Low-frequency fluctuations in an external-cavity laser leading to extreme events

Different routes to large-intensity pulses in Zeeman laser model

In this study, we report a rich variety of large-intensity pulses exhibited by a Zeeman laser model. The instabilities in the system occur via three different dynamical processes, such as quasiperiodic intermittency, Pomeau-Manneville intermittency, and the breakdown of quasiperiodic motion to chaos followed by an interior crisis. This Zeeman laser model is more capable of exploring the major possible types of instabilities when changing a specific system's parameter in a particular range. We exemplified distinct dynamical transitions of the Zeeman laser model. The statistical measures reveal the appearance of the low probability of large-intensity pulses above the qualifier threshold value. Moreover, they seem to follow an exponential decay that shows a Poisson-like distribution. The impact of noise and time delay effects have been analyzed near the transition point of the system.

Controlling the likelihood of extreme events in an optically pumped spin-VCSEL via chaotic optical injection

We report on the manipulation of extreme events (EEs) in a slave spin-polarized vertical-cavity surface-emitting laser (spin-VCSEL) subject to chaotic optical injection from a master spin-VCSEL. The master laser is free-running but yielding a chaotic regime with obvious EEs, while the slave laser originally (i.e., without external injection) operates in either continuous-wave (CW), period-one (P1), period-two (P2), or a chaotic state. We systematically investigate the influence of injection parameters, i.e., injection strength and frequency detuning, on the characteristics of EEs. We find that injection parameters can regularly trigger, enhance, or suppress the relative number of EEs in the slave spin-VCSEL, where the large ranges of enhanced vectorial EEs and average intensity of both vectorial and scalar EEs can be achieved with suitable parameter conditions. Moreover, with the help of two-dimensional correlation maps, we confirm that the probability of occurrence of EEs in the slave spin-VCSEL is associated with the injection locking regions, outside which enhanced relative number of EEs regions can be obtained and expanded with augmenting the complexity of the initial dynamic state of the slave spin-VCSEL.

Extreme events in two laterally-coupled semiconductor lasers

Rogue waves (RWs) are extreme and rare waves that emerge unexpectedly in many natural systems and their formation mechanism and prediction have been extensively studied. Here, we numerically demonstrate the appearance of extreme events (EEs) for the first time, to the best of our knowledge, in the chaotic regimes of a two-element coupled semiconductor laser array. Based on coupled-mode theory, we characterize the occurrence of EEs by calculating the probability distribution, which confirms the RW-type feature of the intensity pulses, i.e., non-Gaussian distribution. Combining with the results of the 0-1 test for chaos, we confirm that EEs originate from deterministic nonlinearities in coupled semiconductor laser systems. We show that EEs can be predicted with a long anticipation time. Furthermore, simulation results manifest that the occurrence probability of EEs can be flexibly tuned by tailoring the coupling parameter space. With the help of two-dimension maps, the effects of key parameters, i.e., the waveguide structure and the pump level, on the formation of EEs are discussed systematically. This work provides a new platform for the research of EEs in a highly integrated structure and opens up a novel investigation field for coupled semiconductor laser arrays.

Experimental study of modulation waveforms for entraining the spikes emitted by a semiconductor laser with optical feedback

The entrainment phenomenon, by which an oscillator adjusts its natural rhythm to an external periodic signal, has been observed in many natural systems. Recently, attention has focused on which are the optimal conditions for achieving entrainment. Here we use a semiconductor laser with optical feedback, operating in the low-frequency fluctuations (LFFs) regime, as a testbed for a controlled entrainment experiment. In the LFF regime the laser intensity displays abrupt spikes, which can be entrained to a weak periodic signal that directly modulates the laser pump current. We compare the performance of three modulation waveforms for producing 1:1 locking (one spike is emitted in each modulation cycle), as well as higher order locking regimes. We characterize the parameter regions where high-quality locking occurs, and those where the laser emits spikes which are not entrained to the external signal. The role of the modulation amplitude and frequency, and the role of the dc value of the laser pump current (that controls the natural spike frequency) in the entrainment quality are discussed.

Multistate intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity

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 period-doubled and chaotic regimes. This latter type of intermittency displays statistical properties similar to those of on-off intermittency.

Vectorial extreme events in VCSEL polarization dynamics

We report on the occurrence of extreme events (EEs) in the polarization dynamics of vertical cavity surface emitting lasers with optical feedback. We have identified two types of EEs based on numerical simulations: vectorial and scalar events corresponding, respectively, to the emission of a high-power pulse in both linear polarizations simultaneously and in single linear polarization. We show that these two types of events follow the typical statistics of rogue waves. Finally, we observe that an emission in both polarizations leads to a larger generation rate of EEs with a saturation over a wide range of feedback strength by comparison to a single-polarization mode emission.

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.