混沌光注入半导体激光器中极端事件的演变

戈杉杉; 王腾午; 戈静怡; 周沛; 李念强

doi:10.7498/aps.72.20230759

摘要

基于相位共轭光反馈混沌激光系统(主激光器)产生的极端事件, 研究了将其输出注入到一个自由运行的半导体激光器(从激光器)的演化情况. 通过注入参数空间中极端事件相对数量的二维统计图分析注入参数对极端事件产生的影响, 发现在主从激光器混沌输出高相关性参数区域, 从激光器中的极端事件的相对数量趋向于一个接近主激光器中极端事件相对数量的稳定值; 在某些特定的弱相关区域, 从激光器中的极端事件的相对数量趋向于增加. 研究结果证明了通过光注入控制极端事件的可能性, 有利于优化混沌激光系统性能或拓展其应用场景.

关键词:

Abstract

Rare ultrahigh pulses, classified as rogue waves (RWs), are inevitable and catastrophic in many different systems. Considering the damage they may produce, it is meaningful to understand the formation mechanism of these pulses and, if possible, control them. However, the rarity of RW and the difficulty in implementing the experiment are major limitations to understanding their formation. In 2007, Solli et al. (Solli D R, Ropers C, Koonath P, Jalali B 2007 Nature 450 1054) introduced the concept of optical RW, i.e. extreme event (EE) by comparing the appearance of oceanic RWs with the propagation of light fields in optical fibers. After that, the research of EEs entered into a flourishing period and different optical systems were proposed to analyze the generation and origin of EEs. Linear system is one of the most widely studied EE systems, such as linear light propagation in glass fibers, random media, and linear interference models. In addition to the linear systems mentioned above, efforts have also been made to produce nonlinear systems of EEs, such as microstructure fibers and tapered gradient exponential nonlinear fibers. In these nonlinear systems, the formation mechanism of EE is studied by using the nonlinear Schrödinger equation. Recently, the EEs in semiconductor laser systems have received a great deal of attention. On the one hand, semiconductor lasers with rich dynamic properties provide a cheap and controllable platform for understanding and predicting EE. The behavior of EE, on the other hand, is a powerful tool for understanding the fundamental mechanism of different laser systems.In this work, based on the EEs generated in a semiconductor laser with phase-conjugate optical feedback (the master laser, ML), we inject its output into another free-running semiconductor laser (the slave laser, SL) and discuss the evolution of EEs in the system by numerical simulation. Herein, we analyze the influence of injection parameters on EEs through the two-dimensional maps of the relative number of EEs in the injection-parameter space. It can be concluded that in an area of high correlation, the relative number of EEs in SL tends to be a stationary value close to that in ML, while it may be enhanced in some weakly correlated regions. The results demonstrate the possibility of controlling EEs by optical injection, which is beneficial to optimizing the performance of chaotic laser systems or expanding their application scope.

Keywords:

作者及机构信息

1.
苏州大学, 光电科学与工程学院, 苏州纳米科技协同创新中心, 苏州　215006

2.
苏州大学, 教育部/江苏省现代光学技术重点实验室, 江苏省先进光学制造技术重点实验室, 苏州　215006

通信作者: 周沛, peizhou@suda.edu.cn ; 李念强, nli@suda.edu.cn

基金项目: 国家自然科学基金(批准号: 62004135, 62001317, 62171305, 62111530301)、江苏省高等学校自然科学研究重大项目(批准号: 20KJA416001, 20KJB510011)和江苏省自然科学基金(批准号: BK20200855)资助的课题.

Authors and contacts

1.
Collaborative Innovation Center of Suzhou Nano Science and Technology, School of Optoelectronic Science and Engineering, Soochow University, Suzhou 215006, China

2.
Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province, Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China

Corresponding author: Zhou Pei, peizhou@suda.edu.cn ; Li Nian-Qiang, nli@suda.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62004135, 62001317, 62171305, 62111530301), the Natural Science Research Project of Jiangsu Higher Education Institutions of China (Grant Nos. 20KJA416001, 20KJB510011), and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20200855).

