We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an elect... more We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electrooptic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator ͑DPSK-d͒. The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations ͑approximately half of the DPSK-d free spectral range͒, as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup.
The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering ... more The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering feedback is studied experimentally, numerically, and analytically. The oscillator loop is characterized by a high cutoff frequency with a response time ϳ 10 ps and by a low cutoff frequency with a response time ϳ 1 s. Moreover, the optoelectronic feedback also consists of a significant delay D of the order of 100 ns. Depending on two key physical parameters, the loop gain  and the nonlinearity operating point ⌽, a large variety of multiple time scale regimes are reported, including slow or fast periodic oscillations with different waveforms, regular or chaotic breathers, slow time envelope dynamics, complex and irregular self-pulsing, and fully developed chaos. Many of these regimes are exhibiting new features that are absent in the classical first-order scalar nonlinear delay differential equations ͑DDEs͒, which differ in the modeling by the low cutoff only. Nearly all kinds of solutions are recovered numerically by a new class of integro-DDE ͑iDDE͒ that take into account both the high and low cutoff frequencies of the feedback loop. For moderate feedback gain, asymptotic solutions are determined analytically by taking advantage of the relative values of the time constants , , and D. We confirm the experimental observation of two distinct routes to oscillatory instabilities depending on the value of ⌽. One route is reminiscent of the square wave oscillations of the classical first-order DDE, but the other route is quite different and allows richer wave forms. For higher feedback gain, these two distinct regimes merge leading to complex nonperiodic regimes that still need to be explored analytically and numerically. Finally, we investigate the theoretical limits of our iDDE model by experimentally exploring phenomena at extreme physical parameter setting, namely, high-frequency locking at strong feedback gain or pulse packages for very large delays. The large variety of oscillatory regimes of our broadband bandpass delay electrooptic oscillator is attractive for applications requiring rich optical pulse sources with different frequencies and/or wave forms ͑chaos-based communications, random number generation, chaos computing, and generation of stable multiple GHz frequency oscillations͒.
Chaotic wavelength transmitters based on a DBR laser submitted to optoelectronic feedback with pe... more Chaotic wavelength transmitters based on a DBR laser submitted to optoelectronic feedback with periodic time delay are considered. We investigate the retrieval of the periodic time delay function from experimental time series. Square-wave and sinusoidal modulations are considered for the frequency clock of a delay module based on a First-In First-Out memory. It is shown that the period of the
HAL (Le Centre pour la Communication Scientifique Directe), 2009
Nous présentons dans cet article une nouvelle architecture optoélectronique pour la génération de... more Nous présentons dans cet article une nouvelle architecture optoélectronique pour la génération de chaos en intensité. Le principe s'appuie sur une dynamiqueélectro-optique non linéaireà retard, dont la non linéarité est construite grâceà un interféromètreà 4 onde réalisé en optique intégrée, et disposant de 2électrodes de modulation indépendantes. Le montage permet de disposer d'une part, d'une dynamique ultra-rapide jusqu'à des fréquences de plusieurs GHz, et d'autre part, de générer un chaos de grande dimension destiné au cryptage physique de données optiques. Au travers d'uneétude numérique et expérimentale, nous avons cherchéà analyser certains des nombreux comportements dynamiques que peut présenter cet oscillateur, en fonction de divers paramètres physiques du montage : régimes de point fixes stables, périodiques, et chaotiques. La mise en oeuvre du montage expérimental a permis de valider le modèle théorique adopté pour les simulations.
... S. Ortin('), M. Jacquo{2), L. Pesquera('), M. Peil(2),L. Larger(2 ... [I]A. Argyris... more ... S. Ortin('), M. Jacquo{2), L. Pesquera('), M. Peil(2),L. Larger(2 ... [I]A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J.Garcia ... and H. Porte, Optical cryptosystem based on synchronization ofhyperchaos generated by a delayedfeedback tunable laser diode, Phys ...
