Phase locking and chaos synchronization in injection-locked semiconductor lasers

We theoretically studied synchronization of chaotic oscillation in semiconductor lasers with chaotic light injection. Feedback-induced chaotic light generated from a master semiconductor laser was injected into a solitary slave semiconductor laser. The slave laser subsequently exhibited synchronized chaotic output for a wide parameter range with strong injection and frequency detuning within the injection-locking regime. Our numerical simulation revealed that the synchronized slave laser exhibits remarkable phase locking, even for chaotic light injection. Consequently, synchronization in phase fluctuations becomes dominant over intensity fluctuations. We found that there exists a parameter range where the slave can synchronize in phase only, with no intensity synchronization. However, synchronization can be completely destroyed, both in phase and in intensity, when the phase locking becomes unstable due to four-wave mixing or excited resonance oscillation. The phase locking was studied analytically and the correspondence between numerical and analytical results was shown. We also analytically examined chaos synchronization based on a linear stability analysis from the viewpoint of modulation response of injection-locked semiconductor lasers to a chaotic light signal. As a result, we verified that such injection-locking-induced chaos synchronization results from a quasilinear response of the bandwidth-broadened slave laser due to strong optical injection.     

Identification of the optimum time-delay for chaos synchronization regimes of semiconductor lasers

It is shown that the optimum correlation for chaos synchronization of master-slave semiconductor lasers occurs at a delay time that is sensitive to both the injection strength and the frequency detuning of the driving field. This effect may be overlooked if the correlation function is not evaluated globally. The correlation function has been used as the de facto method for quantitatively determining the degree of synchronization achieved between unidirectional coupled chaotic semiconductor lasers, see for example . The correlation function is a continuous function of the delay time but is normally evaluated at only two delay times. It is shown that this approach can cause a misidentification of the dominant synchronization process and can also mask important temporal fluctuations in the nature and quality of the chaos synchronization. In essence, two factors contribute to the potential for misidentification, the first is the inherent small time shift required to obtain the optimum correlation and the second is the quasi-periodicity that is present in certain chaotic regimes. This paper shows that a reevaluation of some of the published numerical studies of chaos synchronization is necessary.     

半导体激光器的混沌驱动同步

利用混沌驱动同步法研究了在电流调制下的半导体激光器的混沌同步。首先数值计算了系统最大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数区间。然后分别实现了同地激光器系统和异地激光器系统的混沌驱动同步。响应激光器间相关系数的数值计算表明,两种激光器系统均能达到很好的混沌同步。以三个响应激光器为例,将响应系统推广到多个激光器,并且实现了两种激光器系统的混沌同步。     

激光混沌通信系统同步及调制的研究

利用具有外腔反馈的F-P半导体激光器构成开环结构的混沌通信系统。对该系统中存在的同步类型及性能进行分析。结果证实开环系统中在弱注入时达到完全同步,在强注入时达到等时同步,强注入时使用系统增益校正后的同步误差能够更准确反映同步效果。使用混沌调制方法实现混沌载波对信息的加密,研究调制性能。结果表明校正的相减解调法以及大注入系数条件可以恢复出更好的信息。     

Criteria for synchronization of coupled chaotic external-cavitysemiconductor lasers

We study the synchronization of two unidirectionally coupled single-mode external-cavity semiconductor lasers, that operate in a chaotic regime. A simple theory is developed to obtain synchronization conditions and to analyze the effects of the detuning between the two lasers. We find that numerical simulations are in good agreement with the theory     

利用耦合时延增强激光混沌系统安全性能研究

安全性是混沌通信中的重要问题。基于一个外光反馈半导体激光器驱动两个互耦合激光器的混沌通信系统,研究激光混沌系统中反馈时延与耦合时延特征,并应用龙格-库塔法进行动态仿真。重点分析了当调节一些可控参数(耦合时延和驱动强度)时,能够改变两耦合激光器输出自相关函数中反馈时延和耦合时延幅值的差异,以此掩藏反馈时延,从而得出更优载波。仿真结果说明利用耦合时延可以增强激光混沌系统的安全性。最后给出了在优化载波后系统同步质量的讨论。     

Open-loop chaotic synchronization of injection-locked semiconductorlasers with gigahertz range modulation

