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In this paper, chaotic parallel synchronization and quasi-periodic parallel synchronization between two mutually coupled different semiconductor lasers and other lasers are studied, and the regeneration of chaotic laser and key technology of repeater are discussed. The complex dynamic system and network of laser parallel series are presented in mathematics and in physics, and the network topology diagram and optics path are specified. A mathematical-physical model is given to study how to obtain parallel synchronization via the coupled driving nonlinear equations. The operating principle of the repeater is put forward for chaotic secure communication, and the channel equation of repeater is established because the laser chaotic behavior is extremely sensitive to external influences and system parameter changes. The laser’s chaotically regenerating and transmitting is successfully realized via two sets of repeaters. The chaotic encoding communication with repeaters is successfully completed while the encoding information signal is accurately extracted from the chaotic carrier by a filter and calculating the synchronous difference. We adopt three sets of lasers as a research case to simulate and verify the theory of laser parallel series network we put forward to fit perfectly the obtained numerical results. We study the parameter mismatch problem of the system, where the synchronous difference is numerically calculated by varying some parameters of the lasers. In the case of smaller parameter mismatch, the system has a highly synchronous capability to a certain degree. This is a novel laser chaotic encoding network in chaotic secure communication and characterizes the core technical elements of the repeater. The laser transmitter has four nonlinear interaction variables, where the nonlinear interaction between the amplitude and phase of the two optical fields results in highly nonlinear dynamics. The system has the characteristics of high nonlinearity, multi-variable, high-dimension, and multi-key. So it is highly secure and not easy to crack. The results have an important reference value for the chaos applications in remote secure communication, optical network and laser technology.
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Keywords:
- chaos /
- synchronization /
- laser /
- network
[1] Bayati B M A, Ahmad K A, Naimee M A 2018 J. Opt. Soc. Am. B 35 918
Google Scholar
[2] Kang Z, Sun J, Ma L, Qi Y, Jian S 2014 IEEE J. Quantum Electron. 50 148
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[3] 王顺天, 吴正茂, 吴加贵, 周立, 夏光琼 2015 物理学报 64 154205
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Wang S T, Wu Z M, Wu J G, Zhou L, Xia G Q 2015 Acta Phys. Sin. 64 154205
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[4] 钟东洲, 邓涛, 郑国梁 2015 物理学报 63 070504
Google Scholar
Zhong D Z, Deng T, Zheng G L 2015 Acta Phys. Sin. 63 070504
Google Scholar
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[6] Erzgräbera D, Lenstraa D, Krauskopfc B 2006 Proc. SPIE 6184 618407
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Liu Q X, Pan W, Zhang L Y, Li N Q, Yan J 2015 Acta Phys. Sin. 64 024209
Google Scholar
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[14] Quirce A, Valle A, Thienpont H, Panajotov K 2016 J. Opt. Soc. Am. B 33 90
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[15] Zhang W L, Pan W, Luo B, Li X F, Zou X H, Wang M Y 2007 J. Opt. Soc. Am. B 24 1276
[16] Hong Y H 2015 IEEE J. Select. Topics Quantum Electron. 21 1801007
[17] Wang A B, Wang Y C, Wang J F 2009 Opt. Lett. 34 1144
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[18] 李增, 冯玉玲, 王晓茜, 姚治海 2018 物理学报 67 140501
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Li Z, Feng Y L, Wang X Q, Yao Z H 2018 Acta Phys. Sin. 67 140501
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[19] 张浩, 郭星星, 项水英 2018 物理学报 67 204202
Google Scholar
Zhang H, Guo X X, Xiang S Y 2018 Acta Phys. Sin. 67 204202
Google Scholar
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Google Scholar
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图 1 并行串联复杂动力学网络及中继器光路图 (a) 网络拓扑图; (b)光路图
Figure 1. Parallel series complex dynamical network and optical path of repeater: (a) Network topology; (b) optics path.
图 2 激光器t与r1取得混沌同步过程, 其中内插图分别是两个激光器的混沌吸引子
Figure 2. The laser t synchronizes with the laser r1. The ininserted illustrations show the chaotic attractors of two lasers.
图 5 激光器R1与R2取得混沌同步 (a)同步过程; (b)互相关函数曲线
Figure 5. The laser R1 synchronizes with the laser R2: (a) The synchronous process; (b) the cross-correlation function curve.
图 3 激光器r1与r2取得混沌同步 (a)同步过程; (b)互相关函数曲线
Figure 3. The laser t synchronizes with the laser r2: (a) The synchronous process; (b) the cross-correlation function curve.
图 4 激光器T与R1的混沌同步过程
Figure 4. The laser T synchronizes with the laser R1.
图 6 激光器t与r1取得4周期同步
Figure 6. Period-4 synchronization between the lasers t and r1
图 9 激光器R1与R2取得3周期同步
Figure 9. Period-3 synchronization between the lasers R1 and R2
图 7 激光器r1与r2取得4周期同步
Figure 7. Period-4 synchronization between the lasers r1 and r2
图 8 激光器T与R1取得3周期同步
Figure 8. Period-3 synchronization between the lasers T and R1
图 10 激光器t与r1取得10周期同步
Figure 10. Period-10 synchronization between the lasers t and r1
图 13 激光器R1与R2的另一个10周期同步
Figure 13. Another period-10 synchronization between the lasers R1 and R2.
