T, Zhang Y, Shang W, Hua S, Zhao J 2015 Opt. Express 23 205
Google Scholar
[24] Wu X, Tang D Y, Luan X N, Zhang Q 2011 Opt. Commun. 284 3615
Google Scholar
[25] Huang Y Q, Hu Z A, Cui H, Luo Z C, Luo A P, Xu W C 2016 Opt. Lett. 41 4056
Google Scholar
[26] Cheng Z, Li H, Wang P 2015 Opt. Express 23 5972
Google Scholar
[27] Wang Z, Wang Z, Liu Y G, He R, Wang G, Yang G, Han S 2018 Laser Phys. Lett. 15 055101
Google Scholar
[28] Liu M, Luo A P, Xu W C, Luo Z C 2016 Opt. Lett. 41 3912
Google Scholar
[29] Wang Z, Wang Z, Liu Y G, He R, Wang G, Yang G, Han S 2017 Chin. Opt. Lett. 15 080605
Google Scholar
[30] Wang Z, Wang X, Song Y, Liu J, Zhang H 2020 Phys. Rev. A 101 013825
Google Scholar
[31] Zaviyalov A, Grelu P, Lederer F 2012 Opt. Lett. 37 175
Google Scholar
[32] Lecaplain C, Grelu P 2014 Phys. Rev. A 90 013805
Google Scholar
[33] Wang Z, Ma C, Song Y, Liu J, Zhu H, Duan Y, Zhang H 2020 Opt. Express 28 39463
Google Scholar
[34] Solli D R, Herink G, Jalali B, Ropers C 2012 Nat. Photonics 6 463
Google Scholar
[35] Dudley J M, Dias F, Erkintalo M, Genty G 2014 Nat. Photonics 8 755
Google Scholar
[36] Gao L, Zhu T, Wabnitz S, Liu M, Huang W 2016 Sci. Rep. 6 24995
Google Scholar
[37] Smith N J, Doran N J 1996 Opt. Lett. 21 570
Google Scholar
[38] Tang D Y, Zhao L M, Wu X, Zhang H 2009 Phys. Rev. A 80 023806
Google Scholar
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