Synchronization of mutually coupled systems

General operation conditions to obtain anticipated or retarded synchronization in a mutually coupled system with feedback are analyzed. Different from a unidirectionally coupled system, which type of synchronization will occur in a mutually coupled system does not solely depend on the difference between the feedback-delay time and the coupling-delay time. We find that in addition to the feedback/coupling delay times, feedback strengths and coupling strengths all determine whether the system will preform anticipated or retarded synchronization. Experimental implementation using semiconductor lasers subject to optoelectronic feedback is provided as an example. A set of experimental data is presented and discussed.     

Synchronization of chaos in unidirectionally and bidirectionally coupled multiple time delay laser diodes with electro-optical feedback

We report on chaos synchronization in both unidirectionally and bidirectionally coupled multiple time delay laser diodes with electro-optical feedback. We derive existence and sufficient stability conditions for the synchronization regimes. We calculate the Lyapunov exponents, information dimension, and Kolmogorov-Sinai entropy for a single and double delay time lasers to demonstrate that multiple time delay laser system can offer higher complexity than a single time delay laser. We demonstrate that in coupled multiple time delay lasers additional feedback(s) can play a stabilizing role. We compare the synchronization quality for closed loop and open loop receiver laser configurations and find better synchronization quality for partially open loop receiver (when the receiver laser has only one feedback loop), than the open loop receiver configuration (when the receiver contains no feedback loops). We also study the effect of the feedback phase on the correlation coefficient between the interacting laser systems. Analytical results are fully supported by numerical simulations.     

Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback

The synchronization of chaotic semiconductor lasers with optical feedback is studied numerically in a one-way coupling configuration, in which a small amount of the intensity of one laser (master laser) is injected coherently into the other (slave laser). A regime of anticipated synchronization is found, in which the intensity of the slave laser is synchronized to the future chaotic intensity of the master laser. Anticipation is robust to small noise and parameter mismatches, but in this case the synchronization is not complete. It is also shown that anticipated synchronization occurs in coupled time-delay systems, when the coupling has a delay that is less than the delay of the systems.     

激光局域网络的混沌控制及并行队列同步

本文提出并研究了"单队列-双参数"光电延时反馈控制条件下的激光局域网络的混沌控制及串联的动力学行为的并行队列"交叉驱动-反馈"网络同步实现,建立了该光学局域网络的数学物理控制模型.通过含时延超越方程理论的分析,预言了该光学局域网络是可以实现混沌控制的,且网络两路结点队列是可以实现实时引导控制到多个类周期状态上的,并通过并行队列同步方程理论证明并行串联队列同步是可以获得的.结果发现在可控的激光局域网络两个并行串联队列光路上,分别实现了网络队列结点的混沌控制并能够实现多个类周期的网络结点的并行串联队列同步,实现了络网结点激光器的2周期、3周期、4周期等状态的并行队列同步,以及其他多个类周期的队列并行同步和动态同步.还发现了两个类周期并行队列网络同步控制区域.本文还给出了激光局域网络"并行多点混沌载波同步发射及其在光学超宽带通信中应用"的一个案例并成功实现.这是一种新型的激光混沌局域网络控制系统,具有光局域网络光传送与光联接核心控制技术要素,具有复杂动力学系统与网络的多变量、多空间维度及并行两路不同队列混沌控制技术特点,还具有光网络超宽带通信功能等.其研究结果对局域网络、光网络的控制与同步、激光技术以及混沌的研究具有重要的参考价值.     

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.     

