Toward Neuromorphic Photonic Networks of Ultrafast Spiking Laser Neurons

Xiang S., Zhang Y., Gong J., Guo X., Lin L., Hao Y.

We propose a photonic spiking neural network (SNN) consisting of photonic spiking neurons based on vertical-cavity surface-emitting lasers (VCSELs). The photonic spike timing dependent plasticity (STDP) is implemented in a vertical-cavity semiconductor optical amplifier (VCSOA). A versatile computational model of the photonic SNN is presented based on the rate equation models. Through numerical simulation, a spike pattern learning and recognition task is performed based on the photonic STDP. The results show that the post-synaptic spike timing (PST) is eventually converged iteratively to the first spike timing of the input spike pattern via unsupervised learning. Additionally, the convergence rate of the PST can be accelerated for a photonic SNN with more pre-synaptic neurons. The effects of VCSOA parameters on the convergence performance of the unsupervised spike learning are also considered. To the best of our knowledge, such a versatile computational model of photonic SNN for unsupervised learning and recognition of arbitrary spike pattern has not yet been reported, which would contribute one step forward toward numerical implementation of a large-scale energy-efficient photonic SNN, and hence is interesting for neuromorphic photonic systems and spiking information processing.

Robertson J., Wade E., Hurtado A.

We report experimentally on the electrically controlled, tunable, and repeatable neuron-like spiking regimes generated in an optically injected vertical-cavity surface-emitting laser (VCSEL) operating at the telecom wavelength of 1300 nm. These fast spiking dynamics (obtained at sub-nanosecond speed rates) demonstrate different behaviors observed in biological neurons such as thresholding, phasic and tonic spiking, and spike rate and spike latency coding. The spiking regimes are activated in response to external stimuli (with controlled strengths and temporal duration) encoded in the bias current applied to a VCSEL subject to continuous wave optical injection. These results reveal the prospect for fast (>7 orders of magnitude faster than neurons), novel, electrically controlled spiking photonic modules for future neuromorphic computing platforms.

Zhang Y., Xiang S., Guo X., Wen A., Hao Y.

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.

Dolcemascolo A., Garbin B., Peyce B., Veltz R., Barland S.

Semiconductor lasers with coherent forcing are expected to behave similarly to simple neuron models in response to external perturbations, as long as the physics describing them can be approximated by that of an overdamped pendulum with fluid torque. Beyond the validity range of this approximation, more complex features can be expected. We perform experiments and numerical simulations which show that the system can display resonator and integrator features depending on parameters and that multiple pulses can be emitted in response to larger perturbations.

Xiang S., Gong J., Zhang Y., Guo X., Han Y., Wen A., Hao Y.

We propose to realize photonic spike timing dependent plasticity (STDP) by using a vertical-cavity semiconductor optical amplifier (VCSOA) subject to dual optical pulse injections. The computational model of the photonic STDP is presented for the first time based on the well-known Fabry-Pérot approach. Through numerical simulations, the dependences of photonic STDP on the bias current of VCSOA and the input powers are analyzed carefully. Besides, the effect of the initial wavelength detuning on the photonic STDP is also explored. It is found that, the current scheme requires much lower bias current and input power to obtain controllable STDP curve when compared with the previously reported photonic STDP circuits; the initial wavelength detuning is an effectively controllable parameter to realize wavelength-dependent photonic STDP. The computational model of the photonic STDP based on a VCSOA is interesting and valuable for numerically simulating of large-scale photonic spiking neural network, and provides a guideline to design low power consumption photonic neuromorphic systems.

Deng T., Robertson J., Wu Z., Xia G., Lin X., Tang X., Wang Z., Hurtado A.

We investigate experimentally and theoretically the communication of inhibited spiking dynamics between two interlinked photonic neurons based upon the vertical-cavity surface-emitting lasers (VCSELs). We show that the sub-nanosecond speed spiking dynamics fired by a Transmitter-VCSEL (T-VCSEL) can be inhibited under the arrival of suitable external stimuli and that the inhibited spiking behaviors are propagated into another Receiver-VCSEL (R-VCSEL). Both VCSELs exhibit analogous inhibited spiking dynamics in response to stimuli with different temporal durations and strength. In addition, a very good agreement is found between theoretical simulations and experiments. These results offer greater prospects for future networks of VCSEL-based photonic neurons for neuromorphic computing platforms.

