Relative refractory period in an excitable semiconductor laser

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.

Controllable non-uniformly distributed spiking cluster generation in broadband optoelectronic oscillator

An approach to achieve controllable non-uniformly distributed spiking cluster generation is proposed and demonstrated based on an externally-triggered broadband optoelectronic oscillator (OEO). The theory of controlling the distribution of the spiking pulses in a spiking cluster is established. Based on the theory, the dynamic and the distribution characteristics are analyzed and revealed in the stable spiking oscillation state under different externally-injected trigger signal voltages. The peak-voltage envelop of the cluster and the interval of the spiking pulses are demonstrated to have an approximate negative linearity relationship with the externally-injected trigger signal voltage in both the numerical simulation and the experiment, where a square waveform, a trapezoidal waveform, a parabola waveform, and a half-sinusoidal waveform are used as the externally-injected trigger signals. The results indicate that the spiking pulse distribution in the generated spiking cluster can be well controlled through tuning the externally-injected trigger signal voltage. The proposed scheme can be utilized in spiking encoding and reservoir computing.

Uniform spike trains in optically injected quantum cascade oscillators

It has been experimentally and theoretically analyzed that noise-induced excitability in quantum well and quantum dot semiconductor laser systems usually produces sharp spike patterns of non-uniform amplitude. In this paper, we experimentally record that a quantum cascade oscillator injected externally with a monochromatic laser beam exhibits a series of highly uniform spike trains, which occur in the proximity of the saddle-node bifurcation. Theoretical analysis based on a properly designed single-mode rate equation model endowed with quantum noise reveals that this high uniformity has its primary origin in the ultrashort carrier lifetime of the quantum cascade laser gain medium that is typically close to 1 ps.

Online spike-based recognition of digits with ultrafast microlaser neurons

Classification and recognition tasks performed on photonic hardware-based neural networks often require at least one offline computational step, such as in the increasingly popular reservoir computing paradigm. Removing this offline step can significantly improve the response time and energy efficiency of such systems. We present numerical simulations of different algorithms that utilize ultrafast photonic spiking neurons as receptive fields to allow for image recognition without an offline computing step. In particular, we discuss the merits of event, spike-time and rank-order based algorithms adapted to this system. These techniques have the potential to significantly improve the efficiency and effectiveness of optical classification systems, minimizing the number of spiking nodes required for a given task and leveraging the parallelism offered by photonic hardware.

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.

Merging and disconnecting resonance tongues in a pulsing excitable microlaser with delayed optical feedback

Excitability, encountered in numerous fields from biology to neurosciences and optics, is a general phenomenon characterized by an all-or-none response of a system to an external perturbation of a given strength. When subject to delayed feedback, excitable systems can sustain multistable pulsing regimes, which are either regular or irregular time sequences of pulses reappearing every delay time. Here, we investigate an excitable microlaser subject to delayed optical feedback and study the emergence of complex pulsing dynamics, including periodic, quasiperiodic, and irregular pulsing regimes. This work is motivated by experimental observations showing these different types of pulsing dynamics. A suitable mathematical model, written as a system of delay differential equations, is investigated through an in-depth bifurcation analysis. We demonstrate that resonance tongues play a key role in the emergence of complex dynamics, including non-equidistant periodic pulsing solutions and chaotic pulsing. The structure of resonance tongues is shown to depend very sensitively on the pump parameter. Successive saddle transitions of bounding saddle-node bifurcations constitute a merging process that results in unexpectedly large regions of locked dynamics, which subsequently disconnect from the relevant torus bifurcation curve; the existence of such unconnected regions of periodic pulsing is in excellent agreement with experimental observations. As we show, the transition to unconnected resonance regions is due to a general mechanism: the interaction of resonance tongues locally at an extremum of the rotation number on a torus bifurcation curve. We present and illustrate the two generic cases of disconnecting and disappearing resonance tongues. Moreover, we show how a pair of a maximum and a minimum of the rotation number appears naturally when two curves of torus bifurcation undergo a saddle transition (where they connect differently).

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.

