Characterizing the aggregated encoding method utilizing bursts activated by a VCSEL-neuron with a feedback structure.

The rapid advancement of photonic technologies has facilitated the development of photonic neurons that emulate neuronal functionalities akin to those observed in the human brain. Neuronal bursts frequently occur in behaviors where information is encoded and transmitted. Here, we present the demonstration of the bursting response activated by an artificial photonic neuron. This neuron utilizes a single vertical-cavity surface-emitting laser (VCSEL) and encodes multiple stimuli effectively by varying the spike count during a burst based on the polarization competition in the VCSEL. By virtue of the modulated optical injection in the VCSEL employed to trigger the spiking response, we activate bursts output in the VCSEL with a feedback structure in this scheme. The bursting response activated by the VCSEL-neuron exhibits neural signal characteristics, promising an excitation threshold and the refractory period. Significantly, this marks the inaugural implementation of a controllable integrated encoding scheme predicated on bursts within photonic neurons. There are two remarkable merits; on the one hand, the interspike interval of bursts is distinctly diminished, amounting to merely one twenty-fourth compared to that observed in optoelectronic oscillators. Moreover, the interspike period of bursts is about 70.8% shorter than the period of spikes activated by a VCSEL neuron without optical feedback. Our results may shed light on the analogy between optical and biological neurons and open the door to fast burst encoding-based optical systems with a speed several orders of magnitude faster than their biological counterparts.

Wideband and high-dimensional chaos generation using optically pumped spin-VCSELs.

We propose and numerically demonstrate wideband and high-dimensional chaos signal generation based on optically pumped spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs). Here, we focus on the chaotic characteristics of spin-VCSELs under two scenarios: one is a spin-VCSEL with optical feedback and the other is optical heterodyning the outputs of two free-running spin-VCSELs. Specifically, we systematically investigate the influence of some key parameters on the chaotic properties, i.e., bandwidth, spectral flatness (SF), time delay signature (TDS), correlation dimension (CD), and permutation entropy (PE), and reveal the route to enhance these properties simultaneously. Our simulation results demonstrate for the first time that spin-VCSELs with simple auxiliary configurations allow for chaos generation with desired properties, including effective bandwidth up to 30 GHz and above, no TDS of greater than 0.2, the flatness of 0.75 and above, and the high complexity/dimensionality over a wide range of parameters under both schemes. Therefore, our study may pave the way for potential applications requiring wideband and high-dimensional chaos.

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.

Phase stability diagram, self-similar structures, and multistability in a free-running VCSEL with a small misalignment between the phase and amplitude anisotropies.

We report on the global dynamics of a free-running vertical-cavity surface-emitting laser (VCSEL) with misalignment between the linear phase and amplitude anisotropies due to the fact that this case might occur in practice caused unintentionally by minor manufacturing variations or design, in virtue of high-resolution phase stability diagrams, where two kinds of self-similar structures are revealed. Of interest is that the Arnold tongue cascades covered by multiple distinct periodicities are discovered for the first time in several scenarios specified in the free-running VCSEL, to the best of our knowledge. Additionally, we also uncover the existence of multistability through the basin of the attraction, as well as the eyes of anti-chaos and periodicity characterized by fractal. The findings may shed new light on interesting polarization dynamics of VCSELs, and also open the possibility to detect the above-mentioned structures experimentally and develop some potential applications.

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.

Characterizing the chaotic dynamics of a semiconductor nanolaser subjected to FBG feedback.

Nonlinear dynamics of semiconductor nanolasers subjected to distributed feedbacks from fiber Bragg grating (FBG) are investigated through modified rate equations, which include the unique Purcell cavity-enhanced spontaneous emission factor F and spontaneous emission coupling factor ß. In the analysis, the effects of F, ß, frequency detuning, feedback strength, feedback delay, FBG bandwidth and length on chaotic performance are evaluated. It is observed that the approach of FBG feedback outperforms mirror feedback in terms of concealing time-delay signature and increasing effective bandwidth by choosing intermediate feedback strength and frequency detuning. Additionally, chaotic regions and the corresponding chaotic characteristics are revealed by dynamical mappings of nanolasers subjected to FBG feedback. The results show that decreased F, ß and increased FBG bandwidth can extend the parameter range of chaos. However, the variation of feedback delay and FBG length has no obvious effect on TDS suppression and effective bandwidth enhancement. Most importantly, high quality optical chaos with low TDS and high effective bandwidth induced by increased dispersion is obtained within broad parameter regions considered, which is beneficial to achieving chaos-based applications.