HAL (Le Centre pour la Communication Scientifique Directe), Dec 3, 2007
In this work we show that the nonlinear dynamics of the chaotic carrier can be reconstructed from... more In this work we show that the nonlinear dynamics of the chaotic carrier can be reconstructed from experimental data. Then it is possible to extract the message by using the nonlinear model as a receiver. The transmitter consists of a DBR laser with a feedback loop formed by a delay line and an optical device with a nonlinearity in wavelength. The first step to extract the nonlinear dynamics is the estimation of the delay time T. Then a new type of modular neural network (NN) is used to obtain the transmitter nonlinear dynamics. It is checked using chaotic synchronization that the NN describes correctly the transmitter nonlinear dynamics, although it is a high dimensional system.
We present measurements of the linewidth enhancement factor of a distributed feedback quantum cas... more We present measurements of the linewidth enhancement factor of a distributed feedback quantum cascade laser (DFB-QCL) using the so-called self-mixing technique. The linewidth enhancement factor is investigated by analyzing optical feedback induced changes of the emission properties of the laser. We will demonstrate that our self-mixing setup works well with QCLs in the mid infrared wavelength regime, and that it is possible to use the obtained signal to extract the linewidth enhancement factor. We present a setup that records the self-mixing signal with the voltage signal across the laser device using the laser as a detector itself. In this contribution we will show the advantages of this measurement technique. First measurements of the linewidth enhancement factor yield values that rise from 0.24 to 2.6 with an increase of the injection current of the QCL. We will discuss the influence of the injection current on the linewidth enhancement factor.
We demonstrate the influence of vectorial coupling on the synchronization behavior of complex sys... more We demonstrate the influence of vectorial coupling on the synchronization behavior of complex systems. We study two semiconductor lasers subject to delayed optical feedback which are unidirectionally coherently coupled via their optical fields. Our experimental and numerical results demonstrate a characteristic synchronization scenario in dependence on the relative feedback phase leading cyclically from chaos synchronization to almost uncorrelated states, and back to chaos synchronization. Finally, we reveal the influence of the feedback phase on the dynamics of the solitary delay system.
HAL (Le Centre pour la Communication Scientifique Directe), Dec 8, 2009
A novel electro-optic nonlinear delay architecture is presented, which is combining optical phase... more A novel electro-optic nonlinear delay architecture is presented, which is combining optical phase modulation, differential phase shift keying demodulators of standard DPSK optical communication techniques, and the dynamical principles of the Ikeda ring cavity. Fast, reliable, highly complex, and controlable chaos can be generated. Especially designed for high speed chaos communications, the set-up demonstrated for the first time the capability of 10Gb/s transmission, over an installed metropolitan network of more than 100km. The flexibility of the setup will be also emphasized in order to improve the security of this physical layer encryption.
Les oscillateurs chaotiques optoélectroniques développés pour les communications par chaos [1] ha... more Les oscillateurs chaotiques optoélectroniques développés pour les communications par chaos [1] haut débit présentent intrinsèquement au moins 3échelles de temps caractéristiques, qui s'étalent sur plus de 6 ordres de grandeurs (de quelques 10 psà quelques 10 µs). Pour des valeurs modérées du gain de la boucle d'oscillation (avant d'atteindre les régimes chaotiques utilisés en communications par chaos), des régimes dynamiques complexes révèlant chacune de seséchelles, ontété observés expérimentalement [2] ; ceux-ci sont formés par une enveloppe presque périodique très lente, comprenant des oscillations quasi-rectangulaires rapides, suivi de régimes chaotiques entièrement développés et ultra-rapides. La modélisation du montage expérimental fait appelà un processus diffférentiel linéaire correspondantà un filtre passe-bande, et soumisà une excitation non linéaire retardée de la variable dynamique [3]. Sur la base d'un tel modèle dynamique non linéaireà retard, prenant en compte un terme intégral inhabituel en plus du terme différentiel, des formes d'onde similaires peuventêtre obtenues numériquement, si l'on prend soin de supprimer des transitoires extrêmement longs. La communication proposée expose les résultats expérimentaux obtenus en termes de formes d'onde temporelle, de transformées en ondelettes, et de spectres de Fourier. Les résultats seront comparés aux solutions numériques, et dans le cas très simple des régimes périodiques, une interprétation analytique de la solutionàéchelle de temps multiple sera proposée.