Zhang Y., Xiang S., Guo X., Wen A., Hao Y.

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.

Xiang S., Zhang Y., Guo X., Wen A., Hao Y.

We propose to generate excitatory and inhibitory neuron-like dynamics in vertical-cavity surface-emitting lasers (VCSELs) by applying simultaneously the orthogonally-polarized CW optical injection (OPCWOI) and parallelly-polarized pulse optical injection stimulus. Based on the spin flip model, excitatory and inhibitory neuron-like dynamics accompanying with reverse polarization switching is numerically investigated. It is found that, due to the injection locking effect or beating effect between two injected fields, the excitatory phasic and tonic spiking dynamics can be obtained in the originally dominated polarization mode. Moreover, the unwanted relaxation oscillation followed by the excitatory spiking dynamics at the end of the stimulus pulse, which is present in previous reported photonic neuron based on the VCSELs subject to a single orthogonally-polarized optical pulse injection, can be completely suppressed. In addition, the inhibition of tonic spiking dynamics can also be achieved, and the transition from tonic spiking dynamics to phasic bursting dynamics can be obtained, when the two injected fields have the same frequency. These results are interesting and valuable for the ultrafast photonic neuromorphic systems and neuron-inspired photonic information processing.

Zhang Y., Xiang S., Gong J., Guo X., Wen A., Hao Y.

The generation and storage properties of different spike codes in vertical-cavity surface-emitting lasers with an embedded saturable absorber (VCSELs-SA) are investigated numerically. The results show that different spike codes are generated by injecting an optical pulse into one single VCSEL-SA and can be stored in two mutually coupled VCSELs-SA. In particular, in the case of the generation of spike codes, the effects of the input strength and the temporal duration of the input optical pulse are studied; in the case of the storage of spike codes, the roles of the coupling weight and the coupling delay between the two mutually coupled VCSELs-SA are examined. Simulations reveal that spikes can be triggered if the input strength and the temporal duration exceed the threshold values, and higher values of the input strength and the temporal duration are beneficial for generating more spikes. Moreover, successful storage of a perfectly formed train of spike codes in two mutually coupled VCSELs-SA can also be realized provided that the coupling weight and the coupling delay are larger than the corresponding threshold values.

Shastri B.J., Tait A.N., Ferreira de Lima T., Nahmias M.A., Peng H., Prucnal P.R.

Romeira B., Figueiredo J.M., Javaloyes J.

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.

Deng T., Robertson J., Hurtado A.

We report experimentally and in theory on the controllable propagation of spiking regimes between two interlinked vertical-cavity surface-emitting lasers (VCSELs). We show that spiking patterns generated in a first transmitter VCSEL (T-VCSEL) are communicated to a second receiver VCSEL (R-VCSEL), which responds by firing the same spiking response. Importantly, the spiking regimes from both devices had analogous temporal and amplitude characteristics, including equal number of spikes fired, same spike and interspike temporal durations, and similar spike intensity properties. These responses are analogous to the spiking communication patterns of biological neurons yet at subnanosecond speeds, this is several (up to 8) orders of magnitude faster than the timescales of biological neurons. We have also carried out numerical simulations reproducing with high degree of agreement the experimental findings. These results obtained with inexpensive, commercially available VCSELs operating at important telecom wavelengths (1300 nm) offer great prospects for the scaling of emerging VCSEL-based photonic neuronal models into network configurations for use in novel neuromorphic photonic systems. This offers high potentials for nontraditional computing paradigms beyond digital systems and able to operate at ultrafast speeds.

Xiang S.Y., Zhang H., Guo X.X., Li J.F., Wen A.J., Pan W., Hao Y.

