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.

Enhanced extreme events in three cascade-coupled semiconductor lasers.

Extreme events (EEs) are rare and unpredictable, as have been observed in nature. Up to now, manipulating EEs has remained a challenge. Here, we experimentally observe the enhancement of EEs in a three cascade-coupled semiconductor laser system. Specifically, a continuous-wave optical injection semiconductor laser acts as the chaotic source with rare EEs, which is subsequently injected into a second laser for increasing the number of EEs. Interestingly, we find that the number and region size of EEs can be further enhanced by sequentially injecting into a third laser, i.e., a cascade-injection structure. Our experimental observations are in good agreement with the numerical results, which indicate that EEs can be significantly enhanced in wide injection parameter space due to the cascade-injection effect. Furthermore, our simulations show that the evoluation of the regions with enhanced EEs may be associated with the noise considered.

Enhanced performances of photonic reservoir computing using a semiconductor laser with random distributed optical feedback.

We propose and experimentally demonstrate a photonic time-delay reservoir computing (TDRC) system with random distributed optical feedback under optical injection. To evaluate the performance, we calculate the memory ability and perform two benchmark tasks, i.e., chaotic time series prediction and nonlinear channel equalization task. Our numerical results show that the proposed TDRC has a superior performance compared with the case with conventional single optical feedback. This is attributed to the fact that the random distributed optical feedback offers multiple external cavity modes, which enhance the nonlinearity of the reservoir laser. Additionally, the experimental result also shows that our proposed TDRC scheme outperforms the computer with single optical feedback in the chaotic time series prediction task. To the best of our knowledge, our work offers a novel path to improve the performance of TDRC by introducing random distributed optical feedback.

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.

Chimera states in a large laterally coupled laser array with four different waveguide structures.

Chimera states are rich and fascinating phenomena existing in many networks, where the identical oscillators self-organize into spatially separated coexisting domains of coherent and incoherent oscillations. Here, we report these states in the large laterally coupled laser array with four different waveguiding structures, with which a variety of chimera patterns can be revealed. We present the bifurcation diagrams giving birth to them and find that the chimeras exist in the boundary of the steady state and multi-period oscillation solutions, which applies to all the prevalent waveguiding structures considered. We also find that the waveguiding structures play an important role in the chimera states, e.g., the array composed of the index antiguiding with gain-guiding has a wider chimera region compared to other waveguides considered. Additionally, the effects of the crucial parameters including the laser separation ratio, pump rate, frequency detuning, and linewidth enhancement factor on the observed phenomena are discussed. Our analysis shows that the frequency detuning between lasers and the linewidth enhancement factor affects the lifetime and pattern of chimeras. The results could guide the design of laser arrays or introduce more insight into a new understanding of the dynamical behaviors of networks.

Non-quantum chiral structure in a free-running VCSEL.

We report on the occurrence of a non-quantum chiral structure in a free-running vertical-cavity surface-emitting laser (VCSEL) with a small misalignment between birefringence and dichroism. Through high-resolution phase diagrams, we show how oscillations evolve in parameter space for different values of the misalignment. Unlike a previously reported non-quantum chiral dynamic system involving closed rings in parameter space, this work manifests another case, i.e., the chiral structure exists in some open parameter spaces. Furthermore, the possible underlying physical mechanism of the emergence of the structures is offered through bifurcation analysis.

Numerical investigation of photonic microwave generation in an optically pumped spin-VCSEL subject to optical feedback.

Photonic microwave generation based on period-one (P1) dynamics of an optically pumped spin-polarized vertical-cavity surface-emitting laser (spin-VCSEL) is investigated numerically. Here, the frequency tunability of the photonic microwave generated from a free-running spin-VCSEL is demonstrated. The results show that the frequency of the photonic microwave signals can be widely tuned (from several gigahertz to hundreds of gigahertz) by changing the birefringence. Furthermore, the frequency of the photonic microwave can be modestly adjusted by introducing an axial magnetic field, although it degrades the microwave linewidth in the edge of Hopf bifurcation. To improve the quality of the photonic microwave, an optical feedback technique is employed in a spin-VCSEL. Under the scenario of single-loop feedback, the microwave linewidth is decreased by enhancing the feedback strength and/or delay time, whereas the phase noise oscillation increases with the increase of the feedback delay time. By adding the dual-loop feedback, the Vernier effect can effectively suppress the side peaks around the central frequency of P1, and simultaneously supports P1 linewidth narrowing and phase noise minimization at long times.

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.

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.

Mapping synchronization properties in a three-element laterally coupled laser array.

