Synchronization of feedback-induced chaos in semiconductor lasers by optical injection

Murakami, Atsushi; Ohtsubo, Junji

doi:10.1103/physreva.65.033826

Cited by 85 publications

(47 citation statements)

References 31 publications

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“…Adjustment of both the strength of optical coupling and the frequency detuning between the two laser diodes has been shown to affect the synchronization between the lasers 73,74 . Mapping the synchronization quality in the plane of the coupling parameters unveils two regions of different synchronization properties 75 ( Figure 3c). For strong injection, synchronization occurs through nonlinear amplification of the slave laser and the corresponding parameter region is bounded by bifurcations delimiting injection locking in laser diode.…”

Section: Chaos Synchronisationmentioning

confidence: 98%

“…Increasing the bandwidth of chaos up to about 16.5 GHz 107 has enabled the use of a 12,5 GS/s sampling rate on the 6 LSB output of the digitized chaos, i.e. 75 Gb/s RNG. The same setup but using reverse bit order sequence in the time-shifted laser output before applying the XOR logical operation uses the full 8 bit ADC resolution at the maximum sampling rate (50 GS/s) hence achieving the current record of 400 Gb/s 111 .…”

Section: Random Number Generationmentioning

confidence: 99%

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Physics and applications of laser diode chaos

Sciamanna¹,

Shore²

2015

Nature Photon

598

327

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-An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.The emergence of irregular pulsations and dynamical instabilities from a laser were first noted in the very early stages of the laser development. Pulses whose amplitude "vary in an erratic manner" were reported in the output of the ruby solid-state laser 1 [ Fig. 1 a] and then found in numerical simulations 2 . However the lack of knowledge of what would later be termed "chaos" resulted in these initial observations being either left unexplained or wrongly attributed to noise.The situation changed in the late 1960s with the discovery of sensitivity to initial conditions by Lorenz 3 , later popularized as the "butterfly effect". As illustrated in Fig. 1 (b), numerical simulations of a deterministic model of only three nonlinear equations showed an irregular pulsing with a remarkable feature: the state variables evolve along very different trajectories despite starting from approximately the same initial values [ Fig. 1 b]. The distance δ(t) between nearby trajectories diverges exponentially : δ(t) = δ(0) exp(λt) provided that λ, the effective Lyapunov exponent of the dynamical system, is positive. Consequently such systems are unpredictable in the long term. Plotted in the x-y-z phase space of the state variables, the trajectories converge to an "attractor" which has the geometric property of being bounded in space despite the exponential divergence of nearby trajectories [ Fig. 1 c]. Such attractors are found to have a fractional dimension 4 and are thus termed strange. Aperiodicity, sensitive dependency to initial conditions and strangeness are commonly considered as the main properties for "chaos" The fields of laser physics and chaos theory developed independently until 1975 8 when Haken discovered a striking analogy between the Lorenz equations that model fluid convection and the MaxwellBloch equations modelling light-matter interaction in single-mode lasers. The nonlinear interaction between the wave propagation in the laser cavity (represented by the electric field E) and radiative recombination producing macroscopic polarization (encapsulated in the polarization P and carrier inversion N) yield similar dynamical instabilities to those found in the Lorenz equations. More specifically, in addition to the conventional laser threshold, Haken suggested a second threshold would exist above which "spiking occurs ...

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Section: Chaos Synchronisationmentioning

confidence: 98%

Section: Random Number Generationmentioning

confidence: 99%

Physics and applications of laser diode chaos

Sciamanna¹,

Shore²

2015

Nature Photon

598

327

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“…One of the simplest configurations considers a laser, usually called a drive laser (DL), injecting part of its light into another laser, usually called a response laser (RL) in a unidirectional way. If the DL operates in cw or in a periodic regime, while the RL operates in cw when uncoupled, the RL can, for instance, be locked in frequency to the DL (stable injection locking) or operate in a periodic, quasiperiodic, or even chaotic regime, depending on the coupling strength and the optical frequency detuning between both DL and RL (van Tartwijk and Locquet, Masoller, and Mirasso, 2002;Murakami and Ohtsubo, 2002). If the DL operates in a chaotic regime, that could be induced for instance by an external mirror or by an optoelectronic self-feedback as mentioned in Sec.…”

Section: B Unidirectional Couplingmentioning

confidence: 99%

Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

et al. 2013

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Complex phenomena in photonics, in particular, dynamical properties of semiconductor lasers due to delayed coupling, are reviewed. Although considered a nuisance for a long time, these phenomena now open interesting perspectives. Semiconductor laser systems represent excellent test beds for the study of nonlinear delay-coupled systems, which are of fundamental relevance in various areas. At the same time delay-coupled lasers provide opportunities for photonic applications. In this review an introduction into the properties of single and two delay-coupled lasers is followed by an extension to network motifs and small networks. A particular emphasis is put on emerging complex behavior, deterministic chaos, synchronization phenomena, and application of these properties that range from encrypted communication and fast random bit sequence generators to bioinspired information processing.

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“…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.…”

mentioning

confidence: 99%

Spiking optical patterns and synchronization

et al. 2007

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We analyze the time resolved spike statistics of a solitary and two mutually interacting chaotic semiconductor lasers whose chaos is characterized by apparently random, short intensity spikes. Repulsion between two successive spikes is observed, resulting in a refractory period which is largest at laser threshold. For time intervals between spikes greater than the refractory period, the distribution of the intervals follows a Poisson distribution. The spiking pattern is highly periodic over time windows corresponding to the optical length of the external cavity, with a slow change of the spiking pattern as time increases. When zero-lag synchronization between the two lasers is established, the statistics of the nearly perfectly matched spikes are not altered. The similarity of these features to those found in complex interacting neural networks, suggests the use of laser systems as simpler physical models for neural networks.PACS numbers: 05.45. Xt, 42.65.Sf, 42.55.Px Semiconductor lasers, subjected to optical feedback, display chaotic behavior [1]. The chaotic behavior consists of a very short and random spiking of the laser intensity with the time between spikes depending on how far above lasing threshold the laser is. Two chaotic lasers can be synchronized with each other and this has allowed them to be excellent candidates for novel broadband [2, 3, 4, 5, 6] communication devices. Different configurations, such as delayed optoelectronic [7,8] or coherent optical injection [8,9,10,11] have been used for synchronization of the two lasers. 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. Though the time scales for the two phenomena are vastly different; lasers spiking on 100 ps time scale while neurons spike on ms time scales, much of the dynamics and spiking statistics appear to have common behavior. Here we report on the spiking optical pattern of solitary and two mutually coupled chaotic lasers, observed on a time scale which resolves the individu...

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Synchronization of feedback-induced chaos in semiconductor lasers by optical injection

Cited by 85 publications

References 31 publications

Physics and applications of laser diode chaos

Physics and applications of laser diode chaos

Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

Spiking optical patterns and synchronization

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