Experimental verification of anticipated and retarded synchronization in chaotic semiconductor lasers

Experimental observation of both anticipated and retarded synchronization is demonstrated using unidirectionally coupled semiconductor lasers with delayed optoelectronic feedback. Depending on the difference between the transmission time and the feedback delay time, the lasers fall into either the anticipated or the retarded synchronization regime, where the driven receiver laser leads or lags behind the driving transmitter laser. The two regimes are observed to have the same stability of chaos synchronization in the presence of small perturbations by noise and parameter mismatches. In both regimes the observed time shift between the synchronized chaotic waveforms is found to be equal to the difference between the transmission time and the feedback delay time.     

Synchronization of Chaotic Intensities and Phases in an Array of N Lasers

A linear array of N mutually coupled single-mode lasers is investigated. It is shown that the intensities of N lasers are chaotically synchronized when the coupling between lasers is relatively strong. The chaotic synchronization of intensities depends on the location of the lasers in the array. The chaotic synchronization appears between two outmost lasers, the second two outmost lasers, etc. There is no synchronization between nearest neighbors of the lasers. If the number of N is odd, the middle laser is never synchronized between any lasers. The chaotic synchronization of phases between nearest lasers in the array is examined by using the analytic signal and the Gaussian filter methods based on the peak of the power spectrum of the intensity. It can be seen that the message of chaotic intensity synchronization is conveyed through the phase synchronization.     

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.     

Phase locking and chaotic synchronization in an array of three lasers

A linear array of three lasers that are coupled mutually in space is investigated. It is shown that the phase of the laser fields is locked with intermediate coupling while the laser intensities are totally chaotic and chaotically synchronized. When the intensities of lasers reenter the regime of chaotic synchronization at smaller coupling constant, the laser fields show low degree of phase locking. The phase differences in the fields between three lasers show rich patterns when the coupling is changed. Received 3 August 2001 and Received in final form 27 September 2001     

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.     

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.     

Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers

We present experimental and numerical investigations of the dynamics of two device-identical, optically coupled semiconductor lasers exhibiting a delay in the coupling. Our results give evidence for subnanosecond coupling-induced synchronized chaotic dynamics in conjunction with a spontaneous symmetry-breaking: we find a well-defined time lag between the dynamics of the two lasers, and an asymmetric physical role of the subsystems. We demonstrate that the leading laser synchronizes its lagging counterpart, whereas the synchronized lagging laser drives the coupling-induced instabilities.     

Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers

We analyze theoretically the effect of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs). Chaos in the master laser is induced by delayed optical feedback, and the slave laser is subject to isotropic optical injection from the master VCSEL. We show that the synchronization quality can be enhanced when the chaotic regime in the master VCSEL involves both fundamental orthogonal linearly polarized modes.     

Controlling the leader-laggard dynamics in delay-synchronized lasers

We study experimentally the collective dynamics of two delay-coupled semiconductor lasers. The lasers are coupled by mutual injection of their emitted light beams, at a distance for which coupling delay times are non-negligible. This system is known to exhibit lag synchronization, with one laser leading and the other one lagging the dynamics. Our setup is designed such that light travels along different paths in the two coupling directions, which allows independent control of the two coupling strengths. A comparison of unidirectional and bidirectional coupling reveals that the leader-laggard roles can be switched by acting upon the coupling architecture of the system. Additionally, numerical simulations show that a more extensive control of the network architecture can also lead to changes in the dynamics of the system. Finally, we discuss the relevance of these results for bidirectional chaotic communications.     

Zero-lag long-range synchronization via dynamical relaying

We show that isochronous synchronization between two delay-coupled oscillators can be achieved by relaying the dynamics via a third mediating element, which surprisingly lags behind the synchronized outer elements. The zero-lag synchronization thus obtained is robust over a considerable parameter range. We substantiate our claims with experimental and numerical evidence of such synchronization solutions in a chain of three coupled semiconductor lasers with long interelement coupling delays. The generality of the mechanism is validated in a neuronal model with the same coupling architecture. Thus, our results show that zero-lag synchronized chaotic dynamical states can occur over long distances through relaying, without restriction by the amount of delay.     

