Limits on the excitable behavior of a semiconductor laser with optical feedback

Quantitative identification of dynamical transitions in a semiconductor laser with optical feedback

Identifying transitions to complex dynamical regimes is a fundamental open problem with many practical applications. Semi- conductor lasers with optical feedback are excellent testbeds for studying such transitions, as they can generate a rich variety of output signals. Here we apply three analysis tools to quantify various aspects of the dynamical transitions that occur as the laser pump current increases. These tools allow to quantitatively detect the onset of two different regimes, low-frequency fluctuations and coherence collapse, and can be used for identifying the operating conditions that result in specific dynamical properties of the laser output. These tools can also be valuable for analyzing regime transitions in other complex systems.

Distinguishing signatures of determinism and stochasticity in spiking complex systems

We describe a method to infer signatures of determinism and stochasticity in the sequence of apparently random intensity dropouts emitted by a semiconductor laser with optical feedback. The method uses ordinal time-series analysis to classify experimental data of inter-dropout-intervals (IDIs) in two categories that display statistically significant different features. Despite the apparent randomness of the dropout events, one IDI category is consistent with waiting times in a resting state until noise triggers a dropout, and the other is consistent with dropouts occurring during the return to the resting state, which have a clear deterministic component. The method we describe can be a powerful tool for inferring signatures of determinism in the dynamics of complex systems in noisy environments, at an event-level description of their dynamics.

Language organization and temporal correlations in the spiking activity of an excitable laser: experiments and model comparison

We introduce a method, based on symbolic analysis, to characterize the temporal correlations of the spiking activity exhibited by excitable systems. The technique is applied to the experimentally observed dynamics of a semiconductor laser with optical feedback operating in the low-frequency fluctuations regime, where the laser intensity displays irregular trains of sudden dropouts that can be interpreted as excitable pulses. Symbolic analysis transforms the series of interdropout time intervals into sequences of words, which represent the local ordering of a certain (small) number of those intervals. We then focus on the transition probabilities between pairs of words, showing that certain transitions are overrepresented (resulting in others being underrepresented) with respect to the surrogate series, provided the laser injection current is above a critical value. These experimental observations are in very good agreement with numerical simulations of the delay-differential Lang-Kobayashi model that is commonly used to describe this laser system, which supports the fact that the language organization reported here is generic and not a particular feature of the specific laser employed or the experimental time series analyzed. We also present results of simulations of the phenomenological nondelayed Eguia-Mindlin-Giudici(EMG) model and find that in this model the agreement between the experiments and the simulations is good at a qualitative, but not at a quantitative, level.

Bifurcation analysis of solitary and synchronized pulses and formation of reentrant waves in laterally coupled excitable fibers

We study the dynamics of a reaction-diffusion system comprising two mutually coupled excitable fibers. We consider a case in which the dynamical properties of the two fibers are nonidentical due to the parameter mismatch between them. By using the spatially one-dimensional FitzHugh-Nagumo equations as a model of a single excitable fiber, synchronized pulses are found to be stable in some parameter regime. Furthermore, there exists a critical coupling strength beyond which the synchronized pulses are stable for any amount of parameter mismatch. We show the bifurcation structures of the synchronized and solitary pulses and identify a codimension-2 cusp singularity as the source of the destabilization of synchronized pulses. When stable solitary pulses in both fibers disappear via a saddle-node bifurcation on increasing the coupling strength, a reentrant wave is formed. The parameter region, where a stable reentrant wave is observed in direct numerical simulation, is consistent with that obtained by bifurcation analysis.

Coarse grained variables and deterministic chaos in an excitable system

Temporal coarse graining was applied to the dynamical variables of a semiconductor laser with optical feedback. The chaotic low frequency fluctuations obtained in numerical and experimental data are shown to have properties of a self-excitable deterministic system. External exciting noise is replaced by the ultrafast chaotic oscillations of the system. A low dimensional coarse-grained phase space is defined and time constants are introduced and measured for the exponential drop and recovery of the randomly excited equally shaped spikes.