The cascadability of spiking dynamics in coupled vertical-cavity surface-emitting lasers (VCSELs) subject to orthogonally polarized optical pulse injection (OPOPI) is investigated numerically based on the well-known spin-flip model. For the coupled VCSELs systems, different connection topologies are considered. The effects of stimuli strength, coupling strength, frequency detuning between two coupled VCSELs, and the pump current on the cascadable spiking dynamics are examined by extensive numerical bifurcation analysis. It is found that, the phasic spike generated in one VCSEL with OPOPI can also induce a similar phasic spike in another VCSEL in three considered connection topologies. Besides, such a cascadable spiking behavior can be achieved in wide range of stimuli strength, coupling strength, and frequency detuning. However, failure transfer of the phasic spike between two VCSELs may be caused when the pump currents are relatively large, and hence, low pump currents are desirable for both VCSELs to allow for successful cascadable spiking dynamics. This work is interesting and valuable for constructing reliable optical spiking information processing platform based on polarization dynamics of VCSELs.

Tait A.N., de Lima T.F., Zhou E., Wu A.X., Nahmias M.A., Shastri B.J., Prucnal P.R.

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.

Prucnal P.R., Shastri B.J., Teich M.C.

Owen-Newns D., Jaurigue L., Robertson J., Adair A., Jaurigue J.A., Lüdge K., Hurtado A.

Abstract Photonic technologies hold significant potential for creating innovative, high-speed, efficient and hardware-friendly neuromorphic computing platforms. Neuromorphic photonic methods leveraging ubiquitous, technologically mature and cost-effective Vertical-Cavity Surface Emitting Lasers (VCSELs) are of notable interest. VCSELs have demonstrated the capability to replicate neuronal optical spiking responses at ultrafast rates. Previously, a photonic Spiking Neural Network (p-SNN) using a single VCSEL has been demonstrated for use in classification tasks. Here, it is applied to a more complex time-series prediction task. The VCSEL p-SNN combined with a technique to induce network memory, is applied to perform multi-step-ahead predictions of a chaotic time-series. By providing the feedforward p-SNN with only two temporally separated inputs excellent accuracy is experimentally demonstrated over a range of prediction horizons. VCSEL-based p-SNNs therefore offer ultrafast, efficient operation in complex predictive tasks whilst enabling hardware implementations. The inherent attributes and performance of VCSEL p-SNNs hold great promise for use in future light-enabled neuromorphic computing hardware.

Zhang Y., Huang Z., Xiang S., Guo X., Zhang W., Tan Q., Han G., Hao Y.

Zeng X., xiang S., Han Y., ZHANG Y., Zhang Y., Guo X., Huang Z., Zou T., Shi Y., Hao Y.

Neuromorphic photonic computing based on spiking dynamics holds significant promise for next-generation AI accelerators, enabling high-speed, low-latency, and low-energy computing. However, the architecture of neuromorphic photonic systems is severely constrained by large-scale discrete devices. In this work, we propose a photonic spiking neural network (PSNN) architecture utilizing a directly modulated laser and a distributed feedback laser with a saturable absorber (DML-DFB-SA). The distributed feedback laser with a saturable absorber (DFB-SA) functions as a photonic spiking neuron, exhibiting nonlinear neuron-like dynamics. Specifically, we replace the conventional optical source and external modulator with a single directly modulated laser (DML), which simultaneously serves as the optical carrier and performs electro-optic conversion. This integration results in enhanced system compactness and reduced power consumption. Experimental results show that the energy efficiency of the DML-DFB-SA system reaches 0.625 pJ/MAC, representing a significant improvement in energy efficiency. Besides, since both DML and DFB-SA laser chips can be fabricated on an Indium Phosphide (InP) substrate, large-scale integration of photonic spiking neural networks (PSNNs) becomes practical. Moreover, the DML-DFB-SA system exhibits consistent robustness against the chirp effect of DML in short-distance transmissions, which makes it a promising candidate for PSNN applications. To validate the DML-DFB-SA's operational principle, we utilize a time-multiplexed spike coding scheme, enabling a single neuron to emulate the functionality of ten neurons. Experimental evaluations demonstrate a recognition accuracy of 94% on the MNIST dataset. The proposed system and approach provide a promising framework for developing low-energy, large-scale integrated PSNN chips.

Mørk J., Xiong M., Seegert K., Marchal M., Dong G., Dimopoulos E., Semenova E., Yvind K., Yu Y.

He C., Wu Z., Wang Q., Zheng Y., Duan Z., Deng T., Xia G.

