Anticipation in the Synchronization of Chaotic Semiconductor Lasers with Optical Feedback

Masoller, Cristina

doi:10.1103/physrevlett.86.2782

Cited by 315 publications

(174 citation statements)

References 34 publications

Supporting

Mentioning

168

Contrasting

Unclassified

Order By: Relevance

“…First observed in unidirectionally coupled systems, in contrast to lag synchronization, anticipatory synchronization occurs when a response in a system's state is replicated not simultaneously but anticipated by the response system [13,14,15]. An example of anticipation in synchronization is found in coupled semiconductor lasers [16]. Here, the author followed Ref.…”

mentioning

confidence: 99%

Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers

Shaw

Schwartz

Rogers

et al. 2006

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

A pair of coupled erbium doped fiber ring lasers is used to explore the dynamics of coupled spatiotemporal systems. The lasers are mutually coupled with a coupling delay less than the cavity round-trip time. We study synchronization between the two lasers in the experiment and in a delay differential equation model of the system. Because the lasers are internally perturbed by spontaneous emission, we include a noise source in the model to obtain stochastic realizations of the deterministic equations. Both amplitude synchronization and phase synchronization are considered. We use the Hilbert transform to define the phase variable and compute phase synchronization. We find that synchronization increases with coupling strength in the experiment and the model. When the time series from two lasers are time-shifted in either direction by the delay time, approximately equal synchronization is frequently observed, so that a clear leader and follower cannot be identified. We define an algorithm to determine which laser leads the other when the synchronization is sufficiently different with one direction of time shift, and statistics of switches in leader and follower are studied. The frequency of switching between leader and follower increases with coupling strength, as might be expected since the lasers mutually influence each other more effectively with stronger coupling.

show abstract

mentioning

confidence: 99%

Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers

Shaw

Schwartz

Rogers

et al. 2006

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…the slave "anticipates" by an amount τ the output of the master. This regime and its stability has been theoretically studied in several systems, from the simplest ones described by linear differential equations and maps where the mathematical details can be fully worked out [4,5], to the more complicated ones such as semiconductor lasers [6] operating in the chaotic regime. Experimental evidence of anticipating synchronization has been shown in Chua circuits [7] and in semiconductor lasers with optical feedback [8].…”

mentioning

confidence: 99%

Dynamical Mechanism of Anticipating Synchronization in Excitable Systems

et al. 2004

View full text Add to dashboard Cite

We analyze the phenomenon of anticipating synchronization of two excitable systems with unidirectional delayed coupling which are subject to the same external forcing. We demonstrate for different paradigms of excitable system that, due to the coupling, the excitability threshold for the slave system is always lower than that for the master. As a consequence the two systems respond to a common external forcing with different response times. This allows to explain in a simple way the mechanism behind the phenomenon of anticipating synchronization.The synchronization of nonlinear dynamical systems is a phenomenon common to many fields of science ranging from biology to physics [1], and it has been an active research subject since the work by Huygens in 1665. Recently, the synchronization of chaotic systems in a unidirectional coupling configuration has attracted a great interest due to its potential applications to secure communication systems [2]. Particular attention has been payed to the so-called anticipating synchronization regime, an idea first proposed by Voss in [3]. He showed that, in some parameter regions, two identical chaotic systems can be synchronized by unidirectional delayed coupling in such a manner that the "slave" (the system with coupling) anticipates the "master" (the one without coupling). More specifically, the coupling scheme proposed in [3] for the dynamics of the master, x(t), and slave, y(t) is the following:where y τ ≡ y(t − τ ). For appropriate values of the delay time τ and coupling strength K, the basic result is that y(t) ≈ x(t+τ ), i.e. the slave "anticipates" by an amount τ the output of the master. This regime and its stability has been theoretically studied in several systems, from the simplest ones described by linear differential equations and maps where the mathematical details can be fully worked out [4,5], to the more complicated ones such as semiconductor lasers [6] operating in the chaotic regime. Experimental evidence of anticipating synchronization has been shown in Chua circuits [7] and in semiconductor lasers with optical feedback [8].This same phenomenon has recently been shown to occur also when the dynamics, instead of chaotic, is excitable. In refs.[9] the effects of unidirectional delayed coupling between two identical excitable systems was studied for both the FitzHugh-Nagumo [10] and Hodgkin-Huxley [11] models. It was shown that, when both systems are excited by the same noise, and for a certain range of coupling parameters, the randomly distributed pulses of the master are preceded by those of the slave. This allows for predicting the occurrence of excitable pulses in the master. Since many biological systems (as neurons and heart cells) exhibit excitable behavior and they often operate in feedback regime in a noisy environment, the study of the delayed coupling effects in a presence of noise is certainly of wide concern.The anticipating synchronization regime has been often described as a rather counterintuitive phenomenon because of the possibility of the s...

