Asymmetric dwell-time statistics of polarization chaos from free-running VCSEL

Virte, Martin; Mirisola, Elodie; Sciamanna, Marc; Panajotov, Krassimir

doi:10.1364/ol.40.001865

Cited by 15 publications

(23 citation statements)

References 16 publications

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“…The parameters are as follows: κ and γ are the field and carrier decay rates respectively, γ s is the spin flip relaxation rate, α is the linewidth enhancement factor, γ p and γ a are the phase and amplitude anisotropies respectively. For simplicity, no misalignment between amplitude and phase anisotropies is considered [3], [33], [34]. Unless stated otherwise, we use the same parameter values as in previous work [10], [35]: κ = 600 ns −1 , γ s = 100 ns −1 , γ a = −0.7 ns −1 , γ = 1 ns −1 and α = 3.…”

Section: Spin-flip Model and Parametersmentioning

confidence: 99%

Chaos-Preserving Reduction of the Spin-Flip Model for VCSELs: Failure of the Adiabatic Elimination of the Spin-Population Difference

Virte¹,

Ferranti²

2019

IEEE J. Select. Topics Quantum Electron.

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When studying the dynamics of Vertical-Cavity Surface-Emitting Lasers, and their polarization properties, the spin-flip model appears to be the simplest model qualitatively reproducing all dynamical features that have been observed experimentally. Nonetheless, because of the fast time-scale of the spin-relaxation processes, the specific role and the importance of the spin-population difference -which is one of the specific feature of the spin-flip model -has been continuously questioned. In fact, the debate regarding the possible adiabatic elimination of the spin-population remains fully open.In this paper, our goal is to bring new light into this issue by demonstrating that this variable is essential to preserve the most complex dynamical features predicted by the spin-flip model, such as polarization chaos, and, therefore, needs to be conserved. To do so, we first perform a detailed analysis, focusing on the chaotic dynamics, to determine the minimal embedding dimension for the spin-flip model. As the latter confirms that a reduction of the model could be envisaged, we then consider the adiabatic elimination of the spin-population difference to highlight and explain its failure to reproduce essential dynamical features obtained in the original model.

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Section: Spin-flip Model and Parametersmentioning

confidence: 99%

Chaos-Preserving Reduction of the Spin-Flip Model for VCSELs: Failure of the Adiabatic Elimination of the Spin-Population Difference

Virte¹,

Ferranti²

2019

IEEE J. Select. Topics Quantum Electron.

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“…In the original SFM framework, these two scrolls and two steady-states -along with all the other intermediate states that appears on the route to chaos -are perfectly symmetrical. But this is not completely accurate in practice as asymmetries can easily be observed experimentally 15,16 . Including an anisotropy misalignment therefore breaks the symmetry of the system, which allows to reproduce detailed features of the dynamical scenario and to ensure a higher level of generality.…”

Section: Theoretical Model Sfmmentioning

confidence: 99%

“…α is the linewidth enhancement factor and the injection current is represented by µ. Unless specified otherwise, we use the following parameter values which are similar to those used in previous works [15][16][17] : α = 3, κ = 600 ns −1 , γ = 1 ns −1 , γ s = 100 ns −1 , γ a = −0.7 ns −1 , θ = 0.05 rad. Although the chaotic dynamics appears using these values, it is important to emphasize that chaos is obtained in a large range of parameters and not only in a small region of the parameter space.…”