We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an elect... more We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electrooptic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator ͑DPSK-d͒. The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations ͑approximately half of the DPSK-d free spectral range͒, as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup.
The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering ... more The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering feedback is studied experimentally, numerically, and analytically. The oscillator loop is characterized by a high cutoff frequency with a response time ϳ 10 ps and by a low cutoff frequency with a response time ϳ 1 s. Moreover, the optoelectronic feedback also consists of a significant delay D of the order of 100 ns. Depending on two key physical parameters, the loop gain  and the nonlinearity operating point ⌽, a large variety of multiple time scale regimes are reported, including slow or fast periodic oscillations with different waveforms, regular or chaotic breathers, slow time envelope dynamics, complex and irregular self-pulsing, and fully developed chaos. Many of these regimes are exhibiting new features that are absent in the classical first-order scalar nonlinear delay differential equations ͑DDEs͒, which differ in the modeling by the low cutoff only. Nearly all kinds of solutions are recovered numerically by a new class of integro-DDE ͑iDDE͒ that take into account both the high and low cutoff frequencies of the feedback loop. For moderate feedback gain, asymptotic solutions are determined analytically by taking advantage of the relative values of the time constants , , and D. We confirm the experimental observation of two distinct routes to oscillatory instabilities depending on the value of ⌽. One route is reminiscent of the square wave oscillations of the classical first-order DDE, but the other route is quite different and allows richer wave forms. For higher feedback gain, these two distinct regimes merge leading to complex nonperiodic regimes that still need to be explored analytically and numerically. Finally, we investigate the theoretical limits of our iDDE model by experimentally exploring phenomena at extreme physical parameter setting, namely, high-frequency locking at strong feedback gain or pulse packages for very large delays. The large variety of oscillatory regimes of our broadband bandpass delay electrooptic oscillator is attractive for applications requiring rich optical pulse sources with different frequencies and/or wave forms ͑chaos-based communications, random number generation, chaos computing, and generation of stable multiple GHz frequency oscillations͒.
Chaotic wavelength transmitters based on a DBR laser submitted to optoelectronic feedback with pe... more Chaotic wavelength transmitters based on a DBR laser submitted to optoelectronic feedback with periodic time delay are considered. We investigate the retrieval of the periodic time delay function from experimental time series. Square-wave and sinusoidal modulations are considered for the frequency clock of a delay module based on a First-In First-Out memory. It is shown that the period of the
HAL (Le Centre pour la Communication Scientifique Directe), 2009
Nous présentons dans cet article une nouvelle architecture optoélectronique pour la génération de... more Nous présentons dans cet article une nouvelle architecture optoélectronique pour la génération de chaos en intensité. Le principe s'appuie sur une dynamiqueélectro-optique non linéaireà retard, dont la non linéarité est construite grâceà un interféromètreà 4 onde réalisé en optique intégrée, et disposant de 2électrodes de modulation indépendantes. Le montage permet de disposer d'une part, d'une dynamique ultra-rapide jusqu'à des fréquences de plusieurs GHz, et d'autre part, de générer un chaos de grande dimension destiné au cryptage physique de données optiques. Au travers d'uneétude numérique et expérimentale, nous avons cherchéà analyser certains des nombreux comportements dynamiques que peut présenter cet oscillateur, en fonction de divers paramètres physiques du montage : régimes de point fixes stables, périodiques, et chaotiques. La mise en oeuvre du montage expérimental a permis de valider le modèle théorique adopté pour les simulations.
... S. Ortin('), M. Jacquo{2), L. Pesquera('), M. Peil(2),L. Larger(2 ... [I]A. Argyris... more ... S. Ortin('), M. Jacquo{2), L. Pesquera('), M. Peil(2),L. Larger(2 ... [I]A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J.Garcia ... and H. Porte, Optical cryptosystem based on synchronization ofhyperchaos generated by a delayedfeedback tunable laser diode, Phys ...
