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Chaotic laser parallel series synchronization and its repeater applications in secure communication

Yan Sen-Lin

Chaotic laser parallel series synchronization and its repeater applications in secure communication

Yan Sen-Lin
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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.
      Corresponding author: Yan Sen-Lin, senlinyan@163.com
    [1]

    Bayati B M A, Ahmad K A, Naimee M A 2018 J. Opt. Soc. Am. B 35 918

    [2]

    Kang Z, Sun J, Ma L, Qi Y, Jian S 2014 IEEE J. Quantum Electron. 50 148

    [3]

    王顺天, 吴正茂, 吴加贵, 周立, 夏光琼 2015 物理学报 64 154205

    Wang S T, Wu Z M, Wu J G, Zhou L, Xia G Q 2015 Acta Phys. Sin. 64 154205

    [4]

    钟东洲, 邓涛, 郑国梁 2015 物理学报 63 070504

    Zhong D Z, Deng T, Zheng G L 2015 Acta Phys. Sin. 63 070504

    [5]

    Mulet J, Masoller C, Mirasso C R 2002 Phys. Rev. A 65 063815

    [6]

    Erzgräbera D, Lenstraa D, Krauskopfc B 2006 Proc. SPIE 6184 618407

    [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

    [9]

    刘庆喜, 潘炜, 张力月, 李念强, 阎娟 2015 物理学报 64 024209

    Liu Q X, Pan W, Zhang L Y, Li N Q, Yan J 2015 Acta Phys. Sin. 64 024209

    [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

    [11]

    Mulet J, Mirasso C R, Heil T, Fischer I 2004 J. Opt. B: Quantum Semiclass. Opt. 6 97

    [12]

    Hill M T, Waardt H D, Dorren H J S 2001 IEEE J. Quantum Electron. 37 405

    [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

    [14]

    Quirce A, Valle A, Thienpont H, Panajotov K 2016 J. Opt. Soc. Am. B 33 90

    [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

    [18]

    李增, 冯玉玲, 王晓茜, 姚治海 2018 物理学报 67 140501

    Li Z, Feng Y L, Wang X Q, Yao Z H 2018 Acta Phys. Sin. 67 140501

    [19]

    张浩, 郭星星, 项水英 2018 物理学报 67 204202

    Zhang H, Guo X X, Xiang S Y 2018 Acta Phys. Sin. 67 204202

    [20]

    Liu J, Wu Z M, Xia G Q 2009 Opt. Express 17 12619

    [21]

    Wu J, Wu Z, Liu Y, Fan L, Tang X, Xia G 2013 IEEE/OSA J. Lightwave Technol. 31 461

    [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

    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

    [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

  • 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 参量
    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–3
    1.2 × 1018
    辐射复合因子B/ cm3·s–1 1.2 × 10–10
    DownLoad: CSV
  • [1]

    Bayati B M A, Ahmad K A, Naimee M A 2018 J. Opt. Soc. Am. B 35 918

    [2]

    Kang Z, Sun J, Ma L, Qi Y, Jian S 2014 IEEE J. Quantum Electron. 50 148

    [3]

    王顺天, 吴正茂, 吴加贵, 周立, 夏光琼 2015 物理学报 64 154205

    Wang S T, Wu Z M, Wu J G, Zhou L, Xia G Q 2015 Acta Phys. Sin. 64 154205

    [4]

    钟东洲, 邓涛, 郑国梁 2015 物理学报 63 070504

    Zhong D Z, Deng T, Zheng G L 2015 Acta Phys. Sin. 63 070504

    [5]

    Mulet J, Masoller C, Mirasso C R 2002 Phys. Rev. A 65 063815

    [6]

    Erzgräbera D, Lenstraa D, Krauskopfc B 2006 Proc. SPIE 6184 618407

    [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

    [9]

    刘庆喜, 潘炜, 张力月, 李念强, 阎娟 2015 物理学报 64 024209

    Liu Q X, Pan W, Zhang L Y, Li N Q, Yan J 2015 Acta Phys. Sin. 64 024209

    [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

    [11]