Photonic spiking neural networks with event-driven femtojoule optoelectronic neurons based on Izhikevich-inspired model

Photonic spiking neural networks (PSNNs) potentially offer exceptionally high throughput and energy efficiency compared to their electronic neuromorphic counterparts while maintaining their benefits in terms of event-driven computing capability. While state-of-the-art PSNN designs require a continuous laser pump, this paper presents a monolithic optoelectronic PSNN hardware design consisting of an MZI mesh incoherent network and event-driven laser spiking neurons. We designed, prototyped, and experimentally demonstrated this event-driven neuron inspired by the Izhikevich model incorporating both excitatory and inhibitory optical spiking inputs and producing optical spiking outputs accordingly. The optoelectronic neurons consist of two photodetectors for excitatory and inhibitory optical spiking inputs, electrical transistors' circuits providing spiking nonlinearity, and a laser for optical spiking outputs. Additional inclusion of capacitors and resistors complete the Izhikevich-inspired optoelectronic neurons, which receive excitatory and inhibitory optical spikes as inputs from other optoelectronic neurons. We developed a detailed optoelectronic neuron model in Verilog-A and simulated the circuit-level operation of various cases with excitatory input and inhibitory input signals. The experimental results closely resemble the simulated results and demonstrate how the excitatory inputs trigger the optical spiking outputs while the inhibitory inputs suppress the outputs. The nanoscale neuron designed in our monolithic PSNN utilizes quantum impedance conversion. It shows that estimated 21.09 fJ/spike input can trigger the output from on-chip nanolasers running at a maximum of 10 Gspike/second in the neural network. Utilizing the simulated neuron model, we conducted simulations on MNIST handwritten digits recognition using fully connected (FC) and convolutional neural networks (CNN). The simulation results show 90% accuracy on unsupervised learning and 97% accuracy on a supervised modified FC neural network. The benchmark shows our PSNN can achieve 50 TOP/J energy efficiency, which corresponds to 100 × throughputs and 1000 × energy-efficiency improvements compared to state-of-art electrical neuromorphic hardware such as Loihi and NeuroGrid.

Influence of time-delayed feedback on the dynamics of temporal localized structures in passively mode-locked semiconductor lasers

In this paper, we analyze the effect of optical feedback on the dynamics of a passively mode-locked ring laser operating in the regime of temporal localized structures. This laser system is modeled by a set of delay differential equations, which include delay terms associated with the laser cavity and the feedback loop. Using a combination of direct numerical simulations and path-continuation techniques, we show that the feedback loop creates echoes of the main pulse whose position and size strongly depend on the feedback parameters. We demonstrate that in the long-cavity regime, these echoes can successively replace the main pulses, which defines their lifetime. This pulse instability mechanism originates from a global bifurcation of the saddle-node infinite-period type. In addition, we show that, under the influence of noise, the stable pulses exhibit forms of a behavior characteristic of excitable systems. Furthermore, for the harmonic solutions consisting of multiple equispaced pulses per round-trip, we show that if the location of the pulses coincides with the echo of another, the range of stability of these solutions is increased. Finally, it is shown that around these resonances, branches of different solutions are connected by period-doubling bifurcations.

Photonic matrix multiplication lights up photonic accelerator and beyond

Matrix computation, as a fundamental building block of information processing in science and technology, contributes most of the computational overheads in modern signal processing and artificial intelligence algorithms. Photonic accelerators are designed to accelerate specific categories of computing in the optical domain, especially matrix multiplication, to address the growing demand for computing resources and capacity. Photonic matrix multiplication has much potential to expand the domain of telecommunication, and artificial intelligence benefiting from its superior performance. Recent research in photonic matrix multiplication has flourished and may provide opportunities to develop applications that are unachievable at present by conventional electronic processors. In this review, we first introduce the methods of photonic matrix multiplication, mainly including the plane light conversion method, Mach-Zehnder interferometer method and wavelength division multiplexing method. We also summarize the developmental milestones of photonic matrix multiplication and the related applications. Then, we review their detailed advances in applications to optical signal processing and artificial neural networks in recent years. Finally, we comment on the challenges and perspectives of photonic matrix multiplication and photonic acceleration.

Computing Primitive of Fully VCSEL-Based All-Optical Spiking Neural Network for Supervised Learning and Pattern Classification

We propose computing primitive for an all-optical spiking neural network (SNN) based on vertical-cavity surface-emitting lasers (VCSELs) for supervised learning by using biologically plausible mechanisms. The spike-timing-dependent plasticity (STDP) model was established based on the dynamics of the vertical-cavity semiconductor optical amplifier (VCSOA) subject to dual-optical pulse injection. The neuron-synapse self-consistent unified model of the all-optical SNN was developed, which enables reproducing the essential neuron-like dynamics and STDP function. Optical character numbers are trained and tested by the proposed fully VCSEL-based all-optical SNN. Simulation results show that the proposed all-optical SNN is capable of recognizing ten numbers by a supervised learning algorithm, in which the input and output patterns as well as the teacher signals of the all-optical SNN are represented by spatiotemporal fashions. Moreover, the lateral inhibition is not required in our proposed architecture, which is friendly to the hardware implementation. The system-level unified model enables architecture-algorithm codesigns and optimization of all-optical SNN. To the best of our knowledge, the computing primitive of an all-optical SNN based on VCSELs for supervised learning has not yet been reported, which paves the way toward fully VCSEL-based large-scale photonic neuromorphic systems with low power consumption.

