Noise induced stabilization of chaotic free-running laser diode

Abstract

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.

Chaos in Solitary VCSELs: Exploring the Parameter Space With Advanced Sampling

“…5 that non chaotic samples with µ > µ x mostly appear for lower values of γ p . Besides the low-value of µ x , this can also be explained by a comparatively short region of chaotic dynamics for small birefringence values [26], but also possibly by the coexistence of a chaotic attractor and a steady-state as discussed in [28].…”

“…To do so, we use a two step process as schematically displayed in Fig. 3: • Step 1: we use noisy simulations, including a complex stochastic term modelling spontaneous emission noise for the amplitude and phase for each electrical field as done in [28], to randomly select new starting points. • Step 2: we apply the so-called Wolf's algorithm with the starting points obtained at step 1.…”

“…To avoid these false positives, we set a threshold at 5 ns −1 for the LLE instead of 0. Finally, it should be noted that the goal of the noisy simulation at Step 1 is also to dismiss cases for which chaotic attractors coexist with a stable steady-state as described in [28]. Although these are expected to be relatively rare, such occurrence cannot be simply neglected.…”

“…Although these are expected to be relatively rare, such occurrence cannot be simply neglected. In [28], starting from the chaotic attractor, the system typically reached the stable steady-state within a few ns, to be compared with the 100 ns simulation horizon that we use here. If, despite the noisy simulation, the system remain on the chaotic attractor we can obviously conclude that the chaos is stable enough to justify its inclusion in our analysis.…”