文章全文

参考文献

[1]	Talouneh K, Rimoldi C, Kheradmand R, Tissoni G, Eslami M 2020 Phys. Rev. A 102 033508 Google Scholar
[2]	Solli D R, Ropers C, Koonath P, Jalali B 2007 Nature 450 1054 Google Scholar
[3]	Arecchi F T, Bortolozzo U, Montina A, Residori S 2011 Phys. Rev. Lett. 106 153901 Google Scholar
[4]	Metzger J J, Fleischmann R, Geisel T 2014 Phys. Rev. Lett. 112 203903 Google Scholar
[5]	Birkholz S, Bree C, Veselic I, Demircan A, Steinmeyer G 2016 Sci. Rep. 6 35207 Google Scholar
[6]	Kumar C N, Gupta R, Goyal A, Loomba S, Raju T S, Panigrahi P K 2012 Phys. Rev. A 86 025802 Google Scholar
[7]	Dal Bosco A K, Wolfersberger D, Sciamanna M 2013 Opt. Lett. 38 703 Google Scholar
[8]	Reinoso J A, Zamora-Munt J, Masoller C 2013 Phys. Rev. E 87 062913 Google Scholar
[9]	Zamora-Munt J, Garbin B, Barland S, Giudici M, Leite J R R, Masoller C, Tredicce J R 2013 Phys. Rev. A 87 035802 Google Scholar
[10]	Ahuja J, Nalawade D B, Zamora-Munt J, Vilaseca R, Masoller C 2014 Opt. Express 22 28377 Google Scholar
[11]	Perrone S, Vilaseca R, Zamora-Munt J, Masoller C 2014 Phys. Rev. A 89 033804 Google Scholar
[12]	Mercier E, Even A, Mirisola E, Wolfersberger D, Sciamanna M 2015 Phys. Rev. E 91 042914 Google Scholar
[13]	Choi D, Wishon M J, Barnoud J, Chang C Y, Bouazizi Y, Locquet A, Citrin D S 2016 Phys. Rev. E 93 042216 Google Scholar
[14]	Lee M W, Baladi F, Burie J R, Bettiati M A, Boudrioua A, Fischer A P 2016 Opt. Lett. 41 4476 Google Scholar
[15]	Jin T, Siyu C, Masoller C 2017 Opt. Express 25 31326 Google Scholar
[16]	Uy C H, Rontani D, Sciamanna M 2017 Opt. Lett. 42 2177 Google Scholar
[17]	Huang Y, Zhou P, Zeng Y, Zhang R H, Li N Q 2022 Phys. Rev. A 105 043521 Google Scholar
[18]	Li X Z, Zhou X Q, Gu Y Y, Zhao M S 2022 IEEE J. Sel. Top. Quantum Electron. 28 0600108 Google Scholar
[19]	Bonatto C, Feyereisen M, Barland S, Giudici M, Masoller C, Leite J R, Tredicce J R 2011 Phys. Rev. Lett. 107 053901 Google Scholar
[20]	Jiang N, Zhao A, Xue C, Tang J, Qiu K 2019 Opt. Lett. 44 1536 Google Scholar
[21]	Lawrence J S, Kane D M 2001 Phys. Rev. A 63 033805 Google Scholar
[22]	Rontani D, Mercier E, Wolfersberger D, Sciamanna M 2016 Opt. Lett. 41 4637 Google Scholar
[23]	Feinberg J 1982 Opt. Lett. 7 486 Google Scholar
[24]	Jiang N, Zhao A, Liu S, Zhang Y, Peng J, Qiu K 2020 Opt. Express 28 9477 Google Scholar
[25]	Mu P, Pan W, Yan L, Luo B, Zou X 2017 IEEE Photonics J. 9 1 Google Scholar
[26]	Zhang R, Zhou P, Yang Y, Fang Q, Mu P, Li N 2020 Opt. Express 28 7197 Google Scholar
[27]	Mu P H, Pan W, Li N Q 2018 Opt. Express 26 15642 Google Scholar
[28]	Huang Y, Zhou P, Li N Q 2021 Opt. Express 29 19675 Google Scholar
[29]	Zhao A, Jiang N, Peng J, Liu S, Zhang Y, Qiu K 2022 Opto-Electron. Adv. 5 200026 Google Scholar
[30]	Zeng Y, Zhou P, Huang Y, Li N 2022 Opt. Lett. 47 142 Google Scholar
[31]	Rimoldi C, Barland S, Prati F, Tissoni G 2017 Phys. Rev. A 95 023841 Google Scholar
[32]	Tlidi M, Panajotov K 2017 Chaos 27 013119 Google Scholar

