Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers

Virte, Martin; Panajotov, Krassimir; Sciamanna, Marc

doi:10.1103/physreva.87.013834

Cited by 38 publications

(57 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Normally in this region one would obtain time-periodic solutions (i.e. Hopf bifurcations) (see [24,27] for the case of P = 0). However, analytical results are currently lacking that may help understand the insight of the system for potential applications, such as information coding.…”

Section: Discussionmentioning

confidence: 99%

“…The only stability analysis to have been reported (to our knowledge) is for the case of LP pumping where the SFM equations can be studied by perturbing around the LP modes [8,9,[18][19][20][21][22][23][24][25][26][27]. The stability analysis of the LP solutions provides a system of equations that decouple (in the linear approximation) into two subsets, each of three coupled equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spin-flip model of spin-polarized vertical-cavity surface-emitting lasers: Asymptotic analysis, numerics, and experiments

et al. 2015

View full text Add to dashboard Cite

The spin-flip model describing optically pumped spin-polarized vertical-cavity surface-emitting lasers is considered. The steady-state solutions of the model for elliptically-polarised fields are studied. Asymptotic analysis for the existence and stability of the steady-state solutions is developed, particularly in the presence of pump polarisation ellipticity. The expansion is with respect to small parameters representing the ellipticity and the difference between the total pump power and the lasing threshold. The analytical results are then confirmed numerically, where it is obtained that generally one of the steady-state solutions is stable while the other is not. The theoretical results are shown to be in qualitative agreement with the experiments.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spin-flip model of spin-polarized vertical-cavity surface-emitting lasers: Asymptotic analysis, numerics, and experiments

et al. 2015

View full text Add to dashboard Cite

show abstract

“…Bifurcation analysis based on the widely used spin-flip model (SFM) has also confirmed that such dynamical regimes could arise from the destabilization of the elliptically polarized states created by a pitchfork bifurcation on the lower-frequency linearly polarized state [21,22]. Likewise, various forms of instability could occur in free-running spin VCSELs, such as periodic oscillations and chaos.…”

Section: Introductionmentioning

confidence: 98%

Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers

Susanto

Cemlyn

et al. 2017

Phys. Rev. A

View full text Add to dashboard Cite

A detailed stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers (VCSELs) is presented. We consider both steady-state and dynamical regimes. In the case of steady-state operation, we carry out a small-signal (asymptotic) stability analysis of the steady-state solutions for a representative set of spin-VCSEL parameters. Compared with full numerical simulation, we show this produces surprisingly accurate results over the whole range of pump ellipticity, and spin-VCSEL bias up to 1.5 times the threshold. We then combine direct numerical integration of the extended spin-flip model and standard continuation technique to examine the underlying dynamics. We find that the spin VCSEL undergoes a period-doubling or quasiperiodic route to chaos as either the pump magnitude or polarization ellipticity is varied. Moreover, we find that different dynamical states can coexist in a finite interval of pump intensity, and observe a hysteresis loop whose width is tunable via the pump polarization. Finally we report a comparison of stability maps in the plane of the pump polarization against pump magnitude produced by categorizing the dynamic output of a spin VCSEL from time-domain simulations, against supercritical bifurcation curves obtained by the standard continuation package AUTO. This helps us better understand the underlying dynamics of the spin VCSELs.

show abstract

“…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%

“…These values are consistent with the parameters considered in this paper, and we can therefore suspect that the chaos suppression mechanism discussed prevented the observation of polarization chaos dynamics in these devices. In the end, considering the bifurcation scenario leading to the emergence of polarization chaos, we know that the region of chaotic dynamics will be pushed toward larger injection currents when the birefringence γ p is increased 6,17 . Indeed, the starting point of the route to chaos -when no anisotropy misalignment is considered -is the pitchfork bifurcation destabilizing the linear polarization stable at threshold and creating the two elliptically polarized steady-states from which the two scrolls of the chaotic attractor will emerge.…”

Section: Comparison With Experimental Observationsmentioning

confidence: 99%

Noise induced stabilization of chaotic free-running laser diode

Virte

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers

Cited by 38 publications

References 20 publications

Spin-flip model of spin-polarized vertical-cavity surface-emitting lasers: Asymptotic analysis, numerics, and experiments

Spin-flip model of spin-polarized vertical-cavity surface-emitting lasers: Asymptotic analysis, numerics, and experiments

Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers

Noise induced stabilization of chaotic free-running laser diode

Contact Info

Product

Resources

About