Synchronization of Mutually Coupled Chaotic Lasers in the Presence of a Shutter

Abstract

Two mutually coupled chaotic diode lasers exhibit stable isochronal synchronization in the presence of self feedback. When the mutual communication between the lasers is discontinued by a shutter and the two uncoupled lasers are subject to self-feedback only, the desynchronization time is found to scale as A d τ where A d > 1 and τ corresponds to the optical distance between the lasers. Prior to synchronization, when the two lasers are uncorrelated and the shutter between them is opened, the synchronization time is found to be much shorter, though still proportional to τ . As a consequence of these results, the synchronization is not significantly altered if the shutter is opend/closed faster than the desynchronization time. Experiments in which the coupling between two chaotic-synchronized diode lasers is modulated with an electro-optic shutter are found to be consistent with the results of numerical simulations.PACS numbers: 05.45. Vx, 42.65.Sf, 42.55.Px Chaotic systems are characterized by an irregular motion which is sensitive to initial conditions and tiny perturbations. Nevertheless, two chaotic systems can synchronize their irregular motion when they are coupled [1]. When the coupling is switched off, any tiny perturbation drives the two trajectories apart. The separation is exponentially fast, and it is described by the largest Lyapunov exponents of a single system.In this Letter we show that the trajectory dynamics of coupled chaotic systems which also poses time-delayed self-feedback, is different. In a system with self-feedback, which has also been investigated in the context of secure communication with chaotic lasers [2], the time scale for the separation of the trajectories is found to be much longer than the coupling time. On the other hand, when the coupling is switched on, resynchronization occurs on a faster time scale. We investigate this phenomenon numerically and show first experiments which support our numerical simulations. The demonstrated difference between de-and re-synchronization can be used to improve the security of public-channel communication with chaotic lasers [2].Semiconductor (diode) lasers subjected to delayed optical feedback are known to displays chaotic oscillations. Two coupled semiconductor lasers exhibit chaos synchronization. Different coupling setups such as unidirectional or mutual coupling and variations of the strength of the self and coupling feedback result in different synchronization states: the two lasers can synchronize in a leaderlaggard or anticipated mode [3,4], as well as in two different synchronization states; achronal synchronization in which the lasers assume a fluctuating leading role, or isochronal synchronization where there is no time delay between the two lasers' chaotic signals [2,5,6,7,8].In this Letter we focus on a symmetric setup, the time delay between the lasers is denoted by τ c and the time delay of the self-feedback is denoted by τ d . In the event of τ c = τ d = τ and for a wide range of the mutual coupling strength, σ, and the stre...

Loss Enhanced Phase Locking in Coupled Oscillators

“…Phase locking plays an important role in many coupled ensembles, such as population of chemical oscillators with mutual coherence [1], array of Josephson junctions that are frequency locked [2], coupled laser oscillators that are exploited for synchronization and manipulation of output phase [3][4][5][6][7], and coherence phase dynamics of coupled oscillators [8]. In these, phase locking is possible only by exceeding a threshold of relatively high coupling strength.…”

Spiking optical patterns and synchronization

“…Using optical feedback, configurations consisting of unidirectional [7,8] or mutual coupling [5,6,8,9,10,11] and variations of the strength of the self and coupling feedback have been shown to result in different synchronization states. The lasers can synchronize in a leader-laggard or anticipated mode, as well as in two different synchronization states; achronal or generalized synchronization [12,13,14] where the cross correlation is time shifted by the feedback delay time but neither laser acts as a preferred leader or laggard, or isochronal synchronization (zero-lag) where there is no time delay between the two lasers' chaotic signals [5,6,15,16,17].Zero-lag synchronization of lasers was recently extended to a cluster consisting of three semiconductor lasers, mutually coupled along a line, in such a way that the central laser element acts as a relay of the dynamics between the outer elements [18,19]. The zero-lag synchronized dynamics of remotely located chaotic signal sources has sparked an interest in such systems in part because they have features also seen in biological and neural transmission networks.…”

Scaling behavior of oscillations arising in delay-coupled optoelectronic oscillators

“…These time delays can induce many new phenomena and complex dynamics. This is the case, for example, in neuronal networks [2,3], biological oscillators [4], or coupled optical systems [5][6][7][8][9][10][11][12][13][14][15], and even for a single optical system, the introduction of time-delayed feedback can lead to extremely rich dynamics [16][17][18][19].…”

“…A main focus of recent work has been the question of when cross-coupled delay systems exhibit isochronal chaos synchronization under symmetric coupling and operating conditions [15,22,23]. Examples of experimental systems that have been used to study this issue are semiconductor lasers with optical [6,7,14] and optoelectronic [8] coupling, fiber-ring lasers with optical coupling [12,24], MZM nonlinearities with shared feedback [13], and MZM nonlinearities with discrete-time implementation [25]. In addition, scaling laws of periodic oscillations arising under asymmetric coupling conditions have been studied for cross-coupled semiconductor lasers linked optoelectronically [9,10].…”