Synchronization of chaotic VCSELs by external chaotic signal parameter modulation

Synchronization of chaotic vertical-cavity surface-emitting lasers （VCSELs） is achieved by external chaotic signal modulation successfully. Simulation indicates that we can get chaos synchronization if the intensity of external chaotic signal is large enough. First of all, we use direct current modulation to achieve the chaos of VCSELs, and determine the laser＇s chaotic state by analyzing time series of the output and the corresponding power spectrum. And then we achieve synchronization of the two chaotic systems by external chaotic signal parameter modulation. We also find that the larger the modulation intensity is, the easier it is to achieve synchronization for chaotic VCSELs. This approach can also be applied to systems with a number of modulated lasers.     

Synchronization of chaotic erbium-doped fibre lasers and its application in secure communication

We have investigated the synchronization of chaotic dual-ring erbium-doped fibre lasers using the delay feedback－injection scheme. Numerical simulation shows that two chaotic dual-ring erbium-doped fibre lasers can be well synchronized if the strengths of delay feedback and injection are suitable. Even though the effects of the noises and the difference between the two lasers are considered, the twins can still reach good synchronization. Secure communication could be realized using the scheme of message-masking based on the synchronization of the chaotic dual-ring erbium-doped fibre lasers.     

Chaos synchronization based on intermittent state observer

This paper describes the method of synchronizing slave to the master trajectory using an intermittent state observer by constructing a synchronizer which drives the response system globally tracing the driving system asymptotically. It has been shown from the theory of synchronization error-analysis that a satisfactory result of chaos synchronization is expected under an appropriate intermittent period and state observer. Compared with continuous control method, the proposed intermittent method can target the desired orbit more efficiently. The application of the method is demonstrated on the hyperchaotic R?ssler systems. Numerical simulations show that the length of the synchronization interval τ_s is of crucial importance for our scheme, and the method is robust with respect to parameter mismatch.     

Experimental Investigation of Chaos Synchronization in DFB Diode Lasers with Unsymmetrical Scheme

We experimentally generate high dimension chaotic waveforms with smooth spectrum using a distributed feedback （DFB） semiconductor laser with unidirectional fibre ring long-cavity feedback, and implement the stable chaos synchronization when the chaotic light is injected into a solitary DFB laser diode. The synchronization quality is investigated by time-domain and frequency-domain analysis separately, The frequency-domain analysis indicates that the synchronization has higher quality in the high frequency band. The influences of the injection strength and the frequency detuning on the synchronization are measured. Our experimental results show that the robust synchronization can be maintained with the optical frequency detuning from -11GHz to 40 GHz.     

Synchronous implementation of optoelectronic NOR and XNOR logic gates using parallel synchronization of three chaotic lasers

The parallel synchronization of three chaotic lasers is used to emulate optoelectronic logic NOR and XNOR gates via modulating the light and the current. We deduce a logical computational equation that governs the chaotic synchronization, logical input, and logical output. We construct fundamental gates based on the three chaotic lasers and define the computational principle depending on the parallel synchronization. The logic gate can be implemented by appropriately synchronizing two chaotic lasers. The system shows practicability and flexibility because it can emulate synchronously an XNOR gate, two NOR gates, and so on. The synchronization can still be deteceted when mismatches exist with a certain range.     

Random-injection-based two-channel chaos with enhanced bandwidth and suppressed time-delay signature by mutually coupled lasers: Proposal and numerical analysis

Simultaneous bandwidth(BW) enhancement and time-delay signature(TDS) suppression of chaotic lasing over a wide range of parameters by mutually coupled semiconductor lasers(MCSLs) with random optical injection are proposed and numerically investigated. The influences of system parameters on TDS suppression(characterized by autocorrelation function(ACF) and permutation entropy(PE) around characteristic time) and chaos BW are investigated. The results show that, with the increasing bias current, the ranges of parameters(detuning and injection strength) for the larger BW(> 20 GHz) are broadened considerably, while the parameter range for optimized TDS(< 0.1) is not shrunk obviously.Under optimized parameters, the system can simultaneously achieve two chaos outputs with enhanced BW(> 20 GHz)and perfect TDS suppression. In addition, the system can generate two-channel high-speed truly physical random number sequences at 200 Gbits/s for each channel.     

Synchronization of Phase Oscillators in Networks with Certain Frequency Sequence

Synchronization of Kuramoto phase oscillators arranged in real complex neural networks is investigated. It is shown that the synchronization greatly depends on the sets of natural frequencies of the involved oscillators. The influence of network connectivity heterogeneity on synchronization depends particularly on the correlation between natural frequencies and node degrees. This finding implies a potential application that inhibiting the effects caused by the changes of network structure can be bManced out nicely by choosing the correlation parameter appropriately.     

