Solitary and coupled semiconductor ring lasers as optical spiking neurons

Characterizing the spike timing of a chaotic laser by using ordinal analysis and machine learning

Semiconductor lasers with optical feedback are well-known nonlinear dynamical systems. Under appropriate feedback conditions, these lasers emit optical pulses that resemble neural spikes. Influenced by feedback delay and various noise sources, including quantum spontaneous emission noise, the dynamics are highly stochastic. A good understanding of the spike timing statistics is needed to develop photonic systems capable of using the fast-spiking laser output for novel applications, such as information processing or random number generation. Here we analyze experimental sequences of inter-spike intervals (ISIs) recorded when a sinusoidal signal was applied to the laser current. Different combinations of the DC value and frequency of the signal applied to the laser lead to ISI sequences with distinct statistical properties. This variability prompts an investigation into the relationship between experimental parameters and ISI sequence statistics, aiming to uncover potential encoding methods for optical spikes, since this can open a new way of encoding and decoding information in sequences of optical spikes. By using ordinal analysis and machine learning, we show that the ISI sequences have statistical ordinal properties that are similar to Flicker noise signals, characterized by a parameter α that varies with the signal that was applied to the laser current when the ISIs were recorded. We also show that for this dataset, the (α, permutation entropy) plane is more informative than the (complexity, permutation entropy) plane because it allows better differentiation of ISI sequences recorded under different experimental conditions, as well as better differentiation of original and surrogate ISI sequences.

Artificial optoelectronic spiking neuron based on a resonant tunnelling diode coupled to a vertical cavity surface emitting laser

Excitable optoelectronic devices represent one of the key building blocks for implementation of artificial spiking neurons in neuromorphic (brain-inspired) photonic systems. This work introduces and experimentally investigates an opto-electro-optical (O/E/O) artificial neuron built with a resonant tunnelling diode (RTD) coupled to a photodetector as a receiver and a vertical cavity surface emitting laser as a transmitter. We demonstrate a well-defined excitability threshold, above which the neuron produces optical spiking responses with characteristic neural-like refractory period. We utilise its fan-in capability to perform in-device coincidence detection (logical AND) and exclusive logical OR (XOR) tasks. These results provide first experimental validation of deterministic triggering and tasks in an RTD-based spiking optoelectronic neuron with both input and output optical (I/O) terminals. Furthermore, we also investigate in simulation the prospects of the proposed system for nanophotonic implementation in a monolithic design combining a nanoscale RTD element and a nanolaser; therefore demonstrating the potential of integrated RTD-based excitable nodes for low footprint, high-speed optoelectronic spiking neurons in future neuromorphic photonic hardware.

Refractory times for excitable dual-state quantum dot laser neurons

Excitable photonic systems show promise for ultrafast analog computation, several orders of magnitude faster than biological neurons. Optically injected quantum dot lasers display several excitable mechanisms with dual-state quantum lasers recently emerging as true all-or-none excitable artificial neurons. For use in applications, deterministic triggering is necessary and this has previously been demonstrated in the literature. In this work we analyze the crucially important refractory time for this dual-state system, which defines the minimum time between distinct pulses in any train.

Inhibitory and excitatory integration with a quantum dot laser neuron

Neuromorphic computing has garnered a lot of attention in recent years. Excitable photonic systems in particular demonstrate great potential for ultrafast, controllable spike processing. Optically injected quantum dot lasers display several distinct excitable regimes. We demonstrate here that optically injected dual-state quantum dot lasers can display the classic leaky integrate-and-fire mechanism where the integration of several sub-threshold perturbations can yield an effective supra-threshold perturbation. Intriguingly, a contrasting integrate-and-inhibit mechanism is demonstrated in this work where the integration of two supra-threshold perturbations yields an effective sub-threshold perturbation similar to the pre-pulse inhibition mechanism of biological neurons. This is the first such mechanism in neuromorphic photonics to the best of our knowledge.