Optically injected nanolasers for time-delay signature suppression and communications.

A large number of studies have been carried out to understand the nonlinear dynamics of nanolasers, yet there is a lack of comprehensive consideration on the optimization of chaotic output and its application to chaos secure communications. In this paper, we used an optically injected nanolaser structure to generate broadband chaos without a time-delay signature (TDS), which acts as the chaotic carrier in the proposed communication scheme. Due to the combination of desired TDS suppression enabled by the nanolasers and a two-channel transmission technique, the proposed scheme offers enhanced security for message encryption and decryption. We also considered the influence of some key parameters on the TDS suppression and that of parameter mismatch on chaos synchronization and message recovery. The detailed studies indicate that the proposed nanolaser-based scheme offers satisfactory TDS suppression performance over a wide range of parameters considered and is robust to resist fabrication imperfections-induced mismatch under proper injection conditions.

Enhancing time-delay suppression in a semiconductor laser with chaotic optical injection via parameter mismatch.

Time-delay signature (TDS) suppression of an external-cavity semiconductor laser (ECSL) is important for chaos-based applications and has been widely studied in the literature. In this paper, the chaotic output of an ECSL is injected into a semiconductor laser and TDS suppression in the regenerated time series is revisited. The focus of the current work is the influence of parameter mismatch on the TDS evolution, which is investigated experimentally and compared systematically to simulations. The experimental results demonstrate that it is much easier to achieve desired TDS suppression in the configuration composed of mismatched laser pairs. Numerical simulations confirm the validity of the experimental results. In the experiments and simulations, the influence of the injection parameters on TDS suppression is also studied and good agreement is obtained.

Generation of NLFM microwave waveforms based on controlled period-one dynamics of semiconductor lasers.

We propose an approach to generating nonlinear frequency-modulated (NLFM) microwave waveforms, which is based on controlled period-one (P1) dynamics of an optically injected semiconductor laser (OISL). When the optical injection is modulated, the OISL, which originally operates at a P1 oscillation state, acts as a microwave voltage-controlled oscillator (VCO). In the proposed system, the microwave frequency output depends closely on the optical injection strength controlled by the modulation voltage input, while the electrical modulation signal required to generate a desired NLFM microwave waveform can be calculated on the basis of the "voltage-to-frequency" transfer function of the established VCO system. Our simulations and experiments demonstrate that both single-chirp and dual-chirp NLFM microwave waveforms can be readily generated with a bandwidth up to 9 GHz. Considering peak-to-sidelobe ratio (PSLR) of the compressed pulses, the NLFM signals generated by the VCO exhibit a practical improvement of ∼13 dB when compared with LFM signals with the same bandwidth, and the tunability of the generated NLFM signals is also experimentally demonstrated.

Analysis and characterization of chaos generated by free-running and optically injected VCSELs.

We report on the dynamics of free-running and optically injected VCSELs. In particular, the powerful measures including the 0-1 test for chaos and permutation entropy are used for locating the chaotic dynamics in a free-running VCSEL, which illustrates the effects of some key parameters on the chaotic region. In order to enhance chaotic dynamics, the output of the free-running VCSEL (master) is injected to another free-running VCSEL (slave). Our results show that the chaotic dynamics of the slave VCSEL can be greatly enhanced, i.e., both the bandwidth and complexity, while this occurs only outside of the injection locking region where the correlation between the mater and slave lasers is low. To take advantage of these enhanced chaotic dynamics exhibiting extremely high complexity and broadband bandwidth, a three-laser synchronization scheme is proposed and demonstrated. These findings pave the way to the generation of high-quality chaos (no time-delay signature, high bandwidth and complexity) and notably chaos-based applications based on free-running and optically injected VCSELs.