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.

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.

Pulse-timing symmetry breaking in an excitable optical system with delay

Excitable systems with delayed feedback are important in areas from biology to neuroscience and optics. They sustain multistable pulsing regimes with different numbers of equidistant pulses in the feedback loop. Experimentally and theoretically, we report on the pulse-timing symmetry breaking of these regimes in an optical system. A bifurcation analysis unveils that this originates in a resonance phenomenon and that symmetry-broken states are stable in large regions of the parameter space. These results have impact in photonics for, e.g., optical computing and versatile sources of optical pulses.

Pulse propagation in a 1D array of excitable semiconductor lasers

Nonlinear pulse propagation is a major feature in continuously extended excitable systems. The persistence of this phenomenon in coupled excitable systems is expected. Here, we investigate theoretically the propagation of nonlinear pulses in a 1D array of evanescently coupled excitable semiconductor lasers. We show that the propagation of pulses is characterized by a hopping dynamics. The average pulse speed and bifurcation diagram are characterized as a function of the coupling strength between the lasers. Several instabilities are analyzed such as the onset and disappearance of pulse propagation and a spontaneous breaking of the translation symmetry. The pulse propagation modes evidenced are specific to the discrete nature of the 1D array of excitable lasers.

Effective low-dimensional dynamics of a mean-field coupled network of slow-fast spiking lasers

Low-dimensional dynamics of large networks is the focus of many theoretical works, but controlled laboratory experiments are comparatively very few. Here, we discuss experimental observations on a mean-field coupled network of hundreds of semiconductor lasers, which collectively display effectively low-dimensional mixed mode oscillations and chaotic spiking typical of slow-fast systems. We demonstrate that such a reduced dimensionality originates from the slow-fast nature of the system and of the existence of a critical manifold of the network where most of the dynamics takes place. Experimental measurement of the bifurcation parameter for different network sizes corroborates the theory.

All-optical neuromorphic XOR operation with inhibitory dynamics of a single photonic spiking neuron based on a VCSEL-SA

We propose a simple hardware architecture for solving exclusive OR (XOR) tasks in a single step by using a single photonic spiking neuron based on vertical-cavity surface-emitting lasers with an embedded saturable absorber (VCSEL-SA) subject to dual-polarized pulsed optical injection. We model the inhibitory photonic spiking neuron by extending the Yamada model and spin-flip model to incorporate the two polarization-resolved modes and the saturable absorber. It is shown that, by carefully adjusting the temporal difference according to the inhibitory window, the XOR operation can be realized in a single photonic spiking neuron, which is interesting and valuable for the photonic neuromorphic computing and information processing.

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.

All-optical inhibitory dynamics in photonic neuron based on polarization mode competition in a VCSEL with an embedded saturable absorber

An all-optical spike inhibition scheme based on polarization-mode competition (PMC) in a vertical-cavity surface-emitting laser (VCSEL) with an embedded saturable absorber is proposed and investigated numerically. The inhibitory dynamics is characterized by spike amplitude and first-spike latency (FSL) for the first time, to the best of our knowledge. The effects of time differences between inhibitory and excitatory inputs, inputs strengths, bias current, as well as noise on the spike amplitude and FSL are examined. The results show that a spike can be triggered in the y-polarization mode by excitatory input and can be inhibited in the presence of inhibitory input due to PMC.

Square wave excitability in quantum dot lasers under optical injection

Quantum dot lasers display many unique dynamic phenomena when optically injected. Bistability has been predicted in a region of high injection strength. Experimentally, we show that a square wave phenomenon, rather than a phase-locked bistability, is observed in this region. The squares can manifest as a periodic train but also as noise-driven Type II excitable events. We interpret the appearance of the square waves as a thermally induced breaking of the bistability. Indeed, we find experimentally that over the duration of a square, the relative detuning between the master and the slave evolves deterministically. A relatively simple, physically motivated, rate equation model is presented and displays excellent agreement with the experiment.

