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Research on high quality chaotic signal acquisition based on mutual coupled ring laser

  • Received Date: 2019-08-30
    Accepted Date: 2019-09-27
  • In order to meet the need of chaotic secure communication, a scheme of generating high quality chaotic optical signals by mutually coupled semiconductor ring lasers was proposed. The time series, power spectrum and autocorrelation coefficient distributions under various parameters were obtained by numerical simulation, and the theoretical analysis was carried out. The results show that under certain parameters, the laser can exhibit single-period, multi-period and chaotic dynamic states. In the case of large frequency detuning, the delay characteristics of chaos are well suppressed. By scanning injection parameters in a wide range, the chaotic signal with a maximum bandwidth of 14.0GHz and a low time delay signature can be obtained, which can significantly improve the transmission rate and security of chaotic secure communication. The results of this paper can provide some theoretical reference for the application of ring laser in chaotic secure communication.
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Research on high quality chaotic signal acquisition based on mutual coupled ring laser

  • Institute of Mathematics and Physics, Jingchu University of Technology, Jingmen 448000, China

Abstract: In order to meet the need of chaotic secure communication, a scheme of generating high quality chaotic optical signals by mutually coupled semiconductor ring lasers was proposed. The time series, power spectrum and autocorrelation coefficient distributions under various parameters were obtained by numerical simulation, and the theoretical analysis was carried out. The results show that under certain parameters, the laser can exhibit single-period, multi-period and chaotic dynamic states. In the case of large frequency detuning, the delay characteristics of chaos are well suppressed. By scanning injection parameters in a wide range, the chaotic signal with a maximum bandwidth of 14.0GHz and a low time delay signature can be obtained, which can significantly improve the transmission rate and security of chaotic secure communication. The results of this paper can provide some theoretical reference for the application of ring laser in chaotic secure communication.

引 言
  • 半导体激光器(semiconductor lasers,SL)是目前应用比较广泛的光学器件之一,其电学和光学特性一直倍受关注[1]。SL在外部扰动下可产生光混沌信号[2-4],光学混沌在混沌保密通信[5-6]、随机数产生[7-8]、混沌雷达[9]、光学逻辑与混沌计算[10]等领域有着广泛的应用前景。其中,影响混沌应用的重要的两个参量是混沌信号的时延迟信息和带宽,时延信息一般存在于延迟耦合系统中,明显的时延信息将会给混沌保密通信的安全性带来威胁。而窄带宽的混沌信号将限制混沌通信中的信息传输速率、随机数产生的比特率以及混沌信号的空间分辨率。近年来,人们提出了两种抑制时延信息的方法:一种方法是利用逻辑运算消除时延信息,例如异或操作和最小有效位算法[11-12];另外一种方法是利用非线性动力学系统的物理作用来抑制时延信息,例如利用双光反馈系统来抑制时延信息[13-14],或者采用互耦结构的SL系统来抑制时延信息[15]。此外,为了提高混沌系统的带宽,人们也做了多种尝试,例如,采用双光反馈的结构[16],采用3个级联耦合SL的结构[17],采用混沌光注入SL的方式[18-19]等。

    半导体环形激光器(semiconductor ring lasers, SRL)是一种特殊结构的SL,它具有环形谐振腔的几何结构,因此可以同时输出两个反向传播的模式,即顺时针(clockwise,CW)模式和逆时针(counter clockwise,CCW)模式[20-21],此种特殊结构可在光学逻辑门、光开关、光子微波信号及信息的保密通信等领域有广泛的应用前景。近年来,关于SRL的研究已有大量报道。例如,JAVALOYES等人利用SRL的双稳特性实现了全光的定向光开关[22]。MASHAL等人研究了SRL在光反馈下的动力学特性,发现在适当的反馈参量下,SRL可展示出低频反相波动的现象[23]。NGUIMDO等人发现, SRL在交叉光反馈的结构下,通过调节线宽增强因子的大小可以有效抑制时延信息[24]。LI等人发现, SRL在交叉光反馈的情况下可出现方波振荡,并且两个模式的振荡相位是相反的[25-26]。同时,SRL在外部反馈下也可以产生混沌态,但是由于弛豫振荡频率的限制,混沌带宽只有几个赫兹,并且在反馈时间延迟处有较强的时延信息,这将限制基于SRL的保密通信的传输速率和安全性。

    为了解决此问题,本文中提出了一种新的方案,本方案由两个SRL组成,通过两个SRL相互耦合产生4路混沌信号,并且在两个互耦激光器的相互作用下消除时延特征并在一定程度上增加混沌带宽。本文中将讨论两个激光器耦合之后的非线性动力学特性,计算耦合系数对产生的混沌信号的时延信息和带宽的影响。研究结果可为基于SRL的混沌保密通信提供一定的理论支持。

