Characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback

We numerically investigate the detailed characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback. The emission of the dominant TE mode of a drive laser is rotated 90 deg and fed back to the laser with time delay. The polarization-rotated TE mode is also injected with time delay into the TM mode of a second laser. Two types of synchronization with different time-lags are found, as in the case for synchronization in semiconductor lasers with nonrotated optical feedback. However, a significant difference to the nonrotated optical feedback case is that neither of the two types of synchronization requires matching of optical carrier frequency between the two lasers.     

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。     

Demultiplexing chaos from multimode semiconductor lasers

We show numerically that the injection of two chaotic modes of a multimode semiconductor laser with optical feedback into two single-mode stand-alone semiconductor lasers leads to chaotic synchronization between the respective intensities. The effect of parameter mismatch between the transmitter and receiver lasers is examined, and it is concluded that the observed synchronization is a consequence of injection locking. Under these conditions, the possibility of using this demultiplexing scheme for message transmission is examined.     

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。     

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.     

多变量耦合实现双环掺铒光纤激光器混沌同步

根据双环掺铒光纤激光器的理论模型,提出多变量单向耦合法实现混沌同步,对主从系统模型进行数学推导,研究不同参数条件下双环掺铒光纤激光器的混沌同步,得到实现混沌同步的条件,并在Simulink平台下动态仿真。结果表明,衰减系数不同的两个双环掺铒光纤激光器,主激光器通过定向耦合器驱动从激光器,主从系统可以实现精确混沌同步,且随着反馈强度的增大,实现系统混沌同步的时间越短,反馈强度的取值范围由衰减系数和耦合系数确定;选取不同的系统初值,主从系统可实现混沌同步,系统初值对达到混沌同步时间的影响可忽略不计;在主从系统中引入随机高斯噪声,主从系统仍可实现较好的混沌同步。     

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     

Antiphase dynamics of selectively coupled multimode semiconductor lasers

We analyze the experiment of A. Uchida et al. (2001) reporting on the synchronization of multimode semiconductor lasers coupled unidirectionally through one of the transmitter modes. We show that only the coupled modes are synchronized and that the dynamical regimes of the two lasers are different, though leading to similar power spectra.     

Experiments on chaos synchronization in two separate erbium-dopedfiber lasers

Chaos synchronization in two separate erbium-doped fiber lasers through a 1.5-km-long fiber is experimentally demonstrated. Two identical erbium-doped fiber lasers are fabricated and modulated by an optical modulator near the relaxation oscillation frequency of the fiber laser. At this frequency, the two fiber lasers generate chaotic carriers. When the synchronization conditions such as cavity length, modulation frequency, and laser characteristics are satisfied, the two chaotic fiber lasers are synchronized     

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.     

光反馈垂直腔面发射半导体激光器的混沌驱动同步

基于光反馈垂直腔面发射半导体激光器动力学模型,通过分析光子数密度随光反馈强度变化的分岔情况,确定了激光器处于混沌态时的参数区间。利用混沌信号驱动同步方案,实现了两个被驱动激光器的精确混沌同步,并通过对两个被驱动激光器相关系数的分析,确定了它们达到精确混沌同步的参数区间。研究了参数失配对同步的影响,结果表明该同步方案有很好的稳健性。     

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     

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.      

两台多模激光场强度和相位的混沌同步

对空间耦合的两台多模激光场的强度和相位的动力学行为进行了理论分析.当系统的损失受到调制时,在一定的参数范围内,两台激光输出的总强度之间会出现很好的混沌同步,两台激光的对应模式之间也出现相应的混沌同步,但不同模式之间则是完全的混沌状态,每台激光的各个模式强度之间存在模式竞争现象.每台激光场不同模式的相位和相位差之间出现有趣的关系,与强度的混沌同步存在一定的联系.     

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。     

两维网格空间耦合激光阵列的时空混沌同步

通过数值模拟对两维3×3单模 激光网格阵列的动力学行为进行了研究。阵列中的激光束在光场中通过空间的局部耦合产生相互作用,可以通过对激光参数设置进行调节。数值研究表明,在一个相对较小区域的参数范围内,当任两台激光之间的空间耦合作用距离一定时,相应的激光束的强度之间可以实现混沌同步,并且具有特点: 处于次对角线或与其平行的对角线的对应位置上激光都可以实现混沌同步状态。通过对该激光阵列的功率谱和李雅普诺夫指数的计算和分析,可以确信所研究的强度同步的激光系统处于混沌状态。     

Two-mode chaos synchronization using a multimode external-cavity laser diode and two single-mode laser diodes

Strong optical injection and optical frequency matching have been used to effect an experimental demonstration of two-mode synchronization using a multimode external-cavity chaotic transmitter laser and two single-mode stand-alone receiver lasers. It is shown by means of synchronization diagrams and measured cross-correlation functions that the longitudinal modes of the receiver lasers have been successfully synchronized to frequency matched modes of the transmitter laser operating in the low frequency fluctuation regime.     

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.     

延时反馈双环掺铒光纤激光器互注入系统中的混沌同步研究

分析了延时反馈双环掺铒光纤(EDF)激光器互注入 系统的动态特性,并引入一种量化时间序列复杂度的评 价方法——排列熵(PE,permutation entropy),对激光器输出状 态和混沌同步质量与复杂度的关系进行讨论。研究表明,通过调节反馈 延迟时间和反馈强度可控制系统的输出状态,使系统输出为周期态和混沌态,而且利用PE熵计算激光器 输出信号的复杂度相对于分岔图同样能直观准确的反映出系统动态行为;在激光器独立工作 情况下,输出 信号的混沌区域内夹杂有较多的周期态,而在互注入情况下,混沌区域增宽且较为平坦,同 时输出信号复 杂度的PE值较高,互注入系统有利于参数选择的范围和提高混沌通信系统的安全性;提 高注入强度可 得到高质量的混沌同步,两个激光器在同步和不同步时输出信号的复杂度是 不同的,可见 研究激光器输出信号的复杂度可成为分析混沌同步质量的一种参考。     

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.