    Mulet J, Mirasso C R, Heil T, Fischer I 2004 J. Opt. B: Quantum Semiclass. Opt. 6 97

    [12]

    Hill M T, Waardt H D, Dorren H J S 2001 IEEE J. Quantum Electron. 37 405

    [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

    [14]

    Quirce A, Valle A, Thienpont H, Panajotov K 2016 J. Opt. Soc. Am. B 33 90

    [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

    [18]

    李增, 冯玉玲, 王晓茜, 姚治海 2018 物理学报 67 140501

    Li Z, Feng Y L, Wang X Q, Yao Z H 2018 Acta Phys. Sin. 67 140501

    [19]

    张浩, 郭星星, 项水英 2018 物理学报 67 204202

    Zhang H, Guo X X, Xiang S Y 2018 Acta Phys. Sin. 67 204202

    [20]

    Liu J, Wu Z M, Xia G Q 2009 Opt. Express 17 12619

    [21]

    Wu J, Wu Z, Liu Y, Fan L, Tang X, Xia G 2013 IEEE/OSA J. Lightwave Technol. 31 461

    [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

    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

    [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

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  • Received Date:  18 February 2019
  • Accepted Date:  21 June 2019
  • Available Online:  26 November 2019
  • Published Online:  01 September 2019

Chaotic laser parallel series synchronization and its repeater applications in secure communication

    Corresponding author: Yan Sen-Lin, senlinyan@163.com
  • Electronic Engineering School, Nanjing Xiaozhuang University, Nanjing 211171, China

Abstract: 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.

    • 目前, 随着光通信和光网络的快速发展, 信息安全越来越重要. 人们对加密技术特别是激光混沌加密技术越来越感兴趣. 近年来, 激光混沌保密通信研究已取得了许多重要研究成果, 并被广泛应用[14]. 然而, 一些低维混沌激光系统由于其较弱的非线性仅具有较低的安全性. 而高维混沌激光系统在进行加密时, 能够产生高维度的激光混沌输出, 具有较高的安全性, 因而具有一定的技术优势. 而耦合激光器具有高维非线性动力学特性[519], 并被广泛地应用在双稳态和高频信号发生器等器件中[1016]. 本文主要研究两种不同半导体激光器的相互耦合. 与单个混沌激光器相比较, 如与注入激光器或延时反馈激光器等相比较[1719], 该系统具有更多个空间变量或更多个空间自由度, 并且能够形成更高维的非线性动力学; 而与相同两个激光器耦合比较[519], 具有更多个自由变量和更多个激光参数密钥. 因而, 系统总体上呈现出高度的安全性和难以破译的技术优点, 明显地增加了入侵者的破译难度. 此外, 人们还对混沌多路通信也特别关注. 但目前主要还是单个混沌激光器的多路通信[3,4,2023]. 所以在本文研究中, 我们也将关注该网络系统的并行同步在两个异路混沌通信中的应用等问题. 与以往单个激光器的两路混沌通信系统相比较, 它显示出更加明显的灵活性. 还有在远程混沌通信中, 由于能量分配、器件插入、信道吸收等因素, 信息信号会逐步减弱, 以至于接收机难以接收解调. 所以还需要混沌中继与放大. 由于光放大器成熟应用, 信号放大问题可以由光放大器很好地解决. 但由于混沌信号对系统参数、外界影响等因素具有极其敏感的特性, 进而导致混沌信号极易变异、以至于接收机难以实现同步解调. 因此, 混沌信号再生是实现远程混沌通信中的一项关键技术. 本文提出了一个高维的激光混沌并行同步与中继技术方案, 研究有多个中继站的两路混沌通信等问题.