Preference of Chaotic Synchronization in a Coupled Laser System

In a coupled laser system, the dynamics of the receiving laser is investigated when two separate transmitting lasers are injected into the receiving laser with different coupling strengths. It is shown that the phenomenon of preference of chaotic synchronization appears under appropriate coupling conditions. The receiving laser will entrain the pulses of either one or both transmitting lasers when the coupling is strong while it keeps its own dynamics when the coupling is weak.     

Preference of Chaotic Synchronization in a Coupled Laser System

In a coupled laser system, the dynamics of the receiving laser is investigated when two separate transmitting lasers are injected into the receiving laser with different coupling strengths. It is shown that the phenomenon of preference of chaotic synchronization appears under appropriate coupling conditions. The receiving laser will entrain the pulses of either one or both transmitting lasers when the coupling is strong while it keeps its own dynamics when the coupling is weak.     

Synchronization and control of chaos in coupled chaotic multimode Nd:YAG lasers

In this Letter we numerically investigate the dynamics of a system of two coupled chaotic multimode Nd:YAG lasers with two mode and three mode outputs. Unidirectional and bidirectional coupling schemes are adopted; intensity time series plots, phase space plots and synchronization plots are used for studying the dynamics. Quality of synchronization is measured using correlation index plots. It is found that for laser with two mode output bidirectional direct coupling scheme is found to be effective in achieving complete synchronization, control of chaos and amplification in output intensity. For laser with three mode output, bidirectional difference coupling scheme gives much better chaotic synchronization as compared to unidirectional difference coupling but at the cost of higher coupling strength. We also conclude that the coupling scheme and system properties play an important role in determining the type of synchronization exhibited by the system.     

Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback

Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback is numerically studied based on laser rate equations. The bandwidth of the chaotic carrier frequency in a semiconductor laser with optical feedback is expanded roughly three times by strong optical injection compared with the bandwidth when there is no optical injection. Using a bandwidth-enhanced semiconductor laser as a chaotic transmitter and receiver, we synchronized transmitter and the receiver lasers in a complete chaos synchronization scheme.     

GENERAL SYNCHRONIZATION OF CHAOS IN A SYSTEM OF TWO NON-IDENTICAL LASERS

General synchronization of the chaotic intensity fluctuations of two spatially coupled Nd:YAG lasers with pump modulation is investigated theoretically when the losses of the two lasers are different. It is shown that the chaotic synchronization still exists for medium coupling even though the two lasers are different. For strong coupling the system shows periodic motion of laser intensities. While for weak coupling, the two lasers oscillate independently. It is obvious that the increase of difference between the two lasers reduces the degree of chaotic synchronization.     

Transition between anticipating and lag synchronization in chaotic external-cavity laser diodes

Chaotic synchronization is investigated by use of two diode lasers as transmitter and receiver. The transmitter laser is rendered chaotic by application of optical feedback in an external-cavity configuration. Changes in the spectrum of the synchronized system are shown to be associated with the transition between anticipating and lag synchronization.     

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.     

Chaotic synchronization of two inverse-injection semiconductor lasers for logic gates

A round-coupling configuration of two inverse-injection semiconductor lasers is presented for logic gate applications. Two laser diodes coupled via injection from the opposite laser became chaotic. Chaotic synchronization is achieved between the two lasers. Two all-optical or two optoelectronic logic gates can be implemented by modulating the injected light or laser diode current, respectively, to synchronize or unsynchronize the two chaotic states. Numerical results show the validity and feasibility of the method.     

INVERSE SYNCHRONIZATION OF CHAOTIC SYSTEMS IN AN ERBIUM-DOPED FIBRE DUAL-RING LASER USING THE MUTUAL COUPLING METHOD

Inverse synchronization of chaos is a type of synchronization in which the dynamical variables of two chaotic systems are inversely equal. In this paper, we present a scheme for inverse synchronization of two chaotic systems in an erbium-doped fibre dual-ring laser using the mutual coupling method. For realistic values of the systems, we demonstrate two kinds of results, as follows. (1) Two independent identical chaotic systems can go into inversely synchronized chaotic oscillation for coupling greater than 0.03. (2) When some parameter of one system varies, the state of the coupled systems could go into some periodic states directly or by inverse bifurcation. Simultaneously, they will lose the synchronization as the parameter changes.