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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]:
$ \begin{array}{c} {\rm d}{E_{\rm 1,CW}}/{\rm d}t = \kappa (1 + {\rm i}\alpha )[{g_{\rm 1,CW}}{N_1} - 1]{E_{\rm 1,CW}} - \\ ({k_{\rm d}} + {\rm i}{k_{\rm c}}){E_{\rm 1,CCW}} + {\eta _{\rm CW}}{E_{\rm 2,CW}}(t - \tau ) \times \\ {\rm \exp} [ - {\rm i}({\omega _2}\tau + 2{\rm \pi} \Delta \nu t)] \end{array} $
(1) $ \begin{array}{c} {\rm d}{E_{\rm 1,CCW}}/{\rm d}t = \kappa (1 + {\rm i}\alpha )[{g_{\rm 1,CCW}}{N_1} - 1] \times \\ {E_{\rm 1,CCW}} - ({k_{\rm d}} + {\rm i}{k_{\rm c}}){E_{\rm 1,CCW}}+ {\eta _{\rm CCW}} \times \\ {E_{\rm 2,CCW}}(t - \tau ){\rm \exp} [ - {\rm i}({\omega _2}\tau + 2{\rm \pi} \Delta \nu t)] \end{array} $
(2) $ \begin{array}{*{20}{c}} {{\rm{d}}{E_{2,{\rm{CW}}}}/{\rm{d}}t = \kappa (1 + {\rm{i}}\alpha )[{g_{2,{\rm{CW}}}}{N_2} - 1]{E_{2,{\rm{CW}}}} - }\\ {({k_{\rm{d}}} + {\rm{i}}{k_{\rm{c}}}){E_{2,{\rm{CCW}}}} + {\eta _{{\rm{CW}}}}{E_{1,{\rm{CW}}}}(t - \tau ) \times }\\ {\exp [ - {\rm{i}}({\omega _1}\tau - 2{\rm \pi} \Delta \nu t)]} \end{array} $
(3) $ \begin{array}{*{20}{c}} {{\rm{d}}{E_{2,{\rm{CCW}}}}/{\rm{d}}t = \kappa (1 + {\rm{i}}\alpha )[{g_{2,{\rm{CCW}}}}{N_2} - 1] \times }\\ {{E_{2,{\rm{CCW}}}} - ({k_{\rm{d}}} + {\rm{i}}{k_{\rm{c}}}){E_{2,{\rm{CW}}}} + {\eta _{{\rm{CCW}}}}{E_{1,{\rm{CCW}}}} \times }\\ {(t - \tau )\exp [ - {\rm{i}}({\omega _1}\tau - 2{\rm \pi} \Delta \nu t)]} \end{array} $
(4) $ \begin{array}{c} {\rm{d}}{N_n}/{\rm{d}}t = \gamma [{\mu _n} - {N_n} - \left. {{g_{n,{\rm{CW}}}}{N_n}} \right|{\left. {{E_{n,{\rm{CW}}}}} \right|^2} - \\ \left. {{g_{n,{\rm{CCW}}}}{N_n}} \right|{\left. {{E_{n,{\rm{CCW}}}}} \right|^2}],(n = 1,2) \end{array} $
(5) $ \begin{array}{c} {g_{n,{\rm{CW}}}} = (1 - s{\left| {{E_{n,{\rm{CW}}}}} \right|^2} - m{\left| {{E_{n,{\rm{CCW}}}}} \right|^2}),\\ (n = 1,2) \end{array} $
(6) $ \begin{array}{c} {g_{n,{\rm{CCW}}}} = (1 - s{\left| {{E_{n,{\rm{CCW}}}}} \right|^2} - m{\left| {{E_{n,{\rm{CCW}}}}} \right|^2}),\\ (n = 1,2) \end{array} $
(7) 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; kd和kc为耗散和保守系数; ηCW与ηCCW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; ω1和ω2为两个SRL的角频率, Δν=(ω1-ω2)/(2π)为注入频率失谐; gCW与gCCW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-1,κ=100ns-1,kd=0.033ns-1,kc=0.44ns-1,μn=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:
$ \begin{array}{c} c(\Delta t) = \\ \frac{{\left\langle {[x(t) - \left\langle {x(t)} \right\rangle ][{x_{\rm s}}(t) - \left\langle {{x_{\rm s}}(t)} \right\rangle ]} \right\rangle }}{{\sqrt {\left\langle {{{[x(t) - \left\langle {x(t)} \right\rangle ]}^2}} \right\rangle \left\langle {{{[{x_{\rm s}}(t) - \left\langle {{x_{\rm s}}(t)} \right\rangle ]}^2}} \right\rangle } }} \end{array} $
(8) 式中,x(t)为混沌序列; Δt为时间延迟; 〈·〉表示时间平均; xs(t)=x(t+Δt)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。
基于互耦合环形激光器获取高质量混沌信号
Research on high quality chaotic signal acquisition based on mutual coupled ring laser
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摘要: 为了满足混沌保密通信的需求,提出了一种基于两个半导体环形激光器互耦合产生高质量混沌光信号的方案,采用数值仿真的方法进行了理论分析,得到了各种参量情况下的时间序列、功率谱及自相关系数分布图。结果表明, 在一定的参量条件下,激光器能展现出单周期、多周期及混沌等动力态;在较大的频率失谐下,混沌信号的时延特征能够被较好地抑制;通过大范围扫描注入参量,可得到带宽最大为14.0GHz并且具有较低的时延特征的混沌信号,能显著提高混沌保密通信的传输速率及安全性。此研究结果可为环形激光器在混沌保密通信中的应用提供一定的理论参考。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.
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Key words:
- nonlinear optics /
- chaos /
- bandwidth /
- mutual coupling /
- semiconductor ring laser
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