Deep optical reservoir computing and chaotic synchronization predictions based on the cascade coupled optically pumped spin-VCSELs

In this work, we utilize two cascade coupling modes (unidirectional coupling and bidirectional coupling) to construct a four-layer deep reservoir computing (RC) system based on the cascade coupled optically-pumped spin-VCSEL. In such a system, there are double sub-reservoirs in each layer, which are formed by the chaotic x-PC and y-PC emitted by the reservoir spin-VCSEL in each layer. Under these two coupling modes, the chaotic x-PC and y-PC emitted by the driving optically-pumped spin-VCSEL (D-Spin-VCSEL), as two learning targets, are predicted by utilizing the four-layer reservoirs. In different parameter spaces, it is further explored that the outputs of the double sub-reservoirs in each layer are respectively synchronized with the chaotic x-PC and y-PC emitted by the D-Spin-VCSEL. The memory capacities (MCs) for the double sub-reservoirs in each layer are even further investigated. The results show that under two coupling modes, the predictions of the double sub-reservoirs with higher-layer for these two targets have smaller errors, denoting that the higher-layer double sub-reservoirs possess better predictive learning ability. Under the same system parameters, the outputs of the higher-layer dual parallel reservoirs are better synchronized with two chaotic PCs emitted by the D-Spin-VCSEL, respectively. The larger MCs can also be obtained by the higher-layer double reservoirs. In particular, compared with the four-layer reservoir computing system under unidirectional coupling, the four-layer reservoir computing system under bidirectional coupling shows better predictive ability in the same parameter space. The chaotic synchronizations predicted by each layer double sub-reservoirs under bidirectional coupling can be obtained higher qualities than those under unidirectional coupling. By the optimization of the system parameters, the outputs of the fourth-layer double sub-reservoirs are almost completely synchronized with the chaotic x-PC and y-PC emitted by the D-Spin-VCSEL, respectively, due to their correlation coefficient used to measure synchronization quality can be obtained as 0.99. These results have potential applications in chaotic computation, chaotic secure communication and accurate prediction of time series.

Inducing optical self-pulsation by electrically tuning graphene on a silicon microring

A mechanism for self-pulsation in a proposed graphene-on-silicon microring device is studied. The relevant nonlinear effects of two photon absorption, Kerr effect, saturable absorption, free carrier absorption, and dispersion are included in a coupled mode theory framework. We look at the electrical tunability of absorption and the Kerr effect in graphene. We show that the microring can switch from a stable rest state to a self-pulsation state by electrically tuning the graphene under constant illumination. This switching is indicative of a supercritical Hopf bifurcation since the frequency of the pulses is approximately constant at 7 GHz and the amplitudes initial grow with increasing Fermi level. The CMOS compatibility of graphene and the opto-electronic mechanism allows this to device to be fairly easily integrated with other silicon photonic devices.

Frequency-switched photonic spiking neurons

We propose an approach to generate neuron-like spikes of vertical-cavity surface-emitting laser (VCSEL) by multi-frequency switching. A stable temporal spiking sequence has been realized both by numerical simulations and experiments with a pulse width of sub-nanosecond, which is 8 orders of magnitude faster than ones from biological neurons. Moreover, a controllable spiking coding scheme using multi-frequency switching is designed and a sequence with 20 symbols is generated at the speed of up to 1 Gbps by experiment. Furthermore, we investigate the factors related to time delay of spiking generation, including injection strength and frequency detuning. With proper manipulation of detuning frequency, the spiking generation delay can be controlled upto 60 ns, which is 6 times longer than the delay controlled by intensity. The multi-frequency switching provides another manipulation dimension for spiking generation and will be helpful to exploit the abundant spatial-temporal features of spiking neural network. We believe the proposed VCSEL-neuron, as a single physical device for generating spiking signals with variable time delay, will pave the way for future photonic spiking neural networks.

What Models and Tools can Contribute to a Better Understanding of Brain Activity?

Despite impressive scientific advances in understanding the structure and function of the human brain, big challenges remain. A deep understanding of healthy and aberrant brain activity at a wide range of temporal and spatial scales is needed. Here we discuss, from an interdisciplinary network perspective, the advancements in physical and mathematical modeling as well as in data analysis techniques that, in our opinion, have potential to further advance our understanding of brain structure and function.

Collective and synchronous dynamics of photonic spiking neurons

Nonlinear dynamics of spiking neural networks have recently attracted much interest as an approach to understand possible information processing in the brain and apply it to artificial intelligence. Since information can be processed by collective spiking dynamics of neurons, the fine control of spiking dynamics is desirable for neuromorphic devices. Here we show that photonic spiking neurons implemented with paired nonlinear optical oscillators can be controlled to generate two modes of bio-realistic spiking dynamics by changing optical-pump amplitude. When the photonic neurons are coupled in a network, the interaction between them induces an effective change in the pump amplitude depending on the order parameter that characterizes synchronization. The experimental results show that the effective change causes spontaneous modification of the spiking modes and firing rates of clustered neurons, and such collective dynamics can be utilized to realize efficient heuristics for solving NP-hard combinatorial optimization problems.