Order Parameter Hysteresis on the Complex Network

Collective synchronization is investigated on the small-world network （NW model）. The order parameter is introduced to measure the synchronization of phase. It is found that there are differences between the processes of synchronization and desynchronization. The dependence of order parameter on the coupling strength is shown like a hysteresis loop. The size of the loop demonstrates the non-monotonicity with the change of adding probability, and is relevant to the construction of the network. The area may be maximum, as the adding probability is equal to 0.4. This phenomenon indicates that the clusters in the network play an important role in the processes of synchronization and desynchronization.     

Adaptive generalized synchronization between Chen system and a multi-scroll chaotic system

Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multi-scroll chaotic system is investigated. According to the form of target function a proper adaptive controller is designed, by which the controlled Chen system can be synchronized with a multi-scroll chaotic system including unknown parameters. The Lyapunov direct method is exploited to prove that the synchronization error and parameter identification error both converge to zero. Numerical simulation results verify the feasibility of the proposed method further.     

Generalized chaos synchronization of a weighted complex network with different nodes

This paper proposes a method of realizing generalized chaos synchronization of a weighted complex network with different nodes. Chaotic systems with diverse structures are taken as the nodes of the complex dynamical network, the nonlinear terms of the systems are taken as coupling functions, and the relations among the nodes are built through weighted connections. The structure of the coupling functions between the connected nodes is obtained based on Lyapunov stability theory. A complex network with nodes of Lorenz system, Coullet system, Rõssler system and the New system is taken as an example for simulation study and the results show that generalized chaos synchronization exists in the whole weighted complex network with different nodes when the coupling strength among the nodes is given with any weight value. The method can be used in realizing generalized chaos synchronization of a weighted complex network with different nodes. Furthermore, both the weight value of the coupling strength among the nodes and the number of the nodes have no effect on the stability of synchronization in the whole complex network.     

基于非相干光反馈半导体激光器的双向混沌通信研究

提出了一种基于非相干光反馈半导体激光器的双向混沌通信系统,数值研究了该系统的同步特性及通信性能. 结果表明,当两个激光器参数一致时,系统能获得无延时的高质量混沌同步,实现实时双向通信;当激光器内部参数失配时,系统的同步性能及通信质量会受到一定的影响,但该系统对参数失配的容忍性较好,在一定的参数失配范围内,系统仍能实现较好的双向混沌通信. 关键词： 非相干光反馈 半导体激光器 混沌同步 双向通信     

Theoretical investigations of cascaded chaotic synchronization and communication based on optoelectronic negative feedback semiconductor lasers

In this paper, a novel chaotic relay system, based on cascaded synchronization in optoelectronic negative feedback chaotic semiconductor lasers, is presented. Synchronization characteristics and the influence of parameter mismatches on synchronization performances are investigated. The results show that the complete synchronization can be achieved under suitable system parameters; internal parameter mismatches of the lasers have influence on synchronization quality, but the system possesses more robustness to parameter mismatches compared with cascaded synchronization based on coherent optical feedback. Moreover, communication related issues are also investigated. Under the additive chaos modulation (ACM) encryption scheme, encoded messages can be successfully extracted at both mediator laser (ML) and receiver laser (RL) parts; parameter mismatches of the lasers will affect messages decoding, but the influence is not strong.     

Bidirectional chaos synchronization and communication based on mutually coupled semiconductor lasers with asymmetrical bias currents

In this paper, a bidirectional chaos secret communication system, based on mutually coupled semiconductor lasers (MCSLs) with asymmetrical bias currents, is proposed, and the synchronization characteristics and the communication performances of such a system are numerically investigated. The results show that the stable leader-laggard chaos synchronization can be achieved under relatively large asymmetrical bias current levels. Meantime, the influence of the intrinsic parameter variations of the laser on the synchronization quality is also considered, and the simulation reveals that this system still possesses good robustness to the parameter variations. Moreover, the influences of delay time and mutually coupling strength between the two lasers on chaos communication performance have also been discussed. Finally, unidirectional and bidirectional secret communication performances of such a system are examined under the chaos masking (CMS) encryption scheme, and the security of this system is also discussed.     