Unidirectional chaotic synchronization between two remote injection-locked semiconductor lasers to achieve chaotic communications is investigated numerically. Different from the direct chaotic masking methods, the chaotic carrier wave is generated from different chaotic states in transience instead of a fixed chaotic state in static to prevent it from being reproduced through a reconstructed embedding phase space. The testing digital and sinusoidal message signals in the gigahertz range can be easily recovered without the use of any electronic or optical filter to filter out the synchronization error. The robustness of synchronization is examined by using the intrinsic white noise of the transmitter and the receiver as the perturbation. The effects of parameter mismatches on the quality and robustness of synchronization are analyzed in detail. The results show that different internal parameters have very different tolerances for parameter mismatch. A short discussion on the phase sensitivity of synchronization is also given     

耦合半导体激光器的多调制延时混沌同步

为了研究多调制延时混沌系统的动力学,用数值计算法研究了非相干光反馈与非相干光注入半导体激光器的多常数延时与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与发送激光器频率完全匹配。另外,研究了非相干光反馈半导体激光器输出自相关函数。结果表明,多常数延时和多调制延时两种情况下都能获得高质量的同步,但在多调制延时系统中自相关函数的延时标识可以被隐藏,这一特性大大提高了系统的安全性,非常适用于混沌保密通信系统。     

Synchronization and communication using semiconductor lasers withoptoelectronic feedback

Semiconductor lasers provide an excellent opportunity for communication using chaotic waveforms. We discuss the characteristics and the synchronization of two semiconductor lasers with optoelectronic feedback. The systems exhibit broadband chaotic intensity oscillations whose dynamical dimension generally increases with the time delay in the feedback loop. We explore the robustness of this synchronization with parameter mismatch in the lasers, with mismatch in the optoelectronic feedback delay, and with the strength of the coupling between the systems. Synchronization is robust to mismatches between the intrinsic parameters of the lasers, but it is sensitive to mismatches of the time delay in the transmitter and receiver feedback loops. An open-loop receiver configuration is suggested, eliminating feedback delay mismatch issues. Communication strategies for arbitrary amplitude of modulation onto the chaotic signals are discussed, and the bit-error rate for one such scheme is evaluated as a function of noise in the optical channel     

Multimode synchronization and communication using unidirectionally coupled semiconductor lasers

We study numerically the synchronization of two multimode semiconductor lasers unidirectionally coupled in an open-loop configuration, focusing on the comparison with the results obtained in the single-mode case. Anticipative and isochronous synchronization, and their range of validity, are analyzed from the point of view of the total lasing output, and the synchronization between individual modes is studied. Selective injection is also examined and compared with global injection. In light of these results, message encoding and decoding via multimode synchronization is analyzed.     

偏振选择互注入半导体激光器的混沌同步

研究了偏振选择互注入条件下半导体激光器的同步和混沌滤波效应。将单模互注入速率方程扩展为包含两个偏振态的理论模型,并选择X偏振态作为互注入形式,不仅为激光器产生混沌和实现同步提供了条件,还可以完全抑制Y偏振光,实现了纯偏振模式同步。通过频率失调的引入,保持了激光器主从地位的稳定。研究结果表明,主从激光器实现了时差等于注入延时的混沌同步,输出功率表现出高频振荡并伴随有对称性破坏现象。对主激光器进行调制时,同步系统表现出与单向注入相似的混沌滤波效应;对从激光器进行调制时,系统的混沌滤波效应并不明显。     

Encoded Gbit/s digital communications with synchronized chaoticsemiconductor lasers

We numerically study the synchronization of two chaotic semiconductor lasers in a master-slave configuration. To synchronize the lasers, a small amount of output power from the master laser is injected, after propagating through an optical fiber, into the slave laser. We show that the output of the master laser can be used as a chaotic carrier to encode a digital message which can be recovered after propagating long distances. We also check the robustness of this scheme when the two lasers are slightly different     

Synchronized chaotic optical communications at high bit rates

Basic issues regarding synchronized chaotic optical communications at high bit rates using semiconductor lasers are considered. Recent experimental results on broadband, high-frequency, phase-locked chaos synchronization, and message encoding-decoding at 2.5 Gb/s are presented. System performance at a bit rate of 10 Gb/s is numerically studied for the application of three encryption schemes, namely chaos shift keying, chaos masking, and additive chaos modulation, to three chaotic semiconductor laser systems, namely the optical injection system, the optical feedback system, and the optoelectronic feedback system. By causing synchronization error in the forms of synchronization deviation and desynchronization bursts, the channel noise and the laser noise both have significant effects on the system performance at high bit rates. Among the three laser systems, the optoelectronic feedback system has the best performance while the optical feedback system has the worst. Among the three encryption schemes, only the performance of additive chaos modulation with low-noise lasers is acceptable at high bit rates.     

