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This study employs real-time Fourier transform spectroscopy to investigate the pulsation dynamics of soliton molecules in a mode-locked erbium-doped fiber laser, by modulating pump intensity. By controlling the driving voltage of the pump source, we systematically observe and characterize the influence of external modulation signals on the amplitude, period, pulsation frequency, and the relative phase evolution among the pulsating soliton molecules in their spectra. The results demonstrate that under specific conditions of pump intensity modulation, the pulsation period of soliton molecule spectra can be precisely regulated by the pump modulation frequency. At the same time, the amplitude of soliton molecule pulsations and the evolution of relative phase among the solitons are intricately tied to the pump modulation frequency. At lower modulation frequencies, such as 1 kHz, the relative phase among the pulses in the soliton molecule exhibits a sliding-type dynamics as a function of propagation time. As the modulation frequency gradually increases to 5 kHz, a scenario emerges where three soliton molecules are generated. Notably, both the soliton spacing and relative phase undergo synchronous adjustments influenced by the pump modulation. With the modulation frequency further increasing, say, to 20 kHz, the relative phase evolution among the pulses within the soliton molecule gradually descends into chaos. This observation suggests the plausible existence of an inherent resonant frequency associated with pulsating soliton molecules, which has direct implications for their stability. The findings of this research are of significance in advancing our comprehension of soliton molecule generation and enhancing their stability. In addition, they provide valuable insights into the broader domain of all-optical manipulation and applications of soliton molecules, and their application in pulse encoding in mode-locked laser systems. -
Keywords:
- soliton molecule /
- pump intensity modulation /
- spectral fluctuation /
- dispersive Fourier transform
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Google Scholar
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Google Scholar
[12] Wei Z W, Liu M, Ming S X, Luo A P, Xu W C, Luo Z C 2018 Opt. Lett. 43 5965
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Google Scholar
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Google Scholar
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Google Scholar
Zhang W R, Chen S Y, Li R T, Jiang M, Li C, Ma Y X, Zhou P 2022 Acta Phys. Sin. 71 194204
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图 1 实验装置图. SESAM, 可饱和吸收镜; SG, 信号发生器; LD, 半导体光源; WDM, 波分复用器; EDF, 掺饵光纤; PC, 偏振控制器; OC, 90∶10耦合器; DCF, 色散补偿光纤; OSA, 光谱分析仪; OSC, 实时示波器
Figure 1. Diagram of experimental setup. SESAM, saturable absorber; SG, signal generator; LD, semiconductor light source, WDM, wavelength division multiplexer; EDF, erbium-doped fiber; PC, polarization controller; OC, 90∶10 coupler; DCF, dispersion compensation fiber; OSA, optical spectrum analyzer; OSC, oscilloscope.
图 2 (a) 输入泵浦脉冲波形(实线)和载波信号波形(虚线); (b) 调制电平和泵浦功率关系图
Figure 2. (a) Input pump pulse waveform (solid line) and carrier signal waveform (dashed line); (b) modulation level and pump power relationship diagram.
图 3 当泵浦调制频率为1 kHz时, 孤子分子演化实验结果 (a) DFT光谱随运行圈数的演化; (b) 对应的一阶自相关演化; (c) 脉冲能量演化; (d) 光谱中心波长的脉动演化; (e) 第15970圈的DFT光谱和第22220圈的单次DFT光谱
Figure 3. Output characteristics of bound solitons at 1 kHz pump modulation frequency: (a) Evolution of DFT spectra with the number of cycles in operation; (b) corresponding first-order autocorrelation evolution; (c) pulse energy evolution; (d) pulsation evolution of spectral center wavelength; (e) DFT spectrum of lap 15970 and the single DFT spectrum of lap 22220.
图 4 5 kHz泵浦调制频率时孤子分子输出特性 (a) DFT光谱随运行圈数的演化; (b) 对应的一阶自相关演化; (c) 脉冲能量演化; (d) 光谱中心波长的脉动演化; (e) 相对相位演化图; (f) 脉冲间距; (g) 10290圈单次光谱和10910圈单次光谱
Figure 4. Output characteristics of bound solitons at 5 kHz pump modulation frequency: (a) Evolution of DFT spectra with the number of cycles in operation; (b) corresponding first-order autocorrelation evolution; (c) pulse energy evolution; (d) pulsation evolution of spectral center wavelength; (e) relative phase evolution diagram; (f) pulse spacing; (g) 10290 cycles and 10910 cycles of single spectrum.