Mu Peng-Hua, Wang Yi-Qiao, He Peng-Fei, Xu Yuan

Nanolaser (NL), as an important optical source device, has a significant influence on photonic integrated circuits and has become a research hotspot in recent years. In this work, the synchronization performance of a dual-channel laser chaotic multiplexing system is investigated based on NLs and an active-passive decomposition is used to enhance signal processing and multiplexing efficiency. By establishing a rate equation model, the synchronization characteristics of the system are analyzed, with a focus on two key parameters— Purcell factor (<i>F </i>) and spontaneous emission coupling factor (<i>β </i>)—as well as the effects of system parameters, single-parameter mismatch, and multi-parameter mismatch. Numerical simulations show that with appropriate parameter configurations, the two master NLs can maintain low correlation, ensuring the "pseudo-orthogonality" of chaotic signals while achieving high-quality chaotic synchronization with their paired slave NLs. In this work it is found that both the Purcell factor (<i>F </i>) and the spontaneous emission coupling factor (<i>β </i>) significantly affect the synchronization performance of the system, and the optimal parameter ranges for achieving high-quality synchronization are identified. Additionally, the effects of feedback strength and frequency detuning are explored, revealing that frequency detuning plays a more critical role in the synchronization between the master NLs. The influence of parameter mismatches on system synchronization performance is also emphasized. The system exhibits robustness against single-parameter mismatch and has minimum influence on master-slave synchronization quality. However, multi-parameter mismatch gives rise to more complex effects. Compared with the traditional semiconductor laser systems, this system can maintain “pseudo-orthogonality” over a wider range of parameters, thus achieving higher security and lower channel interference. This research lays a theoretical foundation for chaos synchronization based on NLs and provides new insights for designing secure, stable, and efficient optical communication systems.

Wang Y., Zhang X., Mu P., Tao J.

Abstract In this paper, we propose a parallel injection chaotic system involving three free-running &#xD;vertical-cavity surface-emitting lasers (VCSELs). First, the chaotic synchronization &#xD;performance of the system is evaluated using the cross-correlation function. Then, we analyze &#xD;in detail the effects of injection strength, frequency detuning, and parameter mismatch on the &#xD;chaotic synchronization and information transmission of the system. Numerical studies &#xD;indicate that the proposed parallel injection chaotic system based on three VCSELs can &#xD;achieve high-quality chaotic synchronization over a wide bandwidth and a broad range of &#xD;input parameters. Furthermore, even in the case of parameter mismatch, high-quality chaotic &#xD;synchronization and communication can still be achieved. Additionally, with appropriate &#xD;injection strength, the system can compensate for the efficiency reduction caused by &#xD;parameter mismatch.

Zheng D., Xiang S., Li N., Zhang Y., Guo X., Zhu X., Chen X., Shi Y., Hao Y.

Schegolev Andrey E., Bastrakova Marina V., Sergeev Michael A., Maksimovskaya Anastasia A., Klenov Nikolay V., Soloviev Igor

The extensive development of the field of spiking neural networks has led to many areas of research that have a direct impact on people’s lives. As the most bio-similar of all neural networks, spiking neural networks not only allow for the solution of recognition and clustering problems (including dynamics), but they also contribute to the growing understanding of the human nervous system. Our analysis has shown that hardware implementation is of great importance, since the specifics of the physical processes in the network cells affect their ability to simulate the neural activity of living neural tissue, the efficiency of certain stages of information processing, storage and transmission. This survey reviews existing hardware neuromorphic implementations of bio-inspired spiking networks in the ”semiconductor”, ”superconductor”, and ”optical” domains. Special attention is given to the potentials for effective ”hybrids” of different approaches.

Diamantopoulos N., Fujii T., Yamaoka S., Nishi H., Matsuo S.

Chang J., Huang Y., Han Y., Liu C., Geng Z.

Xiang J., Zhao Y., He A., Xiao J., Su Y., Guo X.