Section: Theoretical Model Sfmmentioning

confidence: 99%

Noise induced stabilization of chaotic free-running laser diode

Virte

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we investigate theoretically the stabilization of a free-running vertical-cavity surface-emitting laser exhibiting polarization chaos dynamics. We report the existence of a boundary isolating the chaotic attractor on one side and a steady-state on the other side, and identify the unstable periodic orbit playing the role of separatrix. In addition, we highlight a small range of parameters where the chaotic attractor passes through this boundary, and therefore where chaos only appears as a transient behaviour. Then, including the effect of spontaneous emission noise in the laser, we demonstrate that, for realistic levels of noise, the system is systematically pushed over the separating solution. As a result, we show that the chaotic dynamics cannot be sustained unless the steady-state on the other side of the separatrix becomes unstable. Finally, we link the stability of this steady-state to a small value of the birefringence in the laser cavity and discuss the significance of this result on future experimental work.Semiconductor lasers -or laser diodes -are small, efficient and cheap laser devices and therefore are widely used for industrial applications. To generate a chaotic output however, since they typically behave as damped oscillators, an external perturbation such as optical feedback or modulation is required 1 .But recently, it has been shown that some specific semiconductor laser structures -namely Vertical-Cavity Surface-Emitting lasers (VCSELs) -could generate chaotic polarization fluctuations without the need for an external forcing due to a competition between two modes in the laser cavity 2 . The specific dynamics of VCSELs has been studied intensively for more than 20 years 3-11 , and polarization chaos has only been observed once, recently and only in nanostructured devices. Yet the theoretical framework reproducing accurately the observed dynamics does not take the specificities of the nanostructures into account 5,6 , which therefore raises the question: why has this dynamics never been observed in standard, commercial VCSELs before? Here we provide some elements of answer to this question. We theoretically highlight the existence of a separatrix between the chaotic dynamics and a steady-state, and demonstrate that the noise easily pushes the system over this boundary which therefore suppresses the chaotic dynamics. Moreover, we show that this mechanism appears for a large range of parameters, and in particular when the birefringence of the laser cavity is small. Finally, we discuss the relevance of this result by comparing available experimental data between chaotic and stable devices, and show that the chaos suppression mechanism described here is coherent with experimental reports.

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“…We can clearly observe a strong gap between the two set of data as a difference of about 2 orders of magnitude is recorded between the residence times of the two levels. Strong fluctuations are also observed but, again, the trend is clear and suggests an asymmetrical behavior as analyzed in [140]. Finally, in the last plot we show the number of jumps versus injection current, which is the number of jumps in the recorded time-series.…”

Section: Time-series and Random Like-hoppingmentioning

confidence: 57%

“…In QD-VCSELs, the two EP states have a strong ellipticity and are typically symmetrical with respect to the polarization direction of the laser eigenmodes, as schematically illustrated in Figure 5.20b. Small asymmetries between EP state 1 (EP1) and EP state 2 (EP2) have already been reported, but were deduced either from asymmetries in the residence time statistics [140] or from the appearance of dynamical bistability [137], since no significant asymmetries could be realized between the polarization orientation of the two EP states. Consequently, the largest amplitude for the random-like hopping is always obtained for projection at 45° of the polarization direction at threshold [138].…”

Section: Orientation Of the Polarization Modesmentioning

confidence: 99%

Next generation access networks: flexible OCDMA systems and cost-effective chaotic VCSEL sources for secure communications

Raddo¹

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Firstly, I would like to thank God for everything in life. I would like to thank my parents, Roberto Raddo and Abgail Raddo as well as my girlfriend Anne-Sophie for their constant support, love, encouragement, and total understanding during my long doctoral journey. I would like to thank Ben-Hur V. Borges, Heidi Ottevaere, Idelfonso T. Monroy, and Martin Virte for their contributions to my doctoral research as my academic advisors. I am grateful for their continuous guidance during this long and challenging path, for their helpfulness, confidence, and advice. Special thanks go to Hugo Thienpont and Heidi Ottevaere for the unique offered opportunity to develop part of the doctoral research in Brussels at B-PHOT. I would like to express my gratitude to my great friends: Israel Lot (thanks also for the book's cover), Larissa Lima (thanks also for helping me out so many times),

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Asymmetric dwell-time statistics of polarization chaos from free-running VCSEL

Cited by 15 publications

References 16 publications

Chaos-Preserving Reduction of the Spin-Flip Model for VCSELs: Failure of the Adiabatic Elimination of the Spin-Population Difference

Chaos-Preserving Reduction of the Spin-Flip Model for VCSELs: Failure of the Adiabatic Elimination of the Spin-Population Difference

Noise induced stabilization of chaotic free-running laser diode

Next generation access networks: flexible OCDMA systems and cost-effective chaotic VCSEL sources for secure communications

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