施引文献

图 1 ML的时序图和峰值强度的统计分布图(红色虚线和竖线代表极端事件的阈值AI = 2)　(a) k_f = 9 ns^–1; (b) k_f = 15 ns^–1; (c) k_f = 30 ns^–1

Fig. 1. Time series and statistical distributions of peak intensity in ML (Red dashed lines and vertical lines represent the threshold of EEs, AI = 2): (a) k_f = 9 ns^–1; (b) k_f = 15 ns^–1; (c) k_f = 30 ns^–1.

下载: 全尺寸图片幻灯片

图 2 k_f = 15 ns^–1, k_inj = 100 ns^–1时, SL的时序图和峰值强度的统计分布图 (红色虚线和竖线代表极端事件的阈值AI = 2)　(a) Δf = 15 GHz; (b) Δf = 0 GHz; (c) Δf = –20 GHz

Fig. 2. Time series and statistical distributions of peak intensity in SL at k_f = 15 ns^–1 and k_inj = 100 ns^–1 (Red dashed lines and vertical lines represent the threshold of EEs, AI = 2): (a) Δf = 15 GHz; (b) Δf = 0 GHz; (c) Δf = –20 GHz.

下载: 全尺寸图片幻灯片

图 3 SL中EE的相对数量随着注入强度变化情况(灰色虚线代表ML中EE的相对数量)　(a) k_f = 9 ns^–1; (b) k_f = 15 ns^–1; (c) k_f = 30 ns^–1

Fig. 3. Relative number of EEs versus injection strength (Gray dashed lines represent the relative number of EEs in ML): (a) k_f = 9 ns^–1; (b) k_f = 15 ns^–1; (c) k_f = 30 ns^–1.

下载: 全尺寸图片幻灯片

图 4 COIS-PCF中EE相对数量在注入参数空间内的二维图(a1)—(c1)以及对应的主从激光器互相关系数的二维映射图(a2)—(c2)　(a) k_f = 9 ns^–1; (b) k_f = 15 ns^–1; (c) k_f = 30 ns^–1

Fig. 4. Maps of relative number of EEs generated from the COIS-PCF in the injection-parameter space (a1)–(c1) and corresponding CC between the ML and SL (a2)–(c2): (a) k_f = 9 ns^–1; (b) k_f = 15 ns^–1; (c) k_f = 30 ns^–1.

下载: 全尺寸图片幻灯片

图 5 k_f = 30 ns^–1时, ML的时序图和峰值强度的统计分布图 (红色虚线代表极端事件的阈值AI = 2)　(a) J_M = 1.05J_th; (b) J_M = 1.30J_th; (c) J_M = 1.50J_th; (d) J_M = 2.00J_th

Fig. 5. Time series and statistical distributions of peak intensity in ML at k_f = 30 ns^–1 (Red dashed lines and vertical lines represent the threshold of EEs, AI = 2): (a) J_M = 1.05J_th; (b) J_M = 1.30J_th; (c) J_M = 1.50J_th; (d) J_M = 2.00J_th.

下载: 全尺寸图片幻灯片

图 6 COIS-PCF中EE相对数量在注入参数空间内的二维图(a1)—(d1)以及对应的主从激光器互相关系数(a2)—(d2)　(a) J_M = 1.05J_th; (b) J_M = 1.30J_th; (c) J_M = 1.50J_th; (d) J_M = 2.00J_th

Fig. 6. Maps of relative number of EEs generated from the COIS-PCF in the injection-parameter space (a1)–(d1) and corresponding CC between the ML and SL (a2)–(d2): (a) J_M = 1.05J_th; (b) J_M = 1.30J_th; (c) J_M = 1.50J_th; (d) J_M = 2.00J_th.