HAL (Le Centre pour la Communication Scientifique Directe), Dec 3, 2007
In this work we show that the nonlinear dynamics of the chaotic carrier can be reconstructed from... more In this work we show that the nonlinear dynamics of the chaotic carrier can be reconstructed from experimental data. Then it is possible to extract the message by using the nonlinear model as a receiver. The transmitter consists of a DBR laser with a feedback loop formed by a delay line and an optical device with a nonlinearity in wavelength. The first step to extract the nonlinear dynamics is the estimation of the delay time T. Then a new type of modular neural network (NN) is used to obtain the transmitter nonlinear dynamics. It is checked using chaotic synchronization that the NN describes correctly the transmitter nonlinear dynamics, although it is a high dimensional system.
We present measurements of the linewidth enhancement factor of a distributed feedback quantum cas... more We present measurements of the linewidth enhancement factor of a distributed feedback quantum cascade laser (DFB-QCL) using the so-called self-mixing technique. The linewidth enhancement factor is investigated by analyzing optical feedback induced changes of the emission properties of the laser. We will demonstrate that our self-mixing setup works well with QCLs in the mid infrared wavelength regime, and that it is possible to use the obtained signal to extract the linewidth enhancement factor. We present a setup that records the self-mixing signal with the voltage signal across the laser device using the laser as a detector itself. In this contribution we will show the advantages of this measurement technique. First measurements of the linewidth enhancement factor yield values that rise from 0.24 to 2.6 with an increase of the injection current of the QCL. We will discuss the influence of the injection current on the linewidth enhancement factor.
We demonstrate the influence of vectorial coupling on the synchronization behavior of complex sys... more We demonstrate the influence of vectorial coupling on the synchronization behavior of complex systems. We study two semiconductor lasers subject to delayed optical feedback which are unidirectionally coherently coupled via their optical fields. Our experimental and numerical results demonstrate a characteristic synchronization scenario in dependence on the relative feedback phase leading cyclically from chaos synchronization to almost uncorrelated states, and back to chaos synchronization. Finally, we reveal the influence of the feedback phase on the dynamics of the solitary delay system.
HAL (Le Centre pour la Communication Scientifique Directe), Dec 8, 2009
A novel electro-optic nonlinear delay architecture is presented, which is combining optical phase... more A novel electro-optic nonlinear delay architecture is presented, which is combining optical phase modulation, differential phase shift keying demodulators of standard DPSK optical communication techniques, and the dynamical principles of the Ikeda ring cavity. Fast, reliable, highly complex, and controlable chaos can be generated. Especially designed for high speed chaos communications, the set-up demonstrated for the first time the capability of 10Gb/s transmission, over an installed metropolitan network of more than 100km. The flexibility of the setup will be also emphasized in order to improve the security of this physical layer encryption.
Les oscillateurs chaotiques optoélectroniques développés pour les communications par chaos [1] ha... more Les oscillateurs chaotiques optoélectroniques développés pour les communications par chaos [1] haut débit présentent intrinsèquement au moins 3échelles de temps caractéristiques, qui s'étalent sur plus de 6 ordres de grandeurs (de quelques 10 psà quelques 10 µs). Pour des valeurs modérées du gain de la boucle d'oscillation (avant d'atteindre les régimes chaotiques utilisés en communications par chaos), des régimes dynamiques complexes révèlant chacune de seséchelles, ontété observés expérimentalement [2] ; ceux-ci sont formés par une enveloppe presque périodique très lente, comprenant des oscillations quasi-rectangulaires rapides, suivi de régimes chaotiques entièrement développés et ultra-rapides. La modélisation du montage expérimental fait appelà un processus diffférentiel linéaire correspondantà un filtre passe-bande, et soumisà une excitation non linéaire retardée de la variable dynamique [3]. Sur la base d'un tel modèle dynamique non linéaireà retard, prenant en compte un terme intégral inhabituel en plus du terme différentiel, des formes d'onde similaires peuventêtre obtenues numériquement, si l'on prend soin de supprimer des transitoires extrêmement longs. La communication proposée expose les résultats expérimentaux obtenus en termes de formes d'onde temporelle, de transformées en ondelettes, et de spectres de Fourier. Les résultats seront comparés aux solutions numériques, et dans le cas très simple des régimes périodiques, une interprétation analytique de la solutionàéchelle de temps multiple sera proposée.
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