Polarization-resolved and polarization- multiplexed spike encoding properties in photonic neuron based on VCSEL-SA

The spike encoding properties of two polarization-resolved modes in vertical-cavity surface-emitting laser with an embedded saturable absorber (VCSEL-SA) are investigated numerically, based on the spin-flip model combined with the Yamada model. The results show that the external input optical pulse (EIOP) can be encoded into spikes in X-polarization (XP) mode, Y-polarization (YP) mode, or both XP and YP modes. Furthermore, the numerical bifurcation diagrams show that a lower (higher) strength of EIOP is beneficial for generating tonic (phasic) spikes; a small amplitude anisotropy contributes to wide (narrow) tonic spiking range in XP (YP) mode; a large current leads to low thresholds of EIOP strength for both XP and YP modes. However, the spike encoding properties are hardly affected by the phase anisotropy. The encoding rate is shown to be improved by increasing EIOP strength. Moreover, dual-channel polarization-multiplexed spike encoding can also be achieved in a single VCSEL-SA. To the best of our knowledge, such single channel polarization-resolved and dual-channel polarization-multiplexed spike encoding schemes have not yet been reported. Hence, this work is valuable for ultrafast photonic neuromorphic systems and brain-inspired information processing.

Feedback control for microring weight banks

Microring weight banks present novel opportunities for reconfigurable, high-performance analog signal processing in photonics. Controlling microring filter response is a challenge due to fabrication variations and thermal sensitivity. Prior work showed continuous weight control of multiple wavelength-division multiplexed signals in a bank of microrings based on calibration and feedforward control. Other prior work has shown resonance locking based on feedback control by monitoring photoabsorption-induced changes in resistance across in-ring photoconductive heaters. In this work, we demonstrate continuous, multi-channel control of a microring weight bank with an effective 5.1 bits of accuracy on 2Gbps signals. Unlike resonance locking, the approach relies on an estimate of filter transmission versus photo-induced resistance changes. We introduce an estimate still capable of providing 4.2 bits of accuracy without any direct transmission measurements. Furthermore, we present a detailed characterization of this response for different values of carrier wavelength offset and power. Feedback weight control renders tractable the weight control problem in reconfigurable analog photonic networks.

Simultaneous excitatory and inhibitory dynamics in an excitable laser

Neocortical systems encode information in electrochemical spike timings, not just mean firing rates. Learning and memory in networks of spiking neurons is achieved by the precise timing of action potentials that induces synaptic strengthening (with excitation) or weakening (with inhibition). Inhibition should be incorporated into brain-inspired spike processing in the optical domain to enhance its information-processing capability. We demonstrate the simultaneous excitatory and inhibitory dynamics in an excitable (i.e., a pulsed) laser neuron, both numerically and experimentally. We investigate the bias strength effect, inhibitory strength effect, and excitatory and inhibitory input timing effect, based on the simulation platform of an integrated graphene excitable laser. We further corroborate these analyses with proof-of-principle experiments utilizing a fiber-based graphene excitable laser, where we introduce inhibition by directly modulating the gain of the laser. This technology may potentially open novel spike-processing functionality for future neuromorphic photonic systems.

Pulse train interaction and control in a microcavity laser with delayed optical feedback

We report experimental and theoretical results on the pulse train dynamics in an excitable semiconductor microcavity laser with an integrated saturable absorber and delayed optical feedback. We show how short optical control pulses can trigger, erase, or retime regenerative pulse trains in the external cavity. Both repulsive and attractive interactions between pulses are observed, and are explained in terms of the internal dynamics of the carriers. A bifurcation analysis of a model consisting of a system of nonlinear delay differential equations shows that arbitrary sequences of coexisting pulse trains are very long transients towards weakly stable periodic solutions with equidistant pulses in the external cavity.

Two distinct excitable responses for a laser with a saturable absorber

Excitable lasers with saturable absorbers are currently investigated as potential candidates for low level spike processing tasks in integrated optical platforms. Following a small perturbation of a stable equilibrium, a single and intense laser pulse can be generated before returning to rest. Motivated by recent experiments [Selmi et al., Phys. Rev. E 94, 042219 (2016)10.1103/PhysRevE.94.042219], we consider the rate equations for a laser containing a saturable absorber (LSA) and analyze the effects of different initial perturbations. With its three steady states and following Hodgkin classification, the LSA is a Type I excitable system. By contrast to perturbations on the intensity leading to the same intensity pulse, perturbations on the gain generate pulses of different amplitudes. We explain these distinct behaviors by analyzing the slow-fast dynamics of the laser in each case. We first consider a two-variable LSA model for which the conditions of excitability can be explored in the phase plane in a transparent manner. We then concentrate on the full three variable LSA equations and analyze its solutions near a degenerate steady bifurcation point. This analysis generalizes previous results [Dubbeldam et al., Phys. Rev. E 60, 6580 (1999)1063-651X10.1103/PhysRevE.60.6580] for unequal carrier density rates. Last, we discuss a fundamental difference between neuron and laser models.