We numerically study the synchronized chaos (SC) and spatiotemporal chaos (STC) in a three-element laterally-coupled laser array in the case of four waveguiding structures. The coupled rate equations are used to analyze the dynamics of the laser array, where spatiotemporal dynamic maps are generated to identify regions of SC, STC, and non-chaos in the parameter space of interest. First, we show that the key parameters of the laser array, i.e., the laser separation ratio, pump rate, linewidth enhancement factor, and frequency detuning play important roles in the array dynamics and synchronization properties. Then we show that the laser array composed of the purely real index guiding exhibits more obvious boundaries between SC and STC in wider parameter space with respect to these composed of either the positive index guiding with gain-indexing, the pure gain guiding, or the index antiguiding with gain-guiding. Finally, we show that the proposed laser array allows for two scenarios of parallel random bit generation (PRBG) by applying the same post-processing on chaos sources based on SC and STC dynamic states. Hence, our results provide a comprehensive study on the collective dynamics in the three-element laterally-coupled laser array and pave the way for PRBG based on laser arrays.

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.

Spatiotemporal chaos induces extreme events in a three-element laterally coupled laser array.

Extreme events are observed in the spatiotemporal chaos dynamics of a three-element laterally coupled laser array. With the help of statistical and dynamical analyses, we confirm that spatiotemporal chaos induces extreme pulses that are high enough to be identified as extreme events and cannot be found in synchronization chaos. Interestingly, our results show that extreme events always preferentially appear in the middle laser as the laser separation ratio is decreased (i.e., upon increasing the coupling strength), and then in the two outer lasers. This thus reveals the importance of the middle laser in the transition between synchronization chaos and spatiotemporal chaos states. Additionally, we show the evolution of extreme events in the plane of the pump level and laser separation ratio by calculating the corresponding proportion. Our results build a relation between extreme events and the spatiotemporal dynamics, which makes it easy to understand the formation mechanism of extreme events.

Bandwidth-enhanced LFM waveform generator based on dynamic control of an optically injected semiconductor laser.

A bandwidth-enhanced linear frequency-modulated (LFM) waveform generation scheme is proposed and demonstrated based on dynamic control of an optically injected semiconductor laser (OISL). The OISL operates at the period-one (P1) oscillation state under proper injection conditions. After photodetection, a tunable microwave signal is obtained with its frequency determined by the optical injection strength and the detuning frequency between the master and slave lasers. For a fixed detuning frequency, an LFM waveform can be generated by introducing an electrical control signal S(t) with a quasi-sawtooth profile to dynamically manipulate the injection strength of the OISL. Then, to overcome the bandwidth limitation by the achievable P1 frequency range under a given detuning frequency, both the injection strength and the detuning frequency are dynamically controlled to achieve a synthesized P1 frequency range, thus generating LFM waveforms with enhanced bandwidths. In our demonstration, LFM waveforms with a synthesized bandwidth of 8 GHz (12-20 GHz) and 24.8 GHz (12.6-37.4 GHz) are generated in the experiment and simulation, respectively.

Extreme events in optically pumped spin-VCSELs.

Extreme events (EEs) are predicted for the first time, to the best of our knowledge, in the chaotic dynamics of a free-running spin-polarized vertical-cavity surface-emitting laser (spin-VCSEL). Here, we not only show two types of EEs, i.e., vectorial and scalar EEs separately corresponding to the emission of a high-power pulse in both linear polarizations (LPs) simultaneously and in single LP, but we also observe a new EE type that only occurs in total intensity. We also confirm that the observed EEs follow similar statistical distributions to conventional rogue waves. Moreover, the effects of pump power and pump ellipticity on the generation of EEs are analyzed. Finally, we compare free-running and optical feedback spin-VCSELs, which provides more insights into the study of EEs. More importantly, this work offers a novel platform for the study of EEs with a simple structure and opens up new research fields into spin-VCSELs.

High-speed photonic reservoir computer based on a delayed Fano laser under electrical modulation.

We propose and numerically demonstrate a high-speed photonic reservoir computing (RC) system using a compact Fano laser (FL) with optical feedback under electrical modulation. Benefiting from its insensitivity to external feedback, an FL has a wider dynamic steady-state region compared with a conventional Fabry-Perot laser, which significantly extends the ranges of desirable RC implementation. Interestingly, we observe two separate regions of good RC performances corresponding to two scenarios of the dynamic steady state of the FL, respectively. Moreover, the robust RC performance versus the feedback phase can be achieved in one of the steady-state regions, where the laser is not destabilized for lower external reflectivity. Owing to the ultra-short photon lifetime in the FL, the information processing rate of our proposed RC system may reach 10 Gbps. More importantly, as a specific type of microscopic laser, the FL offers potential applications to RC-based integrated neuromorphic photonic systems.