Canard resonance: on noise-induced ordering of trajectories in heterogeneous networks of slow-fast systems

We analyse the dynamics of a network of semiconductor lasers coupled via their mean intensity through a non-linear optoelectronic feedback loop. We establish experimentally the excitable character of a single node, which stems from the slow-fast nature of the system, adequately described by a set of rate equations with three well separated time scales. Beyond the excitable regime, the system undergoes relaxation oscillations where the nodes display canard dynamics. We show numerically that, without noise, the coupled system follows an intricate canard trajectory, with the nodes switching on one by one. While incorporating noise leads to a better correspondence between numerical simulations and experimental data, it also has an unexpected ordering effect on the canard orbit, causing the nodes to switch on closer together in time. We find that the dispersion of the trajectories of the network nodes in phase space is minimized for a non-zero noise strength, and call this phenomenon canard resonance.

Time-Multiplexed Spiking Convolutional Neural Network Based on VCSELs for Unsupervised Image Classification

In this work, we present numerical results concerning a multilayer “deep” photonic spiking convolutional neural network, arranged so as to tackle a 2D image classification task. The spiking neurons used are typical two-section quantum-well vertical-cavity surface-emitting lasers that exhibit isomorphic behavior to biological neurons, such as integrate-and-fire excitability and timing encoding. The isomorphism of the proposed scheme to biological networks is extended by replicating the retina ganglion cell for contrast detection in the photonic domain and by utilizing unsupervised spike dependent plasticity as the main training technique. Finally, in this work we also investigate the possibility of exploiting the fast carrier dynamics of lasers so as to time-multiplex spatial information and reduce the number of physical neurons used in the convolutional layers by orders of magnitude. This last feature unlocks new possibilities, where neuron count and processing speed can be interchanged so as to meet the constraints of different applications.

Asymmetric excitable phase triggering in an optically injected semiconductor laser

One of the defining characteristics of excitability is the existence of an excitable threshold: the minimum perturbation amplitude necessary to produce an excitable response. We analyze an optically injected dual state quantum dot laser, previously shown to display a dual state stochastic excitable dynamic. We show that deterministic triggering of this dynamic can be achieved via optical phase perturbations. Further, we demonstrate that there are in fact two asymmetric excitable thresholds in this system corresponding to the two possible directions of optical phase perturbations. For fast enough perturbations, an excitable interval arises, and there is a limit to the perturbation amplitude, above which excitations no longer arise, a phenomenon heretofore unobserved in studies of excitability.

Photonic spiking neural network based on excitable VCSELs-SA for sound azimuth detection

We propose a photonic spiking neural network (SNN) based on excitable vertical-cavity surface-emitting lasers with an embedded saturable absorber (VCSELs-SA) for emulating the sound azimuth detection function of the brain for the first time. Here, the spike encoding and response properties based on the excitability of VCSELs-SA are employed, and the difference between spike timings of two postsynaptic neurons serves as an indication of sound azimuth. Furthermore, the weight matrix contributing to the successful sound azimuth detection is carefully identified, and the effect of the time interval between two presynaptic spikes is considered. It is found that the weight range that can achieve sound azimuth detection decreases gradually with the increase of the time interval between the sound arriving at the left and right ears. Besides, the effective detection range of the time interval between two presynaptic spikes is also identified, which is similar to that of the biological auditory system, but with a much higher resolution which is at the nanosecond time scale. We further discuss the effect of device variations on the photonic sound azimuth detection. Hence, this photonic SNN is biologically plausible, which has comparable low energy consumption and higher resolution compared with the biological system. This work is valuable for brain-inspired information processing and a promising foundation for more complex spiking information processing implemented by photonic neuromorphic computing systems.

Forecasting Events in the Complex Dynamics of a Semiconductor Laser with Optical Feedback

Complex systems performing spiking dynamics are widespread in Nature. They cover from earthquakes, to neurons, variable stars, social networks, or stock markets. Understanding and characterizing their dynamics is relevant in order to detect transitions, or to predict unwanted extreme events. Here we study, under an ordinal patterns analysis, the output intensity of a semiconductor laser with feedback in a regime where it develops a complex spiking behavior. We unveil that, in the transitions towards and from the spiking regime, the complex dynamics presents two competing behaviors that can be distinguished with a thresholding method. Then we use time and intensity correlations to forecast different types of events, and transitions in the dynamics of the system.