Delay dynamics of neuromorphic optoelectronic nanoscale resonators: Perspectives and applications

With the recent exponential growth of applications using artificial intelligence (AI), the development of efficient and ultrafast brain-like (neuromorphic) systems is crucial for future information and communication technologies. While the implementation of AI systems using computer algorithms of neural networks is emerging rapidly, scientists are just taking the very first steps in the development of the hardware elements of an artificial brain, specifically neuromorphic microchips. In this review article, we present the current state of the art of neuromorphic photonic circuits based on solid-state optoelectronic oscillators formed by nanoscale double barrier quantum well resonant tunneling diodes. We address, both experimentally and theoretically, the key dynamic properties of recently developed artificial solid-state neuron microchips with delayed perturbations and describe their role in the study of neural activity and regenerative memory. This review covers our recent research work on excitable and delay dynamic characteristics of both single and autaptic (delayed) artificial neurons including all-or-none response, spike-based data encoding, storage, signal regeneration and signal healing. Furthermore, the neural responses of these neuromorphic microchips display all the signatures of extended spatio-temporal localized structures (LSs) of light, which are reviewed here in detail. By taking advantage of the dissipative nature of LSs, we demonstrate potential applications in optical data reconfiguration and clock and timing at high-speeds and with short transients. The results reviewed in this article are a key enabler for the development of high-performance optoelectronic devices in future high-speed brain-inspired optical memories and neuromorphic computing.

Two-color bursting oscillations

Neurons communicate by brief bursts of spikes separated by silent phases and information may be encoded into the burst duration or through the structure of the interspike intervals. Inspired by the importance of bursting activities in neuronal computation, we have investigated the bursting oscillations of an optically injected quantum dot laser. We find experimentally that the laser periodically switches between two distinct operating states with distinct optical frequencies exhibiting either fast oscillatory or nearly steady state evolutions (two-color bursting oscillations). The conditions for their emergence and their control are analyzed by systematic simulations of the laser rate equations. By projecting the bursting solution onto the bifurcation diagram of a fast subsystem, we show how a specific hysteresis phenomenon explains the transitions between active and silent phases. Since size-controlled bursts can contain more information content than single spikes our results open the way to new forms of neuron inspired optical communication.

Neuromorphic photonic networks using silicon photonic weight banks

Photonic systems for high-performance information processing have attracted renewed interest. Neuromorphic silicon photonics has the potential to integrate processing functions that vastly exceed the capabilities of electronics. We report first observations of a recurrent silicon photonic neural network, in which connections are configured by microring weight banks. A mathematical isomorphism between the silicon photonic circuit and a continuous neural network model is demonstrated through dynamical bifurcation analysis. Exploiting this isomorphism, a simulated 24-node silicon photonic neural network is programmed using “neural compiler” to solve a differential system emulation task. A 294-fold acceleration against a conventional benchmark is predicted. We also propose and derive power consumption analysis for modulator-class neurons that, as opposed to laser-class neurons, are compatible with silicon photonic platforms. At increased scale, Neuromorphic silicon photonics could access new regimes of ultrafast information processing for radio, control, and scientific computing.

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.

Refractory period of an excitable semiconductor laser with optical injection

Injection-locked semiconductor lasers can be brought to a neuronlike excitable regime when parameters are set close to the unlocking transition. Here we study experimentally the response of this system to repeated optical perturbations and observe the existence of a refractory period during which perturbations are not able to elicit an excitable response. The results are analyzed via simulations of a set of dynamical equations which reproduced adequately the experimental results.

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.

Correlations in electrically coupled chaotic lasers

We show how two electrically coupled semiconductor lasers having optical feedback can present simultaneous antiphase correlated fast power fluctuations, and strong in-phase synchronized spikes of chaotic power drops. This quite counterintuitive phenomenon is demonstrated experimentally and confirmed by numerical solutions of a deterministic dynamical system of rate equations. The occurrence of negative and positive cross correlation between parts of a complex system according to time scales, as proved in our simple arrangement, is relevant for the understanding and characterization of collective properties in complex networks.