Synchronization of chaotic injected-laser systems and itsapplication to optical cryptography

We demonstrate that two chaotic systems, each made by two coupled semiconductor lasers, can be synchronized using direct-optical feedback. The robustness of the proposed synchronization scheme against mismatch of source parameters and difference in starting conditions is tested by numerical simulations. Applications to secure data transmission are proposed, namely chaotic masking and chaotic shift keying (CSK)     

Optical Chaotic Communication Using Generalized and Complete Synchronization

We propose a secure optical communication system based on the principles of generalized and complete chaotic synchronization. A transmitter and a receiver both composed by two chaotic external-cavity semiconductor lasers are coupled in a master-slave configuration to provide generalized synchronization, while the master lasers in the transmitter and in the receiver are completely synchronized through the synchronization channel via an optical fiber. A message is added to the transmitter slave laser and sent to the receiver through the information channel to be compared with the output of the receiver slave laser. The system is robust to a small mismatch of the laser parameters or of the coupling between the master and slave lasers, unavoidable in a real system, and can even enable a good communication up to a 5 Gb/s transmission rate using the chaos masking encryption method, when the master laseres are coupled bidirectionally.      

激光耦合同步及其在光纤混沌保密通信中的应用

本文建立了光纤混沌保密通信耦合同步系统模型,实现了外部光注入分布反馈半导体激光器激光混沌在长距离光纤传输中的耦合同步,证明了光纤的交叉相位调制是限制激光混沌在光纤传输中同步的主要原因,导出了这种传输的极限.该同步系统在长距离光纤混沌模拟和数字保密通信中的数值模拟表明,该系统确有较高的保密性能和反破译能力.光纤混沌保密通信是可以实现的.     

两台非全同激光器的混沌同步

对空间上相互耦合的两台非全同固体激光器的动力学行为进行了分析。当两台激光器的抽运受到调制而每台激光器的损失不同时 ,两台激光器输出的强度会出现周期性运动、混沌同步和失去同步的情况。激光中混沌同步的发生 ,同两台激光器之间的耦合程度有关。当耦合较强时发生周期性运动 ,耦合适中时处于混沌状态 ,在特定条件下产生混沌同步 ,而耦合较小时 ,两台激光器的振荡就相对独立。     

Anticipating synchronization based on optical injection-locking in chaotic semiconductor lasers

Numerical studies for anticipating chaos synchronization in semiconductor lasers with optical feedback are presented. Anticipating chaos synchronization in a delay-differential system is believed to occur when all chaos parameters between the two systems are perfectly coincident with each other. However, we find new schemes of anticipating chaos synchronization when the parameters between the two systems have mismatches. Under these conditions, the time lag between the two laser outputs is equal to that of anticipating chaos synchronization, but the physical origin of the phenomenon comes from optical injection-locking or amplification in laser systems. We show the evidence of such chaotic synchronization using trajectories in the phase space of the phase difference and the carrier density in the laser oscillations.     

Private Message Transmission by Common Driving of Two Chaotic Lasers

In this paper, we numerically demonstrate private data transmission using twin semiconductor lasers in which chaotic dynamics and synchronization are achieved by optical injection into the laser pair of a common, chaotic driving-signal, generated by a third laser subject to delayed optical feedback. This laser is selected with different parameters with respect to the twin pair, so that the emissions of the synchronized, matched lasers are highly correlated, whereas their correlation with the driver is low. The digital message modulates the emission of the transmitter, as in a standard CM scheme. Message recovery is then obtained by subtracting, from the transmitted chaos-masked message, the chaos, locally generated by the synchronized receiver laser. Simulations have been performed with the Lang–Kobayashi model, keeping into account both laser and photodetector noise. Private transmission has been demonstrated by investigating the effect of the parameter mismatch, between transmitter and receiver, on synchronization and message recovery.      

Open-versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers

We numerically study the synchronization or entrainment of two unidirectional coupled single-mode semiconductor lasers in a master-slave configuration. The emitter laser is an external-cavity laser subject to optical feedback that operates in a chaotic regime. The receiver can either operate at a chaotic regime similar to the emitter (closed-loop configuration) or without optical feedback and consequently under continuous-wave conditions when it is uncoupled (open-loop configuration). We compute the degree of synchronization of the two lasers as a function of the emitter-receiver coupling constant, the feedback rate of the receiver, and the detuning. We find that the closed-loop scheme has, in general, a larger region of synchronization when compared with the open loop. We also study the possibility of message encoding and decoding in both open and closed loops and their robustness against parameter mismatch. Finally, we compute the time it takes the system to recover the synchronization or entrainment state when the coupling between the two subsystems is lost. We find that this time is much larger in the closed loop than in the open one.