    2.   激光并行串联同步网络与数学物理模型
    • 本文提出的两种不同半导体激光器的耦合发射系统, 能够输出两路混沌信号, 每路还串联多个激光器. 由此形成激光混沌并行串联同步网络与系统, 如图1所示. 其中, 图1(a)是网络拓扑图, 图1(b)是光路图. 图1(a)显示, 耦合激光器送出了两路激光, 分别驱动每路所串联的N个激光器(N是正整数), 这样构成两路串联激光器系统. 事实上, 这也是一个两路并行串联复杂动力学网络系统. 对该网络而言, 各个独立的激光器构成了网络节点(且每个节点激光器都有一个反馈回路). 物理上, 我们把每个网络节点定义为中继器. 其主要功能是: 接收与同步, 再生与发射. 为了实现这两个功能, 每个节点激光器(如: R2或r2)接收上个激光器(R1或r1)信号, 同时还接收另外一路所对应节点(r2或者R2)的上个激光器(r1或R1)的信号, 获取同步并产生混沌. 以此类推, 两路各个激光器获得串联同步. 当然, 最后一组激光器可以作为接收机. 由此, 提出光学光路图1(b). 为了保密通信以及获取两路并行同步, 激光器t, r1, r2, $\cdots $, rN取相同的参数; 激光器T, R1, R2, $\cdots $, rN也取相同的参数. 图1(b)中, 最上层是发射机, 是由两个耦合激光器t和T组成, 输出两路激光EtET. 第2层第一组两个中继器是激光器R1和r1 (它们各存在一个光反馈回路). 对激光器r1而言, 光ET注入驱动激光器r1到混沌态, 光Et注入到激光器r1中使激光器r1获得与激光器t的同步. 对激光器R1而言, 光Et注入驱动激光器R1到混沌态, 光ET光注入到激光器R1中使激光器R1获得与激光器T的同步. 第三层第二组两个中继器是激光器R2和r2 (它们各存在一个光反馈回路), 对激光器r2而言, 光ER1注入驱动激光器r2到混沌态, 光Er1注入到激光器r2中使激光器r2获得与激光器r1的同步. 对激光器R2而言, 光Er2注入驱动激光器R2到混沌态, 光ER2注入到激光器R2中使得激光器R2获得与激光器R1的同步. 以此类推, 最终获得激光器t, r1, r2, r3,$\cdots $, rN – 1, rN的串联同步, 获得激光器T, R1, R2, R3,$\cdots $, RN – 1, RN的串联同步(最后一组激光器rN和RN可作为接收机). 由此产生激光两路并行串联同步.

      Figure 1.  Parallel series complex dynamical network and optical path of repeater: (a) Network topology; (b) optics path.

      脚标t, T, R1, R2, RN – 1, RN, r1, r2, rN – 1, rN分别代表激光器t, T, R1, R2, RN – 1, RN, r1, r2, rN – 1, rN; 变量E, φN分别表示激光振幅、相位和载流子数. 模式增益是$G = (\varGamma {v_{\rm{g}}}a/V)$$\times(N - {N_{{\rm{th}}}})/\sqrt {1 + {E^2}/E_{\rm{s}}^{\rm{2}}} $, 其中vg是光子群速度, a是增益常数, Г = V/Vp是压缩和限制因子, V是腔体积, Vp是激光模式体积, Es是饱和光子场强. Nth = nthV是激光透明时的载流子数, nth是它的密度值; γp = vgαm是光子损耗速率, αm是光子损耗系数. I是驱动电流, q是单位电荷. βc是光线宽增强因子. γe = Anr + B(N/V) + C(N/V)2是载流子非线性损耗速率, Anr是非辐射复合速率, B是辐射复合因子, C是俄歇复合因子; τL = 2ngL/c是光在激光器腔长L内来回一周的时间, c是真空中的光速, ng = c/vg是激光器群速折射率; Δω是激光频率失谐; k是耦合驱动系数; krkR都是注入系数. 为了简化计算, 我们给出三组激光器进行数学讨论. 在本工作中, 取激光器t, r1, r2的腔长是激光器T, R1和R2腔长的2倍, 即有Lt, r1, r2 = 2LT, R1, R2 = 2L. 这样导致和长度与体积有关的参量必须改写:

    3.   并行同步
    • 激光器基本参量见表1, 其他参量取值: kr1 = kr2 = kR1 = kR1 = 0.2和It = Ir1 = Ir2 = 40 mA, IT = IR2 = IR2 = 30 mA. 在该工作条件下, 该网络能够取得并行串联同步, 其结果如图2图5所示. 其中, 图2图3(a)显示第一路激光器t, r1和r2同步过程, 发现经过约10 ns后, 激光器t与激光器r1、激光器r1与激光器r2分别实现混沌同步. 各图的2个小插图是各个激光器混沌吸引子, 显示它们的动力学变化轨迹已完全相同. 这里还以激光器r1和r2同步为例, 采用互相关函数Cr1, r2进行同步质量分析. 公式是

      参量 参量
      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–3
      1.2 × 1018
      辐射复合因子B/ cm3·s–1 1.2 × 10–10

      Table 1.  Laser parameters.

      Figure 2.  The laser t synchronizes with the laser r1. The ininserted illustrations show the chaotic attractors of two lasers.

      Figure 5.  The laser R1 synchronizes with the laser R2: (a) The synchronous process; (b) the cross-correlation function curve.

      Figure 3.  The laser t synchronizes with the laser r2: (a) The synchronous process; (b) the cross-correlation function curve.

      其中P = |E|2为光强度, $\Delta t$为时移, 〈·〉是时间平均值. |Cr1, r2|值范围是0到1, |Cr1, r2|值越大, 同步性能越好, |Cr1, r2| = 1是完全同步. 激光器r1与r2的互相关函数曲线图见图3(b). 其中, 当$\Delta t$ = 0 ns时, |Cr1, r2| = 1表示已完全同步. 以上结果说明这一路三个激光器完全实现了串联混沌同步. 第2路激光器T, R1和R2的串联混沌同步结果如图4图5所示. 由图45(a)可见, 经过10 ns后, 激光器T与激光器R1、激光器R1与激光器R2都分别实现了混沌同步. 图5(b)是激光器R1与R2互相关函数曲线图(CR1, R2定义与Cr1, r2完全相同), 它给出了零时移两激光器的完全同步. 图4图5结果证明了这一路三个激光器实现了串联混沌同步. 至此, 激光网络取得了两路并行串联混沌同步.

      Figure 4.  The laser T synchronizes with the laser R1.

    • 为了进一步证明该网络具有并行串联同步能力, 我们还给出了该网络的多周期并行串联同步. 首先改变一路激光器驱动电流为IT = IR1 = IR2 = 32 mA, 由于发射器是两个不同的激光器, 由此导致两个激光器t和T表现出不同的周期变化行为, 分别呈现出4周期态和3周期态. 它们的并行串联同步结果如图6图9所示. 其中, 图6显示激光器t与r1取得4周期同步, 图7显示激光器r1与r2取得4周期同步. 说明这一路串联的三个激光器都取得了4周期同步. 而图8图9则证明了另一路三个串联激光器的3周期同步结果. 上述结果足以说明该激光网络具有并行串联同步能力以及具有多周期并行同步能力.

      Figure 6.  Period-4 synchronization between the lasers t and r1

      Figure 9.  Period-3 synchronization between the lasers R1 and R2

      Figure 7.  Period-4 synchronization between the lasers r1 and r2

      Figure 8.  Period-3 synchronization between the lasers T and R1

      下面继续改变电流为IT = IR1 = IR2 = 34 mA, 其他多周期并行串联同步同样可以获得, 其结果如图10图13所示. 其中, 图10显示激光器t与r1取得10周期同步, 图11显示激光器r1与r2取得10周期同步. 这三个激光器都取得了10周期串联同步. 而另一路串联的三个激光器同步是另外一个10周期状态同步模样, 其结果见图12图13. 由此可见, 两路激光器分别在不同的10周期状态上都取得了同步. 以上结果进一步证明激光网络具有并行串联同步能力.

      Figure 10.  Period-10 synchronization between the lasers t and r1

      Figure 13.  Another period-10 synchronization between the lasers R1 and R2.

      Figure 11.  Period-10 synchronization between the lasers r1 and r2.