Controlled inhibition of spiking dynamics in VCSELs for neuromorphic photonics: theory and experiments

We report experimentally and theoretically on the controllable inhibition of spiking regimes in a 1300 nm wavelength vertical-cavity surface-emitting laser. Reproducible suppression of spiking dynamics is demonstrated at fast operation speeds (up to sub-ns rates) and with total control on the temporal duration of the spiking inhibition windows. This Letter opens new paths toward a photonic inhibitory neuronal model system for use in future neuromorphic photonic information processing modules and which are able to operate at speeds up to 8 orders of magnitude faster than biological neurons.

Artificial Neuron Based on Integrated Semiconductor Quantum Dot Mode-Locked Lasers

Neuro-inspired implementations have attracted strong interest as a power efficient and robust alternative to the digital model of computation with a broad range of applications. Especially, neuro-mimetic systems able to produce and process spike-encoding schemes can offer merits like high noise-resiliency and increased computational efficiency. Towards this direction, integrated photonics can be an auspicious platform due to its multi-GHz bandwidth, its high wall-plug efficiency and the strong similarity of its dynamics under excitation with biological spiking neurons. Here, we propose an integrated all-optical neuron based on an InAs/InGaAs semiconductor quantum-dot passively mode-locked laser. The multi-band emission capabilities of these lasers allows, through waveband switching, the emulation of the excitation and inhibition modes of operation. Frequency-response effects, similar to biological neural circuits, are observed just as in a typical two-section excitable laser. The demonstrated optical building block can pave the way for high-speed photonic integrated systems able to address tasks ranging from pattern recognition to cognitive spectrum management and multi-sensory data processing.

Multi-channel control for microring weight banks

We demonstrate 4-channel, 2GHz weighted addition in a silicon microring filter bank. Accurate analog weight control becomes more difficult with increasing number of channels, N, as feedback approaches become impractical and brute force feedforward approaches take O(2N) calibration measurements in the presence of inter-channel dependence. We introduce model-based calibration techniques for thermal cross-talk and cross-gain saturation, which result in a scalable O(N) calibration routine and 3.8 bit feedforward weight accuracy on every channel. Practical calibration routines are indispensible for controlling large-scale microring systems. The effect of thermal model complexity on accuracy is discussed. Weighted addition based on silicon microrings can apply the strengths of photonic manufacturing, wideband information processing, and multiwavelength networks towards new paradigms of ultrafast analog distributed processing.

Spike processing with a graphene excitable laser

Novel materials and devices in photonics have the potential to revolutionize optical information processing, beyond conventional binary-logic approaches. Laser systems offer a rich repertoire of useful dynamical behaviors, including the excitable dynamics also found in the time-resolved "spiking" of neurons. Spiking reconciles the expressiveness and efficiency of analog processing with the robustness and scalability of digital processing. We demonstrate a unified platform for spike processing with a graphene-coupled laser system. We show that this platform can simultaneously exhibit logic-level restoration, cascadability and input-output isolation--fundamental challenges in optical information processing. We also implement low-level spike-processing tasks that are critical for higher level processing: temporal pattern detection and stable recurrent memory. We study these properties in the context of a fiber laser system and also propose and simulate an analogous integrated device. The addition of graphene leads to a number of advantages which stem from its unique properties, including high absorption and fast carrier relaxation. These could lead to significant speed and efficiency improvements in unconventional laser processing devices, and ongoing research on graphene microfabrication promises compatibility with integrated laser platforms.

Excitable laser processing network node in hybrid silicon: analysis and simulation

The combination of ultrafast laser dynamics and dense on-chip multiwavelength networking could potentially address new domains of real-time signal processing that require both speed and complexity. We present a physically realistic optoelectronic simulation model of a circuit for dynamical laser neural networks and verify its behavior. We describe the physics, dynamics, and parasitics of one network node, which includes a bank of filters, a photodetector, and excitable laser. This unconventional circuit exhibits both cascadability and fan-in, critical properties for the large-scale networking of information processors based on laser excitability. In addition, it can be instantiated on a photonic integrated circuit platform and requires no off-chip optical I/O. Our proposed processing system could find use in emerging applications, including cognitive radio and low-latency control.

SIMPEL: circuit model for photonic spike processing laser neurons

We propose an equivalent circuit model for photonic spike processing laser neurons with an embedded saturable absorber—a simulation model for photonic excitable lasers (SIMPEL). We show that by mapping the laser neuron rate equations into a circuit model, SPICE analysis can be used as an efficient and accurate engine for numerical calculations, capable of generalization to a variety of different types of laser neurons with saturable absorber found in literature. The development of this model parallels the Hodgkin-Huxley model of neuron biophysics, a circuit framework which brought efficiency, modularity, and generalizability to the study of neural dynamics. We employ the model to study various signal-processing effects such as excitability with excitatory and inhibitory pulses, binary all-or-nothing response, and bistable dynamics.