基于光电反馈的激光混沌并联同步系统研究

提出了基于光电反馈的激光混沌并联同步方案,对可能存在的两种同步——广义同步和完全同步进行了研究,着重讨论了激光器内部参数失配对发射与接收激光器之间以及并联接收激光器之间同步特性的影响.研究结果显示：在一定范围内,同样的内部参数失配下,并联接收激光器之间的同步效果明显优于发射激光器与接收激光器之间的同步效果. 关键词： 半导体激光器 混沌同步 光电反馈 参数失配     

Two chaos synchronization schemes and public-channel message transmission in a mutually coupled semiconductor lasers system

Chaos synchronization and message transmission of a mutually coupled system consisting of two semiconductor lasers (SLs) and a partially transparent mirror (PTM) in between are investigated theoretically. Analytical results show that two types of chaos synchronization schemes, named as isochronal synchronization (IS) and leader/laggard synchronization (LLS), can be achieved by adjusting the reflectivity and position of PTM. By establishing SIMULINK model, numerical simulations illustrate that as the PTM is positioned at the center of two lasers, IS is available when the reflectivity of PTM is moderate. The LLS is achieved when the reflectivity of PTM equals to 0.5, which means feedback strength equals to coupling strength. Its lag time is just determined by the difference of feedback delay time. The investigations of mutual chaos pass filtering (MCPF) effects and the secure chaotic communication simulations indicate that IS allows real-time bidirectional message transmission on a public-channel, while LLS can achieve higher security chaotic communication by using its lag time as cryptography key. The demonstrated system can be used as a rudiment of array chaos communications system.     

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 and encoding in coupled semiconductor lasers of multiple modulated time delays

We numerically investigate the synchronization performance of unidirectionally and bidirectionally coupled chaotic semiconductor lasers subject to multiple modulated time delays optical feedbacks. Moreover, by studying the autocorrelation function of the coherent feedback semiconductor laser output, we find that the signatures of time delays can be erased in systems incorporating modulated feedback time delays, which largely improve the system security. Finally, chaos masking switching (CMS) is utilized to examine the communication ability. Numerical results indicate that the messages could be successfully recovered both in unidirectionally and bidirectionally coupled lasers, which confirms the possibility of applying multiple modulated delay system in optical chaos secure communication.     

Dual-lag synchronization between coupled chaotic lasers due to path-delay interference

We study experimentally the synchronization dynamics of two semiconductor lasers coupled unidirectionally via two different delayed paths. The emitter laser operates in a chaotic regime characterized by low-frequency fluctuations due to optical feedback and induces a synchronized dynamical activity in the receiver laser, which operates in the continuous-wave regime when uncoupled. Different delays in the two coupling paths lead to the coexistence of two time lags in the synchronized dynamics of the oscillators. This dual-lag synchronization degrades the average synchronization quality of the system of coupled lasers and hinders the transmission of information between them. Numerical simulation results agree with the experimental observations, and allow us to explore this phenomenon in a wide parameter range, and quantify the degree of signal transmission degradation caused by this chaotic path-delay interference.     

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.     

多调制延时耦合半导体激光器的混沌同步与编码

数值研究了非相干光反馈与非相干光注入半导体激光器的多调制延时混沌同步,由于该系统是基于非相干注入的,所以不需要接收激光器的频率与发送激光器频率完全匹配。通过对非相干光反馈半导体激光器输出自相关函数的研究,发现在多调制延时系统中,延时标识可以被隐藏,这一特性可以提高系统的安全性,非常适用于混沌保密通信系统。分别利用混沌移位键控(CSK)及混沌隐藏(CMS)编码方法考查了单向耦合和双向耦合系统的通信性能。     

Global coupling with time delay in an array of semiconductor lasers

Synchronization due to a weak global coupling with time delay in a semiconductor laser array is investigated both in the cw and self-pulsing regimes. A generalized form of the Kuramoto phase equations is derived and discussed analytically. The time delay is shown to induce in-phase synchronization in all dynamical regimes. Another form of synchronization is found which leads to local extinction of self-pulsing in the array.     

Low-frequency pulsations in class-B solid-state lasers with delayed feedback

We report on the numerical observation of short-duration low-frequency pulsations in class-B solid-state lasers subject to delayed feedback. The period of these pulsations is much larger than either the delay induced by the feedback or the relaxation oscillation period of the laser without feedback. A link is established between the low-frequency pulsations and the low-frequency fluctuations observed in semiconductor lasers subject to coherent optical feedback.     

