Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback

Rontani, Damien; Locquet, Alexandre; Sciamanna, Marc; Citrin, D. S.

doi:10.1364/ol.32.002960

Cited by 203 publications

(114 citation statements)

References 2 publications

(2 reference statements)

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“…It has been shown to be possible to extract the time-delay from the laser dynamics 97 and hence measures are needed to counteract such a breach of security. Several means for concealling the time-delay value are available : setting the time-delay close to the time-period of the relaxation oscillations 98 , using more than one time-delayed feedback 99 , using stochastically varying or modulated time-delay values in the feedback loop 94 , or exploiting the polarization properties of VCSELs 99 . Optimization of chaos communication parameters also benefits from recent investigations of complexity measures from experimental time-series [100][101][102] .…”

Section: Optimised Communications and Transmission Securitymentioning

confidence: 99%

Physics and applications of laser diode chaos

Sciamanna¹,

Shore²

2015

Nature Photon

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577

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: Optimised Communications and Transmission Securitymentioning

confidence: 99%

Physics and applications of laser diode chaos

Sciamanna¹,

Shore²

2015

Nature Photon

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577

327

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“…Today applications of laser diodes such as secure communications [21][22][23] and random number generation 24,25 make use of high-dimensional chaos obtained from time-delayed optical feedback. The chaos however shows correlation at the time-delay [26][27][28] , hence making it easy to reconstruct the attractor in a low dimensional phase space and therefore reducing both security and randomness. The polarization chaos reported here is of low-dimension but (1) is obtained from a free-running device, i.e.…”

Section: Figure 1: Experimental Observations Showing Chaotic Polarizamentioning

confidence: 99%

Deterministic polarization chaos from a laser diode

et al. 2012

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Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect -i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single-and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.The discovery of deterministic chaos -i.e. the aperiodic deterministic dynamics of a nonlinear system showing sensitivity to initial conditions -has been a major paradigm shift overthrowing two centuries of Laplacian viewpoint of dynamical systems [1][2][3][4][5] . Looking into a system behavior with the use of chaos theory has helped to interpret and control many of such ordered or disordered behaviors in our present day life, such as the bifurcations leading to epilepsy and cancer 6 , the stabilization of cardiac arrhythmias 7 , and the improvement of complex behavioral patterns in robotics 8 .Soon after the invention of the laser, the possibility to observe light chaos raised attention. In 1975, Haken discovered an analogy between the Maxwell-Bloch equations for lasers and the Lorenz equations showing chaos 9 . The Maxwell-Bloch equations are three equations for the field E, the polarization P and the carrier inversion N, each with its own relaxation time. However, while in Lorenz equations the relaxation times of the dynamical variables are of similar order of magnitude, they may take very different values in lasers. If one variable relaxes much faster than the others, this variable is adiabatically eliminated, hence resulting in a reduced number of dynamical equations. Therefore, so-called class A (ex: He-Ne, Ar and Dye), class B (ex: Nd:YAG, CO2 and semiconductor) or class C (ex: NH3) lasers have dynamics governed either by a single equation for the field, two equations for the field and population inversion or the full set of equations, respectively. In class A or class B laser systems chaos cannot be observed unless one adds one or several independent control parameters 10 . Chaos has then been reported in, for example, free-running NH3 lasers 11 , He-Ne lasers with modulation of the external field 12 , CO2

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“…Additionally, the resonance of the external feedback cavity excites many external-cavity modes (ECMs) in the laser field and leads to a periodically modulated spectrum similar to that of a frequency comb with a spacing equal to the reciprocal of the feedback delay [9,10]. Considerable effort has recently been devoted to expand the power spectrum [8,11] or to depress the external-cavity resonances [12], but it is difficult to completely eliminate the effects of the intrinsic oscillations [3,13]. These intrinsic oscillations impose restrictions on random number generation from physical chaos [10] and raise arguments that the extracted numbers are not truly random [14].…”

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confidence: 99%

Optical Heterodyne Generation of High-Dimensional and Broadband White Chaos

Wang¹,

Wang²,

Li³

et al. 2015

IEEE J. Select. Topics Quantum Electron.

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Physical chaos is a fascinating prospect for high-speed data security by serving as a masking carrier or a key source, but suffers from a colored spectrum that divulges system's intrinsic oscillations and degrades randomness. Here, we demonstrate that physical chaos with a white spectrum can be achieved by the optical heterodyning of two delayed-feedback lasers. A white chaotic spectrum with 1-dB fluctuation in a band of 11 GHz is experimentally obtained. The white chaos also has a perfect delta-like autocorrelation function and a high dimensionality of greater than 10, which makes chaos reconstruction extremely difficult and thus improves security. PACS numbers: 42.65. Sf, 05.45.Jn Macroscopic chaos in fast nonlinear optoelectronic or laser systems has motivated remarkable developments in information security. For instance, macroscopic chaos serving directly as a masking carrier improves the rate of secure communications to gigabits per second [1]. Additionally, fast chaos replaces microscopic noise as an entropy source to greatly increase the speed of generating physical random keys [2,3] and as a radar signal to enhance anti-jamming capability and spatial resolution [4,5]. One of the most important factors is that the physical chaos has a spread spectrum and an irregular waveform with larger amplitude than that of microscopic noise, and the use of chaos can avoid the wideband amplification required in a noise generator.Essentially, the randomness and security of chaos is vital to chaos-based information security. However, the randomness of physical chaos is usually degraded by intrinsic oscillations of nonlinear chaos systems. Currently, fast physical chaos generators typically consist of a nonlinear optical or optoelectronic device subject to a feedback loop that partially couples the output back into the device, such as an external-cavity semiconductor laser (ECL) [6] and an optoelectronic oscillator [7]. As a result, the intrinsic oscillations, including the characteristic response frequency of the nonlinear device and the resonance of the feedback loop, introduce deterministic features and periodicity into the chaos and thus limit the randomness. Taking the paradigm of a delay system, i.e., an ECL, as an example, the relaxation oscillation of the semiconductor laser dominates the laser intensity chaos and leads to a strong peak projecting from the power spectrum [8]. Additionally, the resonance of the external feedback cavity excites many external-cavity modes (ECMs) in the laser field and leads to a periodically modulated spectrum similar to that of a frequency comb with a spacing equal to the reciprocal of the feedback delay [9,10]. Considerable effort has recently been devoted to expand the power spectrum [8,11] or to depress the external-cavity resonances [12], but it is difficult to completely eliminate the effects of the intrinsic oscillations [3,13]. These intrinsic oscillations impose restrictions on random number generation from physical chaos [10] and raise arguments that the extracted number...

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Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback

Cited by 203 publications

References 2 publications

Physics and applications of laser diode chaos

Physics and applications of laser diode chaos

Deterministic polarization chaos from a laser diode

Optical Heterodyne Generation of High-Dimensional and Broadband White Chaos

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