Effects of periodic forcing on the temporally correlated spikes of a semiconductor laser with feedback

Optical excitable devices that mimic neuronal behavior can be building-blocks of novel, brain-inspired information processing systems. A relevant issue is to understand how such systems represent, via correlated spikes, the information of a weak external input. Semiconductor lasers with optical feedback operating in the low frequency fluctuations regime have been shown to display optical spikes with intrinsic temporal correlations similar to those of biological neurons. Here we investigate how the spiking laser output represents a weak periodic input that is implemented via direct modulation of the laser pump current. We focus on understanding the influence of the modulation frequency. Experimental sequences of inter-spike-intervals (ISIs) are recorded and analyzed by using the ordinal symbolic methodology that identifies and characterizes serial correlations in datasets. The change in the statistics of the various symbols with the modulation frequency is empirically shown to be related to specific changes in the ISI distribution, which arise due to different phase-locking regimes. A good qualitative agreement is also found between simulations of the Lang and Kobayashi model and observations. This methodology is an efficient way to detect subtle changes in noisy correlated ISI sequences and may be applied to investigate other optical excitable devices.

Excitation transfer between optically injected microdisk lasers

Recently, we have theoretically demonstrated that optically injected microdisk lasers can be tuned in a class I excitable regime, where they are sensitive to both inhibitory and excitatory external input pulses. In this paper, we propose, using simulations, a topology that allows the disks to react on excitations from other disks. Phase tuning of the intermediate connections allows to control the disk response. Additionally, we investigate the sensitivity of the disk circuit to deviations in driving current and locking signal wavelength detuning. Using state-of-the-art fabrication techniques for microdisk laser, the standard deviation of the lasing wavelength is still about one order of magnitude too large. Therefore, compensation techniques, such as wavelength tuning by heating, are necessary.

Excitability in optically injected microdisk lasers with phase controlled excitatory and inhibitory response

We demonstrate class I excitability in optically injected microdisk lasers, and propose a possible optical spiking neuron design. The neuron has a clear threshold and an integrating behavior, leading to an output rate-input rate dependency that is comparable to the characteristic of sigmoidal artificial neurons. We also show that the optical phase of the input pulses has influence on the neuron response, and can be used to create inhibitory, as well as excitatory perturbations.

On-chip optical phase locking of single growth monolithically integrated Slotted Fabry Perot lasers

This work investigates the optical phase locking performance of Slotted Fabry Perot (SFP) lasers and develops an integrated variable phase locked system on chip for the first time to our knowledge using these lasers. Stable phase locking is demonstrated between two SFP lasers coupled on chip via a variable gain waveguide section. The two lasers are biased differently, one just above the threshold current of the device with the other at three times this value. The coupling between the lasers can be controlled using the variable gain section which can act as a variable optical attenuator or amplifier depending on bias. Using this, the width of the stable phase locking region on chip is shown to be variable.

Dynamics of one-dimensional Kerr cavity solitons

We present an experimental observation of an oscillating Kerr cavity soliton, i.e., a time-periodic oscillating one-dimensional temporally localized structure excited in a driven nonlinear fiber cavity with a Kerr-type nonlinearity. More generally, these oscillations result from a Hopf bifurcation of a (spatially or temporally) localized state in the generic class of driven dissipative systems close to the 1 : 1 resonance tongue. Furthermore, we theoretically analyze dynamical instabilities of the one-dimensional cavity soliton, revealing oscillations and different chaotic states in previously unexplored regions of parameter space. As cavity solitons are closely related to Kerr frequency combs, we expect these dynamical regimes to be highly relevant for the field of microresonator-based frequency combs.

Cascadable excitability in microrings

To emulate a spiking neuron, a photonic component needs to be excitable. In this paper, we theoretically simulate and experimentally demonstrate cascadable excitability near a self-pulsation regime in high-Q-factor silicon-on-insulator microrings. For the theoretical study we use Coupled Mode Theory. While neglecting the fast energy and phase dynamics of the cavity light, we can still preserve the most important microring dynamics, by only keeping the temperature difference with the surroundings and the amount of free carriers as dynamical variables of the system. Therefore we can analyse the microring dynamics in a 2D phase portrait. For some wavelengths, when changing the input power, the microring undergoes a subcritical Andronov-Hopf bifurcation at the self-pulsation onset. As a consequence the system shows class II excitability. Experimental single ring excitability and self-pulsation behaviour follows the theoretic predictions. Moreover, simulations and experiments show that this excitation mechanism is cascadable.