Spike latency and response properties of an excitable micropillar laser

We present experimental measurements concerning the response of an excitable micropillar laser with saturable absorber to incoherent as well as coherent perturbations. The excitable response is similar to the behavior of spiking neurons but with much faster time scales. It is accompanied by a subnanosecond nonlinear delay that is measured for different bias pump values. This mechanism provides a natural scheme for encoding the strength of an ultrafast stimulus in the response delay of excitable spikes (temporal coding). Moreover, we demonstrate coherent and incoherent perturbations techniques applied to the micropillar with perturbation thresholds in the range of a few femtojoules. Responses to coherent perturbations assess the cascadability of the system. We discuss the physical origin of the responses to single and double perturbations with the help of numerical simulations of the Yamada model and, in particular, unveil possibilities to control the relative refractory period that we recently evidenced in this system. Experimental measurements are compared to both numerical simulations of the Yamada model and analytic expressions obtained in the framework of singular perturbation techniques. This system is thus a good candidate to perform photonic spike processing tasks in the framework of novel neuroinspired computing systems.

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.

Regenerative memory in time-delayed neuromorphic photonic resonators

We investigate a photonic regenerative memory based upon a neuromorphic oscillator with a delayed self-feedback (autaptic) connection. We disclose the existence of a unique temporal response characteristic of localized structures enabling an ideal support for bits in an optical buffer memory for storage and reshaping of data information. We link our experimental implementation, based upon a nanoscale nonlinear resonant tunneling diode driving a laser, to the paradigm of neuronal activity, the FitzHugh-Nagumo model with delayed feedback. This proof-of-concept photonic regenerative memory might constitute a building block for a new class of neuron-inspired photonic memories that can handle high bit-rate optical signals.

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.

Spatiotemporal Chaos Induces Extreme Events in an Extended Microcavity Laser

Extreme events such as rogue waves in optics and fluids are often associated with the merging dynamics of coherent structures. We present experimental and numerical results on the physics of extreme event appearance in a spatially extended semiconductor microcavity laser with an intracavity saturable absorber. This system can display deterministic irregular dynamics only, thanks to spatial coupling through diffraction of light. We have identified parameter regions where extreme events are encountered and established the origin of this dynamics in the emergence of deterministic spatiotemporal chaos, through the correspondence between the proportion of extreme events and the dimension of the strange attractor.

Temporal summation in a neuromimetic micropillar laser

Neuromimetic systems are systems mimicking the functionalities or architecture of biological neurons and may present an alternative path for efficient computing and information processing. We demonstrate here experimentally temporal summation in a neuromimetic micropillar laser with an integrated saturable absorber. Temporal summation is the property of neurons to integrate delayed input stimuli and to respond by an all-or-none kind of response if the inputs arrive in a sufficiently small time window. Our system alone may act as a fast optical coincidence detector and paves the way to fast photonic spike-processing networks.

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.

Optical spike-timing-dependent plasticity with weight-dependent learning window and reward modulation

Optical spike-timing-dependent plasticity (STDP) synapses form the basis of learning in photonic neuromorphic system. In biological neural systems, STDP synapses generally have multiplicative boundary mechanisms, and can be modulated by a third factor such as dopamine. Analogously, we introduce a third factor into optical STDP: The current-injection of semiconductor optical amplifiers can be modified in an adaptive way according to local or global feedback signals. The local one is present synaptic weight, which elicits an optical weight-dependent STDP, while the global one is a reward signal. We demonstrate that the optical weight-dependent STDP can emulate the behavior of biological STDP synapses more closely, and can be seen as an intermediate configuration between additive and multiplicative STDP, which balances stability and competition among synapses. Simulation studies with scalable photonic neurons further show that optical STDP with reward modulation enables reward-based reinforcement learning.

Demonstration of WDM weighted addition for principal component analysis

We consider an optical technique for performing tunable weighted addition using wavelength-division multiplexed (WDM) inputs, the enabling function of a recently proposed photonic spike processing architecture [J. Lightwave Technol., 32 (2014)]. WDM weighted addition provides important advantages to performance, integrability, and networking capability that were not possible in any past approaches to optical neurocomputing. In this letter, we report a WDM weighted addition prototype used to find the first principal component of a 1Gbps, 8-channel signal. Wideband, multivariate techniques have immediate relevance to modern radio systems, and photonic spike processing networks enabled by WDM could open new domains of information processing that bring unprecedented bandwidth and intelligence to problems in radio communications, ultrafast control, and scientific computing.

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.