Stable route-tracking synchronization between two chaotically pulsing semiconductor lasers

Stable route-tracking synchronization is experimentally demonstrated in two semiconductor lasers with delayed optoelectronic feedback. When the two lasers are stably synchronized, the receiver laser is observed to track the route to chaotic pulsing of the transmitter laser. The stability of the route-tracking synchronization is examined by calculation of the transverse Lyapunov exponents of the coupled system.     

Episodic synchronization via dynamic injection

We report the occurrence of spontaneous synchronizing events between two semiconductor lasers, when the emission of a frequency- and intensity-chaotic driving laser is unidirectionally coupled into a second stable response laser. The driving laser is driven chaotic by delayed optical feedback, the response laser is a device-identical solitary laser. We demonstrate the onset of an episodic synchronization regime when the two lasers are spectrally detuned with respect to each other. By a joint experimental and modeling analysis we can attribute the onset and the duration of the episodes to properties of spectral overlap of both lasers. This effect can even give rise to seemingly anticorrelated intensity behavior. We expect episodic synchronization to be a generic scenario for the loss of synchronization of chaotic oscillators exhibiting frequency cycles.     

Experimental synchronization of chaos in diode lasers with polarization-rotated feedback and injection

We demonstrate experimental chaos synchronization between two chaotic semiconductor lasers subjected to polarization-rotated optical feedback and unidirectional injection. This system allows high-quality synchronization to be obtained between dissimilar lasers in a wide range of chaotic operating regimes. Another feature of this system is its operation at high characteristic frequencies, taking advantage of all-optical implementation. Time series and RF spectra showing synchronization are confirmed by high correlation coefficients in excess of 0.85.     

Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers

A pair of coupled erbium doped fiber ring lasers is used to explore the dynamics of coupled spatiotemporal systems. The lasers are mutually coupled with a coupling delay less than the cavity round-trip time. We study synchronization between the two lasers in the experiment and in a delay differential equation model of the system. Because the lasers are internally perturbed by spontaneous emission, we include a noise source in the model to obtain stochastic realizations of the deterministic equations. Both amplitude synchronization and phase synchronization are considered. We use the Hilbert transform to define the phase variable and compute phase synchronization. We find that synchronization increases with coupling strength in the experiment and the model. When the time series from two lasers are time shifted in either direction by the delay time, approximately equal synchronization is frequently observed, so that a clear leader and follower cannot be identified. We define an algorithm to determine which laser leads the other when the synchronization is sufficiently different with one direction of time shift, and statistics of switches in leader and follower are studied. The frequency of switching between leader and follower increases with coupling strength, as might be expected since the lasers mutually influence each other more effectively with stronger coupling.     

Synchronization of time delayed semiconductor lasers and its applications in digital cryptography

This work aims to demonstrate the effect of synchronization phenomena in chaotic laser systems described by modified Lang-Kobayashi's (L-K) delay differential equations. The synchronized system considered for numerical simulations and for cryptography consists of identical semiconductor lasers operating in single longitudinal mode. The two lasers are bidirectionally coupled by linear optical feedback. As this is essential in simultaneous transmission of messages, we have applied the corresponding coupled chaotic dynamics to secure communications. An investigation of the system together with a novel scheme for digital cryptography and visual recurrence analysis (VRA) of the chaotic time series are presented. Extended statistical tests with the proposed two phase scheme demonstrate the efficiency of these infinite dimensional systems in being tolerant to different types of statistical attacks. The result emphasizes the merits of the uncertainty and high dimensionality of optical chaos system in duplex high speed secure communications.     

Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation

It is shown that identical synchronization of two chaotic semiconductor lasers can be achieved by injection of a common optical signal with randomly varying phase. An optical signal with randomly modulated phase is injected into two semiconductor lasers which have chaotic oscillations due to optical feedback. Strong correlation between complex intensity oscillations of the two lasers is observed even though the intensity of the common injection signal is constant. Characteristic properties of this type of synchronization are shown, in particular, the dependence of the synchronization threshold on the injection strength and the rate of phase modulation, and the dependence of the intensity correlation on the difference in phase of optical feedback.