Unnested islands of period doublings in an injected semiconductor laser (original) (raw)
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Chaos, period-doubling and reverse bifurcations in an optically injected semiconductor laser
Proceedings of 1994 Nonlinear Optics: Materials, Fundamentals and Applications, 1994
Nonlinear dynamics in optical systems is the subject of considerable current research [l]. An isolated, dc-biased semiconductor laser is sufficiently described by only two rate equations: one for the photon density and another for the carrier density [2]. Consequently, tliis system cannot exhibit chaotic behavior. In order to induce chaos in such a system, a third degree of freedom is needed. It was predicted that external optical injection can lead to chaos through the period-doubling mechanism [3], and we liave recently confirmed that prediction .
Different types of chaos in an optically injected semiconductor laser
Applied Physics Letters, 2000
With advanced tools from bifurcation theory routes to chaos via period doubling and the break-up of tori are identified. This allows us to distinguish between different types of chaos in terms of the output characteristics of the laser. We also find locking to a periodic solution inside a region of chaos. This information is important for applications requiring chaotic signals, such as encryption schemes.
Sudden chaotic transitions in an optically injected semiconductor laser
Optics Letters, 2001
We study sudden changes in the chaotic output of an optically injected semiconductor laser. For what is believed to be the first time in this system, we identify bifurcations that cause abrupt changes between different chaotic outputs, or even sudden jumps between chaotic and periodic output. These sudden chaotic transitions involve attractors that exist for large regions in parameter space.
Dynamics, bifurcations and chaos in coupled lasers
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008
Experiments and numerical modelling on two different class B lasers that are subjected to external optical light injection are presented. This presentation includes ways of measuring the changes in the laser output, how to numerically describe the systems and how to construct diagrams of the dynamical states in the plane frequency detuning between lasers and injection strength. The scenarios for the semiconductor laser include an area of frequency locking and islands of chaotic behaviour embedded in and mixed with periodic doubling regimes. Using a rate equation model, the largest Lyapunov exponent is calculated as a measure of the stability of equilibriums and the amount of chaos in chaotic regimes. In the solid-state laser case, different dynamical regions were clearly observed. The found boundaries were identified experimentally, using an identification method, and numerically, from bifurcation analysis, as Hopf, saddle-node, period-doubling and torus bifurcations.
Bifurcations of a three-torus in a twin-stripe semiconductor laser model
1994
The dynamic behaviour of the strongly coupled twin-stripe semiconductor laser is studied theoretically in dependence on the pumping strength (current injection). With the aid of power spectra, next-maximum maps, and estimates of the attractor dimensions bifurcations from a three-toms to a two-toms and from two-toil to chaotic attractors are identified.
Routes to chaos in a semiconductor laser subject to phase-conjugate optical feedback
SPIE Proceedings, 2002
A semiconductor laser subject to phase-conjugate optical feedback can be described by rate equations, which are mathematically delay differential equations (DDEs) with an infinite dimensional phase space. This is why, from the theoretical point of view, this system was only studied by numerical simulation up to now. We employ new numerical techniques for DDEs, namely the continuation of periodic orbits and the computation of unstable manifolds, to study bifurcations and routes to chaos in the system. Specifically we compute 1D unstable manifolds of a saddle-type periodic orbit as intersection curves in a suitable Poincaré section. We are able to explain in detail a transition to chaos as the feedback strength is increased, namely the break-up of a torus and a sudden transition to chaos via a boundary crisis. This allows us to make statements on properties of the ensuing chaotic attractor, such as its dimensionality. Information of this sort is important for applications of chaotic laser signals, for example, in communication schemes.
Controlling chaos may induce new attractors in an optical device
Optics Communications, 1995
The logistic map has been used to describe period doubling bifurcations for periodically modulated lasers. It also represents an asymptotic approximation of Ikeda's map for a passive ring cavity. Because various control methods have been used recently to stabilize branches of periodic solutions in lasers, we investigate the logistic map with a standard Ott, Grebogi and Yorke (OGY) control. We explore the structure of this map plus perturbations and find considerable modifications to its bifurcation diagram. In addition to the original fixed points, we find a new fixed point and new period doubling bifurcations. We show that for certain values of small perturbations the new fixed point of the perturbed logistic map is stable, while its original fixed point becomes unstable. Our analysis suggests that new branches of solutions may exist in lasers as a result of the feedback control.
Experimental bifurcations and homoclinic chaos in a laser with a saturable absorber
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2008
The shape and the peak values of the pulses from a passive Q-switching CO 2 laser with SF 6 as saturable absorber were detected while the laser was tuned in frequency across a longitudinal mode. A succession of stability windows, typical for bifurcation diagrams in the homoclinic scenario, was observed and the widths of those windows were measured. The expansion rate of the undulations in individual pulses was also obtained and compared to Floquet's multipliers given by the ratio of widths in consecutive windows. The dynamics is consistent with a homoclinic tangency to a periodic orbit.
Chaos, 2018
We observe experimentally two regimes of intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity as the feedback level is increased. The first regime encountered corresponds to multistate intermittency involving two or three states composed of several combinations of periodic, quasiperiodic, and subharmonic dynamics. The second regime is observed for larger feedback levels and involves intermittency between perioddoubled and chaotic regimes. This latter type of intermittency displays statistical properties similar to those of on-off intermittency.