show abstract

Section: Abstract: Semiconductor Lasers Instabilities Chaosmentioning

confidence: 99%

“…This is no longer true when coupling semiconductor lasers: the delay becomes an essential parameter. This feature, together with the phase-amplitude coupling characteristic of semiconductor lasers, is critical in experiments on synchronized chaos and results in a spontaneous symmetry breaking which appears as a time lag between the dynamics of two identical lasers [2][3][4][5][6].It was also shown that an asymmetry in the lasers forms a leading/lagging configuration where the leading laser synchronizes the lagging one, but not the converse [3]. Another property of mutually coupled semiconductor lasers is localized synchronization, where one of the lasers exhibits large amplitude oscillations whereas the other laser exhibits small amplitude oscillations.…”

mentioning

confidence: 99%

Semiconductor lasers coupled face-to-face

Viktorov¹,

Yacomotti²,

Mandel³

2004

J. Opt. B: Quantum Semiclass. Opt.

View full text Add to dashboard Cite

We show that for a large coupling time, semiconductor lasers coupled face-to-face exhibit a fast dynamics and a slow stairs-like periodic modulation. The effect can be explained by the nonlinear response of semiconductor lasers to external injection and a breakup of subnanosecond synchronization. Keywords: semiconductor lasers, instabilities, chaosCoupled lasers have attracted attention in recent years because they can exhibit dynamical effects useful to a wide range of problems. Experimental results on the dynamics of mutually coupled lasers were first reported for solidstate lasers [1]. The timescales over which the relaxation mechanisms operate in solid-state lasers are such that, in general, the delay induced by the field propagation between the two lasers is negligible. This is no longer true when coupling semiconductor lasers: the delay becomes an essential parameter. This feature, together with the phase-amplitude coupling characteristic of semiconductor lasers, is critical in experiments on synchronized chaos and results in a spontaneous symmetry breaking which appears as a time lag between the dynamics of two identical lasers [2][3][4][5][6].It was also shown that an asymmetry in the lasers forms a leading/lagging configuration where the leading laser synchronizes the lagging one, but not the converse [3]. Another property of mutually coupled semiconductor lasers is localized synchronization, where one of the lasers exhibits large amplitude oscillations whereas the other laser exhibits small amplitude oscillations. This effect was predicted for nearly identical solid-state lasers [7]. Experiments with two semiconductor lasers showed that even when the lasers are pumped at different levels and the lower-pumped laser drives the other laser, localized synchronization occurs and leads to relaxation at the same frequency in both lasers but with different amplitudes [8].In this letter, we report on a specific dynamical scenario for two semiconductor lasers coupled face-to-face, if the coupling time is greater than the coherence time of the lasers output.We show that, due to the nonlinear response of semiconductor lasers to external injection, there is a regime where the output of each laser is a staircase, each step having a duration equal to twice the coupling time, followed by an abrupt drop-off. This pattern can be periodic or chaotic. There are periodic solutions with different numbers of stairs: in this letter, we focus on the regime with only two stairs, but states with up to seven stairs have been observed. Numerical results suggest that, if the delay is larger than the laser coherence time, the number of stairs as well as the nature of the dynamical stateperiodic or chaotic-is independent of the delay and therefore of the number of steady states.In our model two identical single mode semiconductor lasers (L 1 and L 2 ) are coupled in a face-to-face configuration: the output of each laser is injected into the other laser. We assume that there is no self-coupling caused by reflections from the f...

show abstract

Anticipation in the Synchronization of Chaotic Semiconductor Lasers with Optical Feedback

Cited by 315 publications

References 34 publications

Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers

Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers

Dynamical Mechanism of Anticipating Synchronization in Excitable Systems

Semiconductor lasers coupled face-to-face

Contact Info

Product

Resources

About