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研究了非线性放大环形镜锁模掺铒光纤激光器中多孤子和类噪声脉冲同时产生的演化特性. 当激光器运行在类噪声脉冲状态时, 单个孤子簇里包含着多个不同间距的脉冲, 同时相邻脉冲之间的脉冲间距均保持在数百皮秒的范围内, 说明多孤子脉冲之间存在较弱的相互作用力. 并且, 单个孤子簇中的总脉冲数随着抽运功率的增大而增加. 在最大的抽运功率时,单个孤子簇包络内部有8个脉冲. 此外, 利用时间拉伸色散傅里叶变换技术研究了这种类噪声多孤子脉冲的实时动力学演化特性, 研究表明类噪声脉冲状态下的多孤子脉冲中每个脉冲实际上都是由随机强度的噪声混沌波组成的. 这些研究结果将有助于深入理解类噪声脉冲的物理机制, 也将为探索其他复杂孤子动力学过程奠定基础.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 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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)
Fig. 6. (a) Average spectrum and (b) shot-to-shot spectra at pump power of coexisting pulses.
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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
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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
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[12] Liu J, Li X, Zhang S, Liu L, Yan D, Wang C 2021 Opt. Express 29 30494
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[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
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Google Scholar
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Google Scholar
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Google Scholar
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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
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Google Scholar
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Google Scholar
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Google Scholar
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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
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Google Scholar
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