图 5 20 kHz泵浦调制频率时孤子分子输出特性 (a) DFT光谱随运行圈数的演化; (b) 对应的一阶自相关演化; (c) 脉冲能量演化; (d) 光谱中心波长的脉动演化; (e) 相对相位演化; (f) 脉冲间距; (g) 2850圈单次光谱和3076圈单次光谱
Figure 5. Output characteristics of bound solitons at 20 kHz pump modulation frequency: (a) Evolution of DFT spectra with the number of running cycles; (b) corresponding first-order autocorrelation evolution; (c) pulse energy evolution; (d) pulsation evolution of spectral center wavelength; (e) relative phase evolution diagram; (f) pulse spacing; (g) 2850 cycles and 3076 cycles of single spectrum.
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[1] Tang D Y, Zhao L M, Zhao B, Liu A Q 2005 Phys. Rev. A 72 043816
Google Scholar
[2] Dallaire M, McCarthy N, Piché M 2009 Opt. Express 17 18148
Google Scholar
[3] Zhou M, He J, Li C, Liu Y G, Yue Y, He R, Chen S Y, Zhang L H, Zhu L F, Zhu K Y, Chang K, Wang Z 2021 Opt. Express 29 16362
Google Scholar
[4] Wang Z Q, Zhan L, Majeed A, Zhou Z X 2015 Opt. Lett. 40 1065
Google Scholar
[5] Wang Z Q, Nithyanandan K, Coillet A, Tchofo-Dinda P, Grelu P 2019 Nat. Commun. 10 830
Google Scholar
[6] Goda K, Tsia K, Jalali B 2009 Nature 458 1145
Google Scholar
[7] Xu Y Q, Wei X M, Ren Z B, Wong K K, Tsia K K 2016 Sci. Rep. 6 27937
Google Scholar
[8] Mahjoubfar A, Churkin D V, Barland S, Broderick N, Turitsyn S K, Jalali B 2017 Nat. Photonics 11 341
Google Scholar
[9] 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
[10] Liu X M, Yao X K, Cui Y D 2018 Phys. Rev. Lett. 121 023905
Google Scholar
[11] Herink G, Kurtz F, Jalali B, Solli D R, Ropers C 2017 Science 356 50
Google Scholar
[12] Wei Z W, Liu M, Ming S X, Luo A P, Xu W C, Luo Z C 2018 Opt. Lett. 43 5965
Google Scholar
[13] Zhou Y, Ren Y X, Shi J W, Wong K K 2022 Commun. Phys. 5 302
Google Scholar
[14] Krupa K, Nithyanandan K, Andral U, Tchofo-Dinda P, Grelu P 2017 Phys. Rev. Lett. 118 243901
Google Scholar
[15] Liu S, Cui Y, Karimi E, Malomed B A 2022 Optica 9 240
Google Scholar
[16] Li J, Li H, Wang Z, Du W, Zhang Z, Liu Y 2022 Opt. Laser Technol. 155 108429
Google Scholar
[17] Du Y, Zeng C, He Z, Gao Q, Mao D 2022 Chin. Opt. Lett. 20 011401
Google Scholar
[18] 张万儒, 陈思雨, 粟荣涛, 姜曼, 李灿, 马阎星, 周朴 2022 71 194204
Google Scholar
Zhang W R, Chen S Y, Li R T, Jiang M, Li C, Ma Y X, Zhou P 2022 Acta Phys. Sin. 71 194204
Google Scholar
[19] Peng J S, Zeng H 2018 Laser Photon. Rev. 12 1800009
Google Scholar
[20] Gui L, Wang P, Ding Y H, Zhao K J, Bao C Y, Xiao X S, Yang C X 2018 Appl. Sci. 8 201
Google Scholar
[21] Liu Y S, Huang S Y, Li Z L, Liu H G, Sun Y X, Xia R, Yan L S, Luo Y Y, Liu H H, Sun Q Z, Tang X H, Shum P P 2023 Light Sci. Appl. 12 123
Google Scholar
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