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.     

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.     

Synchronization of chaotic mode hopping

We propose and demonstrate a scheme for generating synchronized chaotic mode hopping in two wavelength-tunable lasers whose tuning range covers multiple longitudinal modes. Chaotic mode hopping resulting in large hops in wavelength is induced by delayed electrical feedback. We show that, by coupling part of the output of one laser into another, one can synchronize the chaotic mode hopping of two separate lasers and obtain synchronized chaotic on-off modulation patterns in multiple corresponding wavelength bands.     

Simultaneous bidirectional message transmission in a chaos-based communication scheme

We introduce a chaos-based communication scheme allowing for bidirectional exchange of information. Coupling [corrected] two semiconductor lasers through a partially transparent optical mirror, placed in the pathway connecting the lasers [corrected] delay dynamics is induced in both lasers. We numerically demonstrate that this dynamics can be identically synchronized, and moreover, information introduced on both ends of the link can be simultaneously transmitted. This scheme allows one to negotiate a key through a public channel.     

Enhanced coherence of weakly coupled lasers

We present the phase-locking and coherence properties between two weakly coupled lasers. We show how the degree of coherence between the two lasers can be enhanced by nearly 1 order of magnitude after taking into account the effects of coupling on both their phases as well as their amplitudes. Specifically, correlations between synchronized spikes in the amplitude dynamics and the phase dynamics of the lasers allow for an interference pattern with a fringe visibility of 90%, even when the coupling strength is far below the critical value and they are not phase locked.     

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.     

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.     

Active synchronization of two mode-locked lasers with optical cross correlation

Two mode-locked Ti:sapphire lasers of different wavelengths were precisely synchronized by a simple feedback system employing sum-frequency generation (cross correlation). When the timing error exceeded the pulse duration, the periodic bunch of the sum-frequency pulse was used for rough timing adjustment. Using cross correlation with a stretched pulse, we struck a balance between wide locking range and sensitive timing detection. When the two lasers were well-synchronized, we obtained a continuous cross-correlation pulse train for 3 min. The holding time of the laser synchronization was extended to over one hour by adding a motorized stage to the PZT-mounted cavity mirror. We estimated the rms timing jitter between the two lasers by a scanning cross-correlation measurement. We confirmed that the rms timing jitter of the two lasers during 1.8 s was 28 fs. Received: 30 January 2002 / Revised version: 14 June 2002 / Published online: 8 August 2002     

Independently tunable 1.3 W femtosecond Ti:sapphire lasers passively synchronized with attosecond timing jitter and ultrahigh robustness

A stable passively synchronized femtosecond laser has been realized by coupling two 1.3 W mode-locked Ti:sapphire lasers with a Kerr medium. An ultralong tolerance of 10 microm for the cavity length mismatch and a timing jitter of less than 0.4 fs were obtained. The relative carrier-envelope phase slip was directly observed by measuring the heterodyne output between the two lasers.     

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.     

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.     

Passive synchronization of femtosecond Er- and Yb-fiber lasers by?injection locking

We demonstrated a self-starting passively synchronized Er- and Yb-fiber laser system. Synchronization was implemented by the master-slave configuration where partial output power of the Er-fiber laser was injected into the Yb-fiber laser via a 2-m-long single-mode fiber. The output pulses both were in femtosecond range, and the cavity mismatch tolerance was 160 μm, corresponding to 1267 Hz in frequency domain. The RMS (root mean square) timing jitter between these two lasers was calculated as 14.7 fs (5-kHz bandwidth) in one second.     

Investigation of passively synchronized dual-wavelength Q-switched lasers based on V:YAG saturable absorber

In this paper the results of a theoretical and experimental investigation of synchronized passive Q-switching of two Nd:YVO₄-based solid-state lasers operating at two different wavelengths, is described. A V:YAG saturable absorbing material was used as a passive Q-switch performing the synchronization of the two laser fields. This material provides Q-switching operation at both 1064 and 1342 nm wavelengths simultaneously, saturating the same energy level. By adjusting the pump power of both lasers, it was possible to optimize the overlap of the two pulse trains and to switch between different states of synchronization. A theoretical model based on rate equations, which has been developed in order to investigate optical performance of the laser system, is in a good agreement with the experimental results. The principle of synchronized Q-switching can lead to new, pulsed all-solid-state light sources at new wavelengths based on sum-frequency mixing processes.     

Multi-state optical flip-flop memory based on ring lasers coupled through the same gain medium

We investigate a system consisting of multiple ring lasers coupled by a single gain medium. All the ring lasers share a common feedback arm. The output power of an individual laser shows periodic oscillations as a function of time. The periodicity of the oscillation is determined by the ratio of the roundtrip times of the feedback arm and the ring cavity. In the case that two of such ring lasers are coupled, either their oscillation periodicities are synchronized, or the system is bi-stable. In the latter operation regime, the system can act as an optical flip-flop memory whose state be switched by injection of external light. The concept can be extended to multi-state operations; an eight-state optical flip-flop memory is experimentally demonstrated.     

Experiments on chaos synchronization in two separate microchip lasers

Synchronization of chaos generated in two Nd:YVO(4) microchip lasers is experimentally demonstrated with master-slave coupling schemes. For synchronization of chaos, precise locking of the sustained relaxation-oscillation frequency is required, as is optical frequency locking. One needs to match both the pump-modulation parameters for chaos generation and the laser parameters of the two lasers to generate perfectly synchronized chaotic spectra in the master-slave type I coupling scheme.     

Passively synchronized erbium (1550-nm) and ytterbium (1040-nm) mode-locked fiber lasers sharing a cavity

Erbium and ytterbium fiber lasers were firmly synchronized by nonlinear interaction in active media placed in the same cavity. A two-color femtosecond-picosecond pulse train at largely separate wavelengths of 1.55 and 1.04 microm was generated. Optimizing the laser cavity to enhance the cross-phase modulation in the gain materials has yielded a large mismatch of 20 microm between the two laser cavities.     

Wavelength-independent all-optical synchronization of a Q-switched 100-ps microchip laser to a femtosecond laser reference source

We present a Q-switched microchip laser emitting 1064-nm pulses as short as 100 ps synchronized to a cavity dumped femtosecond laser emitting 800-nm pulses as short as 80 fs. The synchronization is achieved by presaturating the saturable absorber of the microchip laser with femtosecond pulses even though both lasers emit at widely separated wavelengths. The mean timing jitter is 40 ps and thus considerably shorter than the pulse duration of the microchip laser.     

基于反馈参数调制的掺铒光纤激光器混沌同步

提出了一种基于反馈参数调制控制超混沌同步的方法，并应用于双环掺铒光纤激光器系统.针对此种方法所具有的相位模糊问题，设计出了自动消除反相位的电路，数值模拟表明只要适当选择反馈强度值，就能实现两双环掺铒光纤激光器系统的精确同步. 关键词： 超混沌同步 双环掺铒光纤激光器 反馈参数调制法 反相位     

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.