1.   数值模型及描述
  • 图 1是两个SRL的互相耦合的结构图。其中CW和CCW分别代表了两个传播方向,E1, CW(E1, CCW)和E2, CW(E2, CCW)分别代表了两个激光器两个方向输出的复电场。SRL 1的CW(CCW)方向的电场分别注入到SRL 2的CW(CCW方向),同时SRL 2的两个方向的电场也注入到SRL 1。考虑复电场E1, CW(E1, CCW)和E2, CW(E2, CCW),以及载流子数Nn(n=1, 2),两个SRL相互耦合下的速率方程表示为[24]

    Figure 1.  Diagram of the mutual coupling structure for two SRL

    式中, t表示时间; α代表线宽增强因子; κ代表电场衰减率; γ代表载流子衰减率; kdkc为耗散和保守系数; ηCWηCCW为两个方向的注入系数; τ为注入延迟时间,本文中固定为5ns; ω1ω2为两个SRL的角频率, Δν=(ω1-ω2)/(2π)为注入频率失谐; gCWgCCW为两个方向的增益系数; s为自饱和系数; m为互饱和系数; μn(n=1, 2)为两个SRL的注入电流,当μn=1时达到阈值。仿真所使用的参量取值为[24]γ=0.2ns-1κ=100ns-1kd=0.033ns-1kc=0.44ns-1μn=2.4,α=3.5,s=0.005,m=0.01。

    为了量化混沌信号的带宽和时延特征,本文中采用标准带宽和自相关函数进行计算。标准带宽的定义为功率谱中直流分量到功率的80%所包含的频率的跨度[23]。自相关函数的数学定义式为:

    式中,x(t)为混沌序列; Δt为时间延迟; 〈·〉表示时间平均; xs(t)=x(tt)为时间移动Δt后时间序列的值。自相关系数的取值范围为[-1, 1],取绝对值后,0~0.09为没有相关性,0.10~0.30为弱相关,0.30~0.50为中等相关,0.50~1.00为强相关。

2.   结果及讨论
  • 研究了SRL1与SRL2互耦情况下的非线性动力学特性。对于相互耦合的两个SRL,注入系数有两种情况,即对称情况ηCW=ηCCW和不对称情况ηCWηCCW。通过仿真发现,在不对称情况下进行耦合时,由于模式竞争,会使SRL 1中的一个模式被抑制,从而只有一个方向产生混沌信号。因此,为了得到多路混沌信号,本文中将采用对称耦合的形式,即ηCW=ηCCW。由于对称耦合时,SRL的所有输出都是相同的,这里只给出了SRL 1的CW方向的输出。图 2中给出了Δν=-7.0GHz时不同注入系数下的时间序列和功率谱。当ηCW=ηCCW=1ns-1时,时间序列(见图 2a)出现了规则的周期振荡,对应的功率谱(见图 2b)在f=7.0GHz出有一个较大的峰值,后面的较小的峰值为高次谐波,f为周期振荡频率,此频率与两个激光器的频率失谐相等,此时激光器工作在单周期振荡状态。当ηCW=ηCCW=4ns-1时,时间序列(见图 2c)出现了多个不等的峰值,功率谱(见图 2d)f=7.0GHz的前面出现了多个分数倍的谐波,此时激光器工作在多周期振荡状态。当ηCW=ηCCW=10ns-1时,时间序列(见图 2e)出现了无规则的振荡,功率谱(见图 2f)明显展宽并无明显峰值,此时激光器处于混沌振荡状态,通过计算,此时混沌的带宽为2.4GHz。从上面的分析可以看出,SRL在互耦的情况下可以展现出不同的动力学态,由于在保密通信中主要使用混沌态,下面将针对产生的混沌态的特性展开讨论。

    Figure 2.  Time series and power spectrum of CW direction of SRL1 under different injection intensities

  • 研究了频率失谐值对时延特征的影响。图 3是当ηCW=ηCCW=15ns-1时,不同频率失谐情况下产生的混沌信号的自相关系数C分布图。当Δν=-10.0GHz时(见图 3a),自相关系数C在±10ns附近出现了极大值,此处峰值的出现是由于时间延迟引起的,时间延迟的大小为SRL 1发出的激光往返回到发射端所需要的时间(2τ)。此时C=0.23,为弱相关,时延特征不明显。当Δν=-5.0GHz时(见图 3b),在时间延迟处的相关系数值增大到C=0.41,为中等相关,时延特征较为明显。当Δν=5.0GHz时(见图 3c),时间延迟处的相关系数值增大到C=0.53,为强相关,时延特征非常明显,不利于混沌保密通信。当Δν=10GHz时(见图 3d),时间延迟处的相关系数值降到了C=0.20,此时为弱相关,时延特征不明显。总体上看,在频率失谐值较大时,时延特征不明显,而对于较小的频率失谐,时延特征变得较为明显。出现此类现象的物理原因是由于SRL存在一个本征频率(弛豫振荡频率)${f_{\rm RO}} = \sqrt {2(\mu - 1)\gamma \kappa } /(2{\rm \pi} ) = 1.2{\rm GHz}$,当频率失谐较小时,注入光容易与fRO引起共振,从而增强了时延特征。但当频率失谐较大时,共振较弱,从而抑制了时延特征。