      Figure 12.  Another period-10 synchronization between the lasers T and R1.

    4.   中继器并行同步及信道编码方程
    • 必须指出, 由于发射器是由两个不同的激光器耦合而成, 两激光器定会呈现出不同的混沌变化, 并能输出两个不同的混沌载波. 所以该并行串联同步网络可以应用到有中继器的两个异信道通信中. 首先讨论有中继器的两个异信道混沌编码方程. 基本原则是, 数字信息信号S(t)分别隐藏在发射器两个混沌载波中, 分两路分次发送给下组两个中继器. 经过中继器同步再生后, 再传送给接收机.

      先进行激光器t1, r1和r2串联组成的通信信道分析. 写出激光器t1, r1和r2信道编码方程, 把(2a)和(2b)式右边中的Et改写成为(Et + γ × S), 其中γ是深度因子, S变化在字节“1”或“0”上, 这样可完成字节“1”或“0”信息向激光器r1的传送. 经过同步解调后, 再把取得的信息信号经过载波Er1传送给激光器r2. 与此同时, (3a)和(3b)式右边中的Er1改写成(Er1 + γ × Sd), 其中γ是深度因子, Sd是同步解调出来的信息信号, 原则上有Sd = S. 然后由接收器按照字节“0”或者“1”字节同步解调原则完成同步解调, 最后完成这一路有中继器的混沌通信.

      第二路是激光器T, R1和R2串联组成通信信道分析. (2d)和(2e)式右边中的ET写成(ET + γ × S), 其中γ是深度因子, S是信息信号, 接着向激光器R1传送. 经过同步解调后再把取得的信息信号经过载波ER1传送给激光器R2. 与此同时, (3d)和(3e)式右边中的ER1写成(ER1 + γ × Sd), 其中γ是深度因子, Sd是同步解调出来的信息信号, 原则上有Sd = S. 最后, 接收器按照字节“0”或者“1”字节的同步解调原则完成第二路有中继器的混沌通信.

    • 在工作中, 各个激光器参量取3.1节的值. 先给出激光器t, r1和r2串联通路通信结果. 信息信号速率是0.1 Gbit/s, 取γ值为0.005. 这个深度系数相当于激光器载波Et平均值的6%. 如此小深度完全是为了保密通信安全的需要. 图14是调制与解调过程. 其中, 图14(a)是混沌波隐藏了信息, 外界是难以从波形中提取信息信号的. 图14(b)是中继器的同步解调, “0”字节同步明显可见. 但是, 由于信息信号字节“1”干扰了同步并导致出现同步差, 而这个同步差刚好就是“1”字节. 图14(c)是滤波器滤波后结果(SF1表示滤波后的信息), 我们计算出该同步差的平均值是0.005, 这个值刚好等于γ值. 图14(d)是按照同步代表字节“0”, 同步差0.005代表“1”字节的原则提取的信息信号, 这也是字节归一化原则.

      Figure 14.  Synchronous decoding process.

      这个结果刚好验证了网络理论的正确性. 图14(e)是接收机的同步解调, 完全同步是“0”字节, 有同步差的是字节“1”. 经过滤波器滤波后, 该同步差平均值是0.005, 等于γ值, 滤波结果见图14(f)(SF2表示滤波后的信息). 图14(g)是归一化后的同步解调出来的信息信号, 其中SD = Sd/γ = S. 至此, 该路通信成功完成.

      下面给出另外一路激光器T, R1和R2串联通路通信结果. 信息信号速率是0.1 Gbit/s, γ = 0.005. 这个深度值相当于激光器载波ET平均值的3%. 图15是同步调制与解调过程. 其中, 图15(a)是信息信号成功隐藏于混沌载波中, 图15(b)图15(c)分别是中继器以及接收机的同步解调结果, 图15(d)是归一化后同步解调出来的信息信号. 由此两路通信分别完成.

      Figure 15.  Another synchronous decoding process.