Continuous tuning of unidirectional emission wavelength by bending a notched-elliptical polymer microdisk.

An approach of continuously tunable unidirectional emission through bending a notched-elliptical polymer microdisk is proposed. The characteristics of the bending-dependent action are carefully analyzed, and the resonance wavelength for unidirectional emission can be tuned continuously through bending the device. Such a whispering-gallery-mode microresonator enables unidirectional emission with ultra-low divergence, of which the emission efficiency and Q factor are stabilized, demonstrating the whole structure is robust and relatively insensitive within a certain bending angle range. A maximum resonance wavelength shift of ∼100 nm and Q factor of 1500 can be achieved with the total size of the microdisk less than 10 µm. This kind of microresonator is promising for applications in multilevel integrated photonics circuits and may open the door to new functionalities of resonator devices, from sensing to optical amplification.

Optical chaos generated in semiconductor lasers with intensity-modulated optical injection:a numerical study.

We numerically report on an optical chaos signal generation scheme based on a semiconductor laser subject to intensity-modulated (IM) optical injection. In this scheme, the characteristics of the chaos signal obtained by destabilizing period-one nonlinear dynamics are numerically investigated. With the aid of bifurcation diagrams and the 0-1 tests for chaos, the chaotic dynamics excited by continuous-wave and IM optical injection are located, and the effects of injection and modulation parameters on chaotic regions are illustrated. Moreover, effective bandwidths and auto-correlation characteristics of chaos signals from the IM optical injection system are systematically investigated. The results show that although chaotic signals under the IM optical injection scenario have a limitation in unambiguous range detection in most parameter regions, wideband chaotic dynamics in large injection and modulation parameter regions can be easily achieved. This study paves the way for potential applications requiring no time-delay signature and broad bandwidth chaos, such as high-speed chaos communications and random bit generation.

Photonic generation of high-performance microwave frequency combs using an optically injected semiconductor laser with dual-loop optoelectronic feedback.

An approach to generating microwave frequency combs (MFCs) with superior performance is proposed and experimentally demonstrated based on an optically injected semiconductor laser (OISL). The OISL operates at the period-one (P1) oscillation state under proper injection conditions. A sinusoidal voltage signal is used to modulate the P1 state for the initial MFC generation, and then two optoelectronic feedback loops are introduced to enhance the performance of the MFC: a short-delay feedback loop is firstly applied to improve comb contrast based on Fourier domain mode locking (FDML), and a long-delay feedback loop is added to reduce the comb linewidth based on the self-injection-locking technique. In the proof-of-concept experiment, a K-band MFC (18-26 GHz) with a line spacing of 8.45 MHz is obtained, where a comb linewidth of approximately 500 Hz and a comb contrast over 45 dB are simultaneously achieved. Additionally, each comb component exhibits superior performance in terms of phase noise, all below -90dBc/Hz at 10 kHz offset, demonstrating an excellent coherence among these combs.

High-speed secure key distribution based on chaos synchronization in optically pumped QD spin-polarized VCSELs.

We propose and numerically demonstrate a high-speed secure key distribution (SKD) based on polarization-keying chaos synchronization in two quantum dot (QD) spin-polarized vertical-cavity surface-emitting lasers (VCSELs) without any external feedback. In this scheme, high-quality chaos synchronization can be obtained when the response lasers have the same polarization ellipticity. The proposed SKD scheme is benefited from the feasible tunability of the pump polarization ellipticity, and no other complex components are necessary. Moreover, the open-loop configuration is constructed in the commonly driven lasers and results in a short synchronization recovery time of hundreds of picoseconds, which is much shorter than that in most previous reports. Combined with these merits, a 1.34 Gb/s SKD with a bit error ratio lower than 3.8 × 10-3 can be achieved. The current study provides a new way to realize high-speed physical key distribution.

Broad tunable photonic microwave generation in an optically pumped spin-VCSEL with optical feedback stabilization.

We propose and numerically demonstrate a photonic microwave generation scheme based on the dynamic period-one oscillation of a solitary spin-polarized vertical-cavity surface-emitting laser (spin-VCSEL). The evolution of the oscillation amplitude, frequency, power, and linewidth of the generated microwave is systematically investigated by using two-dimensional maps. The results show that the generated microwave signals with a dominant linewidth of about 3 MHz have a broad tunable frequency (from several gigahertz to hundreds of gigahertz), which benefits from the birefringence-induced oscillation in spin-VCSELs. Moreover, with the help of optical feedback, the microwave linewidth can be effectively minimized (∼51kHz) by increasing the feedback strength and feedback delay time. Importantly, this Letter offers prospects for applications requiring a feasible and resource-efficient microwave source in microwave photonic fields.