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.      

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.      

Regimes of chaotic synchronization in external-cavity laser diodes

Chaotic synchronization is investigated experimentally using two diode lasers as transmitter and receiver. The transmitter laser is rendered chaotic by application of an optical feedback in an external-cavity configuration. Experimental conditions are found under which the synchronization diagram makes a transition from a positive to a negative gradient. A regime of operating conditions is identified in which the receiver laser is found to anticipate the dynamics of the transmitter laser. The anticipation time does not depend on the external-cavity length, but rather on the time of flight between the two lasers. Changes in the spectrum of the synchronized system are shown to be associated with the transition between anticipating and lag synchronization.     

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.     

Enhancing Chaotic Communication Performances by Manchester Coding

A numerical analysis of an optical chaotic transmission system, based on the synchronization of two chaotic lasers, in a master-slave closed loop configuration is presented. At the transmitter, the master chaotic wave is superposed on the information message; at the receiver, the message is recovered by subtracting the synchronized slave chaotic wave from the received signal. The performances are analyzed in terms of the Q-factor, considering two different message modulation formats: the nonreturn-to-zero and the Manchester coding. The Manchester coding shows enhanced performances due to the shift of the signal spectrum to higher frequencies.     

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.     

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.     

Performance characterization of high-bit-rate optical chaotic communication systems in a back-to-back configuration

A comparative study of three data-encoding techniques in optical chaotic communication systems is reported. The chaotic carrier is generated by a semiconductor laser subjected to optical feedback and the data are encoded on it by chaotic modulation (CM), chaotic masking (CMS), or chaotic shift keying (CSK) methods. In all cases, the receiver-which is directly connected to the transmitter-consists of a semiconductor laser similar to that of the transmitter subjected to the same optical feedback. The performance of this back to back configuration is numerically tested by calculating the Q-factor of the eye diagram of the received data for different bit rates from 1 to 20 Gb/s. The CM scheme appears to have the best performance relative to the CMS and CSK scheme, before and after filtering the residual high-frequency oscillations remaining due to nonperfect synchronization between the transmitter and receiver. Moreover, in all encoding methods, a decrease in the Q-factor is observed when the repetition bit-rate of the encoding message increases. In order to achieve as high Q-factor values as possible, a well-synchronized chaotic master-slave system is required.     

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     

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     

GHz Bandwidth Message Transmission Using Chaotic Vertical-Cavity Surface-Emitting Lasers

Chaotic message encoding and decoding in unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs) with polarization-preserved and polarization-selected optical injection has been studied experimentally. A GHz message has been successfully encoded in the chaotic transmitter and decoded from the receiver with polarization-preserved optical injection. In contrast decoding using polarization-selected optical injection was achieved at only 330 MHz. It has also been demonstrated that GHz message extraction can be achieved using both normal and inverse chaos synchronization thus providing an opportunity for exploiting polarization properties of VCSELs for duplexed chaotic message transmission.     

Optimised Message Extraction in Laser Diode Based Optical Chaos Communications

Synchronization quality and message extraction using chaotic laser diode as transmitter-receiver pairs has been experimentally studied. The experimental results demonstrate that the conditions for maximum signal to noise ratio (SNR) of the extracted message are not identical to those for achieving maximum chaos synchronization quality. It is also shown that synchronization quality and message extraction not only depend on having well-matched lasers as transmitter and receiver, but also depend on the roles of the laser diodes.      

Synchronized chaotic mode hopping in DBR lasers with delayedopto-electric feedback

We propose and demonstrate a scheme for generating synchronized chaotic mode hopping in two wavelength-tunable lasers. Chaotic mode hopping resulting in large hops in wavelength is induced by delayed feedback of an electrical signal proportional to the intensity of the laser output which passes through an optical filter. Mode hopping among up to 11 modes was experimentally observed and optical signals in each wavelength band show a different on-off modulation time series. Analysis of the time series indicates high dimensionality. By using a unidirectional coupling method that injects part of the output of one laser into another, we can synchronize the chaotic mode hopping of two separate lasers and obtain synchronized chaotic on-off modulation patterns in multiple corresponding wavelength bands. The robustness of the synchronization with respect to the parameter mismatch and the effects of the coupling strength are investigated. The chaotic mode hopping dynamics and synchronization are well described with a numerical model that includes the characteristics of the laser tuning and the filter transmission. A multiplexed data transmission scheme using chaotic carriers is proposed and experiments demonstrate that multiple messages can be simultaneously recovered when chaos synchronization is achieved     

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.     

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     

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。     

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.     

Message encoding and decoding using chaotic external-cavity diodelasers

Synchronization of chaotic external-cavity diode lasers has been studied in a master-slave configuration. A message is encoded into the chaotic master laser by amplitude modulation and transmitted to the slave laser. A scheme for decoding the message at the slave is demonstrated     

Secure Communication via Synchronization of Lur’e Systems Using Sampled-Data Controller

In this paper, synchronization of chaotic Lur’e systems using sampled-data control is applied to the secure communication problem. The message is transmitted and masked by the techniques of n-cipher and a public key obtained by the chaotic Lur’e system. The decryption of the transmitted encrypted message to recover the original message at the receiver can be achieved by synchronizing the transmitter and receiver chaotic systems. Sampled-data feedback control is used for synchronization, and a sufficient condition for obtaining feedback gain is derived in terms of linear matrix inequalities using a discontinuous Lyapunov functional. The secure communication system is simulated via Matlab along with the Chua system to show the effectiveness of the proposed result.     

非相干光反馈的半导体激光器混沌保密通信性能分析及其仿真

首先研究了非相干光反馈同步系统内部参数失配对系统同步性能的影响,并与相干光反馈的完全同步系统以及广义同步系统进行了比较,其次研究了非相干光反馈采用三种不同的信号调制解调方式(CSK,CMS,ACM),对三种不同频率(250 MHz,2.5GHz和12.5GHz)的信号进行了调制解调。通过MATLAB仿真实验可知,非相干光反馈混沌同步系统相对于相干光反馈完全同步系统更易于实现,同时保留了一定的对参数失配的敏感特性,从而确保了该系统比相干光反馈广义同步具有更高的安全性;在信号解调时,CSK只能解调出250MHz信号,CMS能解调出2.5GHz信号,ACM能够解调出高达12.5GHz的信号。