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Excitability is a generic prediction for an optically injected semiconductor laser. However, the details of the phenomenon differ depending on the type of device in question. For quantum-well lasers very complicated multipulse trajectories can be found, while for quantum-dot lasers the situation is much simpler. Experimental observations show the marked differences in the pulse shapes while theoretical considerations reveal the underlying mechanism responsible for the contrast, identifying, the increased stability of quantum-dot lasers to perturbations as the root. [ABSTRACT FROM AUTHOR]

We report the discovery of a codimension-two phenomenon in the phase diagram of a second-order self-sustained nonlinear oscillator subject to a constant external periodic forcing, around which three regimes associated with the synchronization phenomenon exist, namely phase-locking, frequency-locking without phase-locking, and frequency-unlocking states. The triple point of synchronization arises when a saddle-node homoclinic cycle collides with the zero-amplitude state of the forced oscillator. A line on the phase diagram where limit-cycle solutions contain a phase singularity departs from the triple point, giving rise to a codimension-one transition between the regimes of frequency unlocking and frequency locking without phase locking. At the parameter values where the critical transition occurs, the forced oscillator exhibits a separatrix with a π phase jump, i.e., a particular trajectory in phase space that separates two distinct behaviors of the phase dynamics. Close to the triple point, noise induces excitable pulses where the two variants of type-I excitability, i.e., pulses with and without 2π phase slips, appear stochastically. The impacts of weak noise and some other dynamical aspects associated with the transition induced by the singular phenomenon are also discussed.

Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been considered a necessary ingredient to generate super rogue waves, i.e., an enhanced wave amplification, where the wave amplitudes exceed by far those of ordinary rogue waves. Here we show, experimentally and theoretically, that optical super rogue waves emerge in the simple case of linear light diffraction in one transverse dimension. The underlying physics is a long-range correlation on the random initial phases of the light waves. When subgroups of random phases appear recurrently along the spatial phase distribution, a more ordered phase structure greatly increases the probability of constructive interference to generate super rogue events (non-Gaussian statistics with superlong tails). Our results consist in a significant advance in the understanding of extreme waves formation by linear superposition of random waves, with applications in a large variety of wave systems.

It is shown that a highly randomlike behavior of light polarization states in the output of a free-running laser diode, covering the whole Poincaré sphere, arises as a result from a fully deterministic nonlinear process, which is characterized by a hyperchaotic dynamics of two polarization modes nonlinearly coupled with a semiconductor medium, inside the optical cavity. A number of statistical distributions were found to describe the deterministic data of the low-dimensional nonlinear flow, such as lognormal distribution for the light intensity, Gaussian distributions for the electric field components and electron densities, Rice and Rayleigh distributions, and Weibull and negative exponential distributions, for the modulus and intensity of the orthogonal linear components of the electric field, respectively. The presented results could be relevant for the generation of single units of compact light source devices to be used in low-dimensional optical hyperchaos-based applications.

We investigate the occurrence of extreme and rare events, i.e., giant and rare light pulses, in a periodically modulated CO_{2} laser model. Due to nonlinear resonant processes, we show a scenario of interaction between chaotic bands of different orders, which may lead to the formation of extreme and rare events. We identify a crisis line in the modulation parameter space, and we show that, when the modulation amplitude increases, remaining in the vicinity of the crisis, some statistical properties of the laser pulses, such as the average and dispersion of amplitudes, do not change much, whereas the amplitude of extreme events grows enormously, giving rise to extreme events with much larger deviations than usually reported, with a significant probability of occurrence, i.e., with a long-tailed non-Gaussian distribution. We identify recurrent regular patterns, i.e., precursors, that anticipate the emergence of extreme and rare events, and we associate these regular patterns with unstable periodic orbits embedded in a chaotic attractor. We show that the precursors may or may not lead to the emergence of extreme events. Thus, we compute the probability of success or failure (false alarm) in the prediction of the extreme events, once a precursor is identified in the deterministic time series. We show that this probability depends on the accuracy with which the precursor is identified in the laser intensity time series.

We investigate the transition from unidirectional to delayed bidirectional coupling of semiconductor lasers. By tuning the coupling strength in one direction we show how the locking region evolves as a function of the detuning and coupling strength. We consider two representative values of the relaxation oscillation damping: one where the relaxation oscillations are very underdamped and one where they are very overdamped. Qualitatively different dynamical scenarios are shown to emerge for each case. Several features of the delayed bidirectional system can be seen as remaining from the unidirectional system while others clearly arise due to the delayed coupling and are similar to effects seen in delayed feedback configurations.

Experimental observations of rare giant pulses or rogue waves were done in the output intensity of an optically injected semiconductor laser. The long-tailed probability distribution function of the pulse amplitude displays clear non-Gaussian features that confirm the rogue wave character of the intensity pulsations. Simulations of a simple rate equation model show good qualitative agreement with the experiments and provide a framework for understanding the observed extreme amplitude events as the result of a deterministic nonlinear process.

A network of phase-coupled oscillators constitutes a system in which excitable 2pi phase slips can be induced by noise. We show that such an excitation in one of the oscillators can be regenerated by subsequent oscillators and become self-sustained for certain topologies. We focus on the simplest such topology: two mutually coupled oscillators.Our analysis is bolstered [corrected] by an experimental confirmation of the phenomenon via a pair of mutually delay coupled quantum-dot lasers. Both the intensities and phases of the laser outputs were measured confirming the interpretation.

We report the discovery of a remarkable "periodicity hub" inside the chaotic phase of an electronic circuit containing two diodes as a nonlinear resistance. The hub is a focal point from where an infinite hierarchy of nested spirals emanates. By suitably tuning two reactances simultaneously, both current and voltage may have their periodicity increased continuously without bound and without ever crossing the surrounding chaotic phase. Familiar period-adding current and voltage cascades are shown to be just restricted one-parameter slices of an exceptionally intricate and very regular onionlike parameter surface centered at the focal hub which organizes all the dynamics.

We report strong evidence of remarkably close periodic repetitions of the structuring of the parameter space of a damped-driven Duffing oscillator as the amplitude of the drive increases. Families of period-adding cascades and some intricate networks of periodic oscillations embedded in chaotic phases are also found to recur closely as the driving force grows. Such surprising regularities suggest that some hitherto unknown renormalization mechanism may be operating in higher codimension, controlling the alternation of chaos and order in parameter space of certain flows.

We study the hierarchical structuring of islands of stable periodic oscillations inside chaotic regions in phase diagrams of single-mode semiconductor lasers with optical injection. Phase diagrams display remarkable accumulation horizons: boundaries formed by the accumulation of infinite cascades of self-similar islands of periodic solutions of ever-increasing period. Each cascade follows a specific period-adding route. The riddling of chaotic laser phases by such networks of periodic solutions may compromise applications operating with chaotic signals such as, e.g., secure communications.

We show the standard two-level continuous-time model of loss-modulated CO2 lasers to display the same regular network of self-similar stability islands known so far to be typically present only in discrete-time models based on mappings. Our results suggest that the two-parameter space of class B laser models and that of a certain class of discrete mappings could be isomorphic.