链式互耦合半导体激光器的实时混沌同步

通过在互耦合外腔半导体激光器之间增加中继激光器,建立了一种链式互耦合半导体激光器混沌同步系统模型.理论分析了系统的实时混沌同步条件,数值研究了注入电流、互耦合条件、反馈条件等对系统实时混沌同步品质的影响,揭示了同步质量在反馈强度和互耦合强度二维参数空间的分布规律.结果表明:注入电流较大时,满足互耦合强度和反馈强度相同,互耦合延时和反馈延时相等,系统中所有激光器之间可同时实现稳定高品质实时混沌同步;中心激光器和边激光器之间的稳定实时混沌同步分布在在互耦合强度和反馈强度较小的区域以及互耦合强度和反馈强度相近的区域;边激光器之间由于同时接收到中心激光器实施的相同注入,能够较容易的实现稳定高品质的实时混沌同步.该系统可进一步扩展成为实现远距离的双向实时混沌同步或阵列激光器系统的实时混沌同步.     

Synchronization properties and effects of parameter mismatches in unidirectionally coupled chaotic vertical-cavity surface-emitting lasers

We numerically investigate the effects of parameter mismatches on chaos synchronization in vertical-cavity surfaceemitting lasers (VCSELs). We assume injection-locked chaos synchronization in a unidirectionally coupled and openloop optical feedback system. The accuracy of chaos synchronization is greatly affected by the mismatches of the device parameters and operation conditions between the two lasers. In particular, the oscillation frequency of the laser is one of the important parameters in a system of injection-locked chaos synchronization. However, the variations of the device characteristics of VCSELs are very large compared with those of other types of semiconductor lasers. We study the effects of parameter mismatches related to the oscillation frequency of VCSELs on chaos synchronization. We proved that mismatches in terms of the birefringence and the injection current play crucial roles for the quality of chaos synchronization.     

Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback

In this paper, a bidirectional chaos communication system based on the optoelectronic feedback semiconductor lasers (SLs) is presented, and the synchronization characteristics and the communication performances of such system are simulated numerically. The results show that the high-quality synchronization with zero lag time and simultaneous bidirectional message transmission can be realized under the suitable system parameters; the internal parameter mismatches of the lasers have influence on the synchronization quality and communication performance, but this system still possesses good robustness to parameter mismatches. Meanwhile, the security can be ensured through a suitable encoding-decoding technique.     

电流调制半导体激光器的混沌及其同步

研究了电流调制半导体激光器的混沌及其同步.通过数值计算系统的最大Lyapunov指数随调制强度的变化情况,确定了激光器处于混沌态的参量区间.利用差值耦合与和值耦合两种方案实现了两激光器的混沌同步.两激光器相关系数的数值计算表明,两种方案的同步效果都很好,而和值耦合更易于实现两激光器的同步.以标准化系数为例,分析了两激光器参量不匹配对混沌同步的影响,当标准化系数的偏差保持在小范围内时,两激光器仍可达到较好的同步,而差值耦合同步的鲁棒性优于和值耦合.     

Impact of unpredictability on chaos synchronization of vertical-cavity surface-emitting lasers with variable-polarization optical feedback

The effects of unpredictability degree on the chaos synchronization properties of vertical-cavity surface-emitting lasers with variable-polarization optical feedback are investigated numerically. For variable-polarization optical injection, only low-unpredictability chaos can be well synchronized, while high-unpredictability chaos cannot be synchronized even with large injection strength. On the other hand, for the polarization-preserved optical injection, the synchronization quality is hardly affected by the unpredictability degree, and high-quality synchronization can be achieved for both low- and high-unpredictability chaos due to injection locking.     

双路激光混沌复用系统的混沌同步及安全性能研究

针对一种新型的双路激光混沌复用系统, 建立相应的速率方程模型, 详细分析了两个主激光器的单个参数失配、多个参数同时失配、反馈强度差异以及频率失谐对混沌同步性能的影响, 并对此复用系统的安全性能和频谱性能进行了研究. 研究结果表明: 采用参数失配方案, 通过合理选择两个主激光器的参数, 可以保证两个主激光器之间的同步性能较差而两对主从激光器间实现高品质的混沌同步, 因此满足双路激光混沌复用的条件; 两个主激光器之间的参数失配对它们之间的同步性能影响较大, 然而对配对主从激光器间同步性能的影响并不明显, 进一步说明参数失配方案的有效性和可行性. 另外, 通过自相关函数和频谱分别分析混沌复用信号的时域和频域特征, 发现双路激光混沌复用系统可提供更高的安全性.     

Synchronization of Chaotic Oscillations in Mutually Coupled Semiconductor Lasers

Synchronization of chaotic oscillations in mutually coupled semiconductor lasers is experimentally investigated. Synchronization of chaotic outputs from mutually injected lasers is observed not only in low frequency fluctuation regimes but also in high frequency fluctuation regions on the nano-second time scale. It is shown that the synchronization of our results is based not on complete chaos synchronization but on injection phenomena in laser systems, so called generalized chaos synchronization.