    Figure 3.  Distribution of autocorrelation coefficients under different frequency detuning when ηCW=ηCCW=15ns-1

    研究了SRL输出的混沌信号的时延特征在不同注入强度随下随频率失谐的变化关系。图 4中给出了当注入系数分别取15ns-1,20ns-1,30ns-1时,时间延迟(2τ)处自相关系数的峰值随频率失谐的变化。当ηCW=ηCCW=15ns-1时,如图中空心圆所示,在零频率失谐处,自相关系数出现了极大值C=0.64,为强相关。随着频率失谐绝对值的增大,自相关值逐渐减小。在负频率失谐区域,当频率失谐位于-15.0GHz~-8.0GHz时,自相关值小于0.30,为弱相关,此时混沌信号不易被破解。当频率失谐位于-8.0GHz~0GHz之间时,自相关值大于0.30,为中等相关或强相关,此时的时延特征明显,不利于混沌保密通信。对于正失谐区域,当频率失谐位于0GHz~9.0GHz之间时,为强相关与中等相关,在9.0GHz~15.0GHz之间为弱相关。并且正失谐部分的相关系数的最小值小于负失谐。当ηCW=ηCCW=20ns-1时,如图中矩形所示,此时在零频率失谐处,互相关系数的极大值为C=0.52,比注入系数等于15ns-1要低,并且当频率失谐的绝对值大于12.0GHz时,相关系数的值都小于0.20。图中零频率失谐两边的相关系数的分布不对称,右边一直缓慢下降,而左边在0GHz~6.0GHz之间下降后又缓慢上升,最后再在-10.0GHz以后缓下降。当ηCW=ηCCW=30ns-1时,如图中三角形所示,此时零频率失谐处的相关系数降到了0.40,当频率失谐小于-5.0GHz和大于12.0GHz时,相关系数都小于0.20,时延特征得到了很好抑制。总体上说,随着注入系数的增加,时延特征逐渐减弱,并且对于相同的注入系数,频率失谐绝对值越大,时延特征越不明显。出现此类现象的原因是由于注入系数较大时,注入到腔内的光子数增多,本征频率共振的影响将减弱。除了时延特征,混沌带宽也是混沌通信的一个重要指标,接下来,将研究混沌带宽随频率失谐和注入系数的变化规律。

    Figure 4.  Distribution of autocorrelation coefficients with frequency detuning at time delay

  • 为了研究SRL产生的混沌带宽随频率失谐和注入系数的分布,本文中大范围扫描了耦合参量,图 5是带宽在参量空间的2维映射图。如图 5所示,频率失谐在-7.0GHz~7.0GHz之间时,随着注入系数的增加,带宽并没有明显增加,并且均在5.0GHz以下。频率失谐在-15.0GHz~-7.0GHz之间,当注入系数大于16ns-1时,带宽出现了加强,但呈离散状分布,最大可以达到9.0GHz。当频率失谐位于7.0GHz~15.0GHZ之间时,随着注入系数的增加,出现了大面积的带宽加强区域,并且当注入系数位于28ns-1附近时,带宽增加到了14.0GHz。此时由于频率失谐较大,时延特征也得到了较好的抑制。将此混沌信号应用于混沌保密通信,既能满足高速通信的要求,又能有效防止第三方窃听。

    Figure 5.  Distribution of chaotic bandwidth generated by SRL with frequency detuning and injection coefficient

3.   结 论
  • 本文中理论研究了两个半导体环形激光器(SRL)在互耦情况下产生的混沌信号的特性。研究发现,当频率失谐为Δν=-7.0GHz、注入系数分别为1ns-1,4ns-1和10ns-1时,SRL输出的时间序列表现为单周期、多周期及混沌态。对于产生的混沌信号,利用自相关函数,计算了时间延迟处的自相关系数关于频率失谐的分布,当注入系数分别为15ns-1,20ns-1,30ns-1时,对于较大的频率失谐能有效抑制时延特征。通过大范围扫描注入参量,得到了带宽高达14.0GHz的低时延混沌信号,能够满足混沌保密通信的需求。所得究结果可为SRL的实际应用提供一定的理论参考。

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