下载: 全尺寸图片幻灯片

map

[1]	Talouneh K, Rimoldi C, Kheradmand R, Tissoni G, Eslami M 2020 Phys. Rev. A 102 033508 Google Scholar
[2]	Solli D R, Ropers C, Koonath P, Jalali B 2007 Nature 450 1054 Google Scholar
[3]	Arecchi F T, Bortolozzo U, Montina A, Residori S 2011 Phys. Rev. Lett. 106 153901 Google Scholar
[4]	Metzger J J, Fleischmann R, Geisel T 2014 Phys. Rev. Lett. 112 203903 Google Scholar
[5]	Birkholz S, Bree C, Veselic I, Demircan A, Steinmeyer G 2016 Sci. Rep. 6 35207 Google Scholar
[6]	Kumar C N, Gupta R, Goyal A, Loomba S, Raju T S, Panigrahi P K 2012 Phys. Rev. A 86 025802 Google Scholar
[7]	Dal Bosco A K, Wolfersberger D, Sciamanna M 2013 Opt. Lett. 38 703 Google Scholar
[8]	Reinoso J A, Zamora-Munt J, Masoller C 2013 Phys. Rev. E 87 062913 Google Scholar
[9]	Zamora-Munt J, Garbin B, Barland S, Giudici M, Leite J R R, Masoller C, Tredicce J R 2013 Phys. Rev. A 87 035802 Google Scholar
[10]	Ahuja J, Nalawade D B, Zamora-Munt J, Vilaseca R, Masoller C 2014 Opt. Express 22 28377 Google Scholar
[11]	Perrone S, Vilaseca R, Zamora-Munt J, Masoller C 2014 Phys. Rev. A 89 033804 Google Scholar
[12]	Mercier E, Even A, Mirisola E, Wolfersberger D, Sciamanna M 2015 Phys. Rev. E 91 042914 Google Scholar
[13]	Choi D, Wishon M J, Barnoud J, Chang C Y, Bouazizi Y, Locquet A, Citrin D S 2016 Phys. Rev. E 93 042216 Google Scholar
[14]	Lee M W, Baladi F, Burie J R, Bettiati M A, Boudrioua A, Fischer A P 2016 Opt. Lett. 41 4476 Google Scholar
[15]	Jin T, Siyu C, Masoller C 2017 Opt. Express 25 31326 Google Scholar
[16]	Uy C H, Rontani D, Sciamanna M 2017 Opt. Lett. 42 2177 Google Scholar
[17]	Huang Y, Zhou P, Zeng Y, Zhang R H, Li N Q 2022 Phys. Rev. A 105 043521 Google Scholar
[18]	Li X Z, Zhou X Q, Gu Y Y, Zhao M S 2022 IEEE J. Sel. Top. Quantum Electron. 28 0600108 Google Scholar
[19]	Bonatto C, Feyereisen M, Barland S, Giudici M, Masoller C, Leite J R, Tredicce J R 2011 Phys. Rev. Lett. 107 053901 Google Scholar
[20]	Jiang N, Zhao A, Xue C, Tang J, Qiu K 2019 Opt. Lett. 44 1536 Google Scholar
[21]	Lawrence J S, Kane D M 2001 Phys. Rev. A 63 033805 Google Scholar
[22]	Rontani D, Mercier E, Wolfersberger D, Sciamanna M 2016 Opt. Lett. 41 4637 Google Scholar
[23]	Feinberg J 1982 Opt. Lett. 7 486 Google Scholar
[24]	Jiang N, Zhao A, Liu S, Zhang Y, Peng J, Qiu K 2020 Opt. Express 28 9477 Google Scholar
[25]	Mu P, Pan W, Yan L, Luo B, Zou X 2017 IEEE Photonics J. 9 1 Google Scholar
[26]	Zhang R, Zhou P, Yang Y, Fang Q, Mu P, Li N 2020 Opt. Express 28 7197 Google Scholar
[27]	Mu P H, Pan W, Li N Q 2018 Opt. Express 26 15642 Google Scholar
[28]	Huang Y, Zhou P, Li N Q 2021 Opt. Express 29 19675 Google Scholar
[29]	Zhao A, Jiang N, Peng J, Liu S, Zhang Y, Qiu K 2022 Opto-Electron. Adv. 5 200026 Google Scholar
[30]	Zeng Y, Zhou P, Huang Y, Li N 2022 Opt. Lett. 47 142 Google Scholar
[31]	Rimoldi C, Barland S, Prati F, Tissoni G 2017 Phys. Rev. A 95 023841 Google Scholar
[32]	Tlidi M, Panajotov K 2017 Chaos 27 013119 Google Scholar

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混沌光注入半导体激光器中极端事件的演变