图 11 激光器r1与r2取得10周期同步
Figure 11. Period-10 synchronization between the lasers r1 and r2.
图 12 激光器T与R1的另一个10周期同步
Figure 12. Another period-10 synchronization between the lasers T and R1.
图 14 同步调制解调过程
Figure 14. Synchronous decoding process.
图 15 另一路同步调制解调过程
Figure 15. Another synchronous decoding process.
表 1 激光器参量
Table 1. Laser parameters.
参量 值 参量 值 腔长L/ μm 350 俄歇复合因子C/ cm6·s–1 3.5 × 10–29 腔宽w/ μm 2 饱和光子场振幅|Es| / m–3/2 1.6619 × 1011 腔厚d/ μm 0.15 增益常数α/ cm2 2.3 × 10–16 压缩和限制因子Γ 0.29 光线宽增强因子βc 6 群速度折射率ng 3.8 耦合驱动系数k 0.1 光子损耗系数αm/ cm–1 49 频率ω/ Rad·s–1 1438 × 1012 非辐射复合速率Anr/ s–1 1.0 × 108 激光透明时
载流子密度nth/ cm–31.2 × 1018 辐射复合因子B/ cm3·s–1 1.2 × 10–10 
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[1] Bayati B M A, Ahmad K A, Naimee M A 2018 J. Opt. Soc. Am. B 35 918
Google Scholar
[2] Kang Z, Sun J, Ma L, Qi Y, Jian S 2014 IEEE J. Quantum Electron. 50 148
Google Scholar
[3] 王顺天, 吴正茂, 吴加贵, 周立, 夏光琼 2015 物理学报 64 154205
Google Scholar
Wang S T, Wu Z M, Wu J G, Zhou L, Xia G Q 2015 Acta Phys. Sin. 64 154205
Google Scholar
[4] 钟东洲, 邓涛, 郑国梁 2015 物理学报 63 070504
Google Scholar
Zhong D Z, Deng T, Zheng G L 2015 Acta Phys. Sin. 63 070504
Google Scholar
[5] Mulet J, Masoller C, Mirasso C R 2002 Phys. Rev. A 65 063815
Google Scholar
[6] Erzgräbera D, Lenstraa D, Krauskopfc B 2006 Proc. SPIE 6184 618407
Google Scholar
[7] Arroyo-Almanza D A, Pisarchik A N, Fischer I, Mirasso C R, Soriano M C 2013 Opt. Commun. 301 67
[8] Erzgräber H, Wieczorek S 2009 Phys. Rev. E 80 026212
Google Scholar
[9] 刘庆喜, 潘炜, 张力月, 李念强, 阎娟 2015 物理学报 64 024209
Google Scholar
Liu Q X, Pan W, Zhang L Y, Li N Q, Yan J 2015 Acta Phys. Sin. 64 024209
Google Scholar
[10] Wunsche H J, Bauer S, Kreissl J, Ushakov O, Korneyev N, Henneberger F, Wille E, Erzgräber H, Peil M, Elsaor W, Fischer I 2005 Phys. Rev. Lett. 94 163901
Google Scholar
[11] Mulet J, Mirasso C R, Heil T, Fischer I 2004 J. Opt. B: Quantum Semiclass. Opt. 6 97
Google Scholar
[12] Hill M T, Waardt H D, Dorren H J S 2001 IEEE J. Quantum Electron. 37 405
Google Scholar
[13] Tang X, Wu Z M, Wu J G, Deng T, Fan L, Zhong Z Q, Chen J J, Xia G Q 2015 Laser Phys. Lett. 12 015003
Google Scholar
[14] Quirce A, Valle A, Thienpont H, Panajotov K 2016 J. Opt. Soc. Am. B 33 90
Google Scholar
[15] Zhang W L, Pan W, Luo B, Li X F, Zou X H, Wang M Y 2007 J. Opt. Soc. Am. B 24 1276
[16] Hong Y H 2015 IEEE J. Select. Topics Quantum Electron. 21 1801007
[17] Wang A B, Wang Y C, Wang J F 2009 Opt. Lett. 34 1144
Google Scholar
[18] 李增, 冯玉玲, 王晓茜, 姚治海 2018 物理学报 67 140501
Google Scholar
Li Z, Feng Y L, Wang X Q, Yao Z H 2018 Acta Phys. Sin. 67 140501
Google Scholar
[19] 张浩, 郭星星, 项水英 2018 物理学报 67 204202
Google Scholar
Zhang H, Guo X X, Xiang S Y 2018 Acta Phys. Sin. 67 204202
Google Scholar
[20] Liu J, Wu Z M, Xia G Q 2009 Opt. Express 17 12619
Google Scholar
[21] Wu J, Wu Z, Liu Y, Fan L, Tang X, Xia G 2013 IEEE/OSA J. Lightwave Technol. 31 461
Google Scholar
[22] 穆鹏华, 潘炜, 李念强, 闫连山, 罗斌, 邹喜华, 徐明峰 2015 物理学报 64 124206
Google Scholar
Mu P H, Pan W, Li N Q, Yan L S, Luo B, Zou X H, Xu M F 2015 Acta Phys. Sin. 64 124206
Google Scholar
[23] Li N Q, Pan W, Luo B, Yan L S, Zou X H, Jiang N, Xiang S Y 2012 IEEE Photon. Technol. Lett. 24 1072
Google Scholar
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