    5.   参数失配合
    • 下面简单讨论参数失配问题. 当激光器t与激光器r1、激光器r1与激光器r2完全不同步时, 计算出非同步差是: $ \langle |E_{\rm t}-E_{\rm r1}| \rangle = 0.0365 = {\varDelta }_{1},$ $\langle | E_{\rm r1}-E_{r2}| \rangle = 0.0423 = {\varDelta }_{2}. $ 完全同步时是:

      先计算电流参数失配. 取值It = 30 mA, Ir1 = 30.1 mA, Ir2 = 30.2 mA. 计算出$\langle | E_{\rm t}-E_{\rm r1}| \rangle = $ $1.0281\times10^{-5} $$ \langle | E_{\rm r1}-E_{\rm r2}| \rangle = 1.4187\times10^{-5}$ 非同步差与这两个比值分别是${\varDelta }_{1}/\langle |E_{\rm t}-E_{\rm r1}| \rangle = $ 3550与$ {\varDelta }_{2}/\langle |E_{\rm r1}-E_{\rm r2}| \rangle = 2982.$ 我们认为非同步与同步是可以识别的.

      线宽增强因子参数失配. 激光器T取量值是βc, 激光器r1取量值是0.999βc, 激光器r2取量值是1.001βc. 计算出$ \langle | E_{\rm T}-E_{\rm r1}| \rangle =1.1824\times 10^{-5},$ $ \langle | E_{\rm r1}\!-\!E_{\rm r2}| \rangle \!=\! 1.1960 \!\times\! 10^{-5}$ 比值是 $ {\varDelta }_{1}/\langle | E_{\rm t}\!-\!E_{\rm r1}| \rangle $ = 3086, 以及比值是 ${\varDelta }_{2}/\langle | E_{{\rm r}1}-E_{{\rm r}2}| \rangle = 3536 $ 倍, 即非同步与同步是可以识别的.

      增益常数参数失配. 激光器t取量值是a, 激光器r1取量值是0.999a, 激光器r1取量值是0.998a. 计算出: $ \langle |E_{\rm t}-E_{\rm r1}| \rangle = 1.6597\times 10^{-4},$$ \langle | E_{\rm r1} \!-\!E_{\rm r2}| \rangle \!=\! 3.3007 \!\times\! 10^{-4},$ 比值是 ${\varDelta}_{1}/\langle | E_{\rm t} \!-\!E_{\rm r1}| \rangle $ = 220, 以及比值是 ${\varDelta }_{2}/\langle | E_{\rm r1}-E_{\rm r2}| \rangle = 128.$ 显然, 非同步与同步是可以识别的.

      激光透明时的载流子数参数失配. 激光器T取量值是2Nth, 激光器r1取量值是2 × 0.999Nth, 激光器r1取量值是$2\!\times\!1.001N_{\rm th}$. 计算出$\langle |E_{\rm t}\!-\! E_{\rm r1}| \rangle =\! 2.8618 \!\times \!10^{-4}\!$$ \langle | E_{\rm r1} \!-\! E_{\rm r2}| \rangle \!=\! 3.7413 \times\! $$10^{-4}, $ 比值是$\dfrac{\varDelta _1}{\langle | E_{\rm t} \!-\! E_{\rm r1}| \rangle} \!=\! 127$$\dfrac{\varDelta _2}{\langle | E_{\rm r1}\!-\! E_{\rm r2}| \rangle}$ = 114.即非同步与同步是可以识别的.

    6.   结 论
    • 本文提出耦合不同半导体激光器并行串联非线性复杂动力网络及其并行串联同步系统. 发射器的两个激光器可以和其他两路多个激光器之间实现混沌或多周期并行同步. 成功实现了中继器同步解调与混沌再生发送, 分别完成两个异信道混沌加密. 研究了系统参数失配合问题, 在较小的参数失配情况下, 系统仍具有一定的同步能力. 这是一种新型的激光混沌编码网络系统, 具有高度非线性、多变量、多维度、多密钥的特点, 具有高度的安全性、不易被破解等优点. 其结果对混沌保密通信、光网络以及激光技术的应用研究具有重要的参考价值.

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