AbstractGuided by brain‐like temporal processing and event‐driven manner, neuromorphic computing has emerged as a competitive paradigm to realize artificial intelligence with high energy efficiency. Silicon photonics offers an ideal hardware platform with mutual foundry fabrication process and well‐developed device libraries, however, its huge potential to build integrated neuromorphic systems is significantly hindered due to the lack of scalable on‐chip photonic spiking neurons. Here, the first integrated electrically‐driven spiking neuron based on a silicon microring under the carrier injection working mode is reported, which is capable of emulating fundamental neural dynamics including excitability threshold, temporal integration, refractory period, controllable spike inhibition, and precise time encoding at a speed of 250 MHz. By programming time‐multiplexed spike representations, photonic spiking convolution is experimentally realized for image edge feature detection. Besides, a spiking convolutional neural network is constructed by combining photonic convolutional layers with a software‐implemented fully‐connected layer, which yields a classification accuracy of 94.1% on the benchmark Modified National Institute of Standards and Technology database. Moreover, it is theoretically verified that it's promising to further improve the operation speed to a gigahertz level by developing an electro‐optical co‐simulation model. The proposed microring neuron constitutes the final building block of scalable spike activation, thus representing a great breakthrough to boost the development of on‐chip neuromorphic information processing.

Tamura M., Morison H., Tait A.N., Shastri B.J.

AbstractIncreasingly, artificial intelligent systems look to neuromorphic photonics for its speed and its low loss, high bandwidth interconnects. Silicon photonics has shown promise to enable the creation of large scale neural networks. Here, we propose a monolithic silicon opto-electronic resonator spiking neuron. Existing designs of photonic spiking neurons have difficulty scaling due to their dependence on certain nonlinear effects, materials, and devices. The design discussed here uses optical feedback from the transmission of a continuously pumped microring PN modulator to achieve excitable dynamics. It is cascadable, capable of operating at GHz speeds, and compatible with wavelength-division multiplexing schemes for linear weighting. It is a Class 2 excitable device via a subcritical Hopf bifurcation constructed from devices commonly found in many silicon photonic chip foundries.

Hu L., Zhuge X., Wang J., Wei X., Zhang L., Chai Y., Xue X., Ye Z., Zhuge F.

AbstractBrain‐inspired neuromorphic computing is recognized as a promising technology for implementing human intelligence in hardware. Neuromorphic devices, including artificial synapses and neurons, are regarded as essential components for the construction of neuromorphic hardware systems. Recently, optoelectronic neuromorphic devices are increasingly highlighted due to their potential applications in next‐generation artificial visual systems, attributed to their integrated sensing, computing, and memory capabilities. In this review, recent advancements in optoelectronic synapses and neurons are examined, with an emphasis on their structural characteristics, operational principles, and the replication of neuromorphic functions. For optoelectronic synaptic devices, such as memristor‐ and transistor‐based ones, attention is given to the two primary weight update modes: the light‐electricity synergistic mode and the all‐optical mode. Optoelectronic neurons are discussed in terms of different device types, including threshold switch neurons and semiconductor laser neurons. Last, the challenges that impede the progress of optoelectronic neuromorphic devices are identified, and potential future directions are suggested.

Zhang X., Mu P., Liu G., Wang Y., Li X.

Significant progress has been made in the research of all-optical neural networks in recent years. In this paper, we theoretically explore the properties of a neural system composed of semiconductor ring lasers (SRLs). Our study demonstrates that external optical signals generated by a tunable laser (TL) are injected into the first semiconductor ring laser photonic neuron (SRL1). Subsequently, the responses of SRL1 in the clockwise (CW) and counterclockwise (CCW) directions are unidirectionally injected into the CW and CCW directions of the second semiconductor ring laser photonic neuron (SRL2), respectively, which then exhibits similar spiking inhibition behaviors. Numerical simulations reveal that the spiking inhibition behavior of the SRL response can be precisely controlled by adjusting the perturbation time and intensity of the external injection signal, and this behavior is highly repeatable. Most importantly, we successfully achieve the stable transmission of these responses between the two SRL photonic neurons. These inhibition behaviors are analogous to those of biological neurons, but with a response speed reaching the sub-nanosecond level. Additionally, we indicate that SRL photonic neurons undergo a refractory-period-like phenomenon when subjected to two consecutive perturbations. These findings highlight the immense potential for the design and implementation of future all-optical neural networks, providing critical theoretical foundations and support for them.