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

Weightless photonic spike processing of time-of-flight signals with delay learning

Time-of-flight (ToF) signal processing has become increasingly crucial in depth perception applications. We propose a photonic spike processing method for ToF signals based on synaptic delay plasticity, which adjusts the spike timing of encoded signals to achieve low-latency processing without the need for weight loading and control. This method employs photonic neurons that directly encode optical pulses of ToF signals into temporal spike sequences, eliminating the necessity for a time-to-digital converter (TDC). We use tunable optical delay lines to emulate the photonic synaptic regulation of spike timing. In addition, we demonstrate the efficacy of a photonic spiking neural network that trains the synaptic delay parameters using the ModelNet dataset, achieving an accuracy of 96.36%. In experiments, the processing delay of ToF signals is 58.66 ns, representing a reduction of two orders of magnitude compared with traditional TDC-based methods. This approach facilitates applying synaptic diversity in photonic neuromorphic information processing.

Free-space optical spiking neural network

Neuromorphic engineering has emerged as a promising avenue for developing brain-inspired computational systems. However, conventional electronic AI-based processors often encounter challenges related to processing speed and thermal dissipation. As an alternative, optical implementations of such processors have been proposed, capitalizing on the intrinsic information-processing capabilities of light. Among the various Optical Neural Networks (ONNs) explored within the realm of optical neuromorphic engineering, Spiking Neural Networks (SNNs) have exhibited notable success in emulating the computational principles of the human brain. The event-based spiking nature of optical SNNs offers capabilities in low-power operation, speed, temporal processing, analog computing, and hardware efficiency that are difficult or impossible to match with other ONN types. In this work, we introduce the pioneering Free-space Optical Deep Spiking Convolutional Neural Network (OSCNN), a novel approach inspired by the computational model of the human eye. Our OSCNN leverages free-space optics to enhance power efficiency and processing speed while maintaining high accuracy in pattern detection. Specifically, our model employs Gabor filters in the initial layer for effective feature extraction, and utilizes optical components such as Intensity-to-Delay conversion and a synchronizer, designed using readily available optical components. The OSCNN was rigorously tested on benchmark datasets, including MNIST, ETH80, and Caltech, demonstrating competitive classification accuracy. Our comparative analysis reveals that the OSCNN consumes only 1.6 W of power with a processing speed of 2.44 ms, significantly outperforming conventional electronic CNNs on GPUs, which typically consume 150-300 W with processing speeds of 1-5 ms, and competing favorably with other free-space ONNs. Our contributions include addressing several key challenges in optical neural network implementation. To ensure nanometer-scale precision in component alignment, we propose advanced micro-positioning systems and active feedback control mechanisms. To enhance signal integrity, we employ high-quality optical components, error correction algorithms, adaptive optics, and noise-resistant coding schemes. The integration of optical and electronic components is optimized through the design of high-speed opto-electronic converters, custom integrated circuits, and advanced packaging techniques. Moreover, we utilize highly efficient, compact semiconductor laser diodes and develop novel cooling strategies to minimize power consumption and footprint.

A Spatial-Channel-Temporal-Fused Attention for Spiking Neural Networks

Spiking neural networks (SNNs) mimic brain computational strategies, and exhibit substantial capabilities in spatiotemporal information processing. As an essential factor for human perception, visual attention refers to the dynamic process for selecting salient regions in biological vision systems. Although visual attention mechanisms have achieved great success in computer vision applications, they are rarely introduced into SNNs. Inspired by experimental observations on predictive attentional remapping, we propose a new spatial-channel-temporal-fused attention (SCTFA) module that can guide SNNs to efficiently capture underlying target regions by utilizing accumulated historical spatial-channel information in the present study. Through a systematic evaluation on three event stream datasets (DVS Gesture, SL-Animals-DVS, and MNIST-DVS), we demonstrate that the SNN with the SCTFA module (SCTFA-SNN) not only significantly outperforms the baseline SNN (BL-SNN) and two other SNN models with degenerated attention modules, but also achieves competitive accuracy with the existing state-of-the-art (SOTA) methods. Additionally, our detailed analysis shows that the proposed SCTFA-SNN model has strong robustness to noise and outstanding stability when faced with incomplete data, while maintaining acceptable complexity and efficiency. Overall, these findings indicate that incorporating appropriate cognitive mechanisms of the brain may provide a promising approach to elevate the capabilities of SNNs.

Optical neural networks: progress and challenges

Artificial intelligence has prevailed in all trades and professions due to the assistance of big data resources, advanced algorithms, and high-performance electronic hardware. However, conventional computing hardware is inefficient at implementing complex tasks, in large part because the memory and processor in its computing architecture are separated, performing insufficiently in computing speed and energy consumption. In recent years, optical neural networks (ONNs) have made a range of research progress in optical computing due to advantages such as sub-nanosecond latency, low heat dissipation, and high parallelism. ONNs are in prospect to provide support regarding computing speed and energy consumption for the further development of artificial intelligence with a novel computing paradigm. Herein, we first introduce the design method and principle of ONNs based on various optical elements. Then, we successively review the non-integrated ONNs consisting of volume optical components and the integrated ONNs composed of on-chip components. Finally, we summarize and discuss the computational density, nonlinearity, scalability, and practical applications of ONNs, and comment on the challenges and perspectives of the ONNs in the future development trends.

Hybrid photonic deep convolutional residual spiking neural networks for text classification

Spiking neural networks (SNNs) offer powerful computation capability due to its event-driven nature and temporal processing. However, it is still limited to shallow structure and simple tasks due to the training difficulty. In this work, we propose a deep convolutional residual spiking neural network (DCRSNN) for text classification tasks. In the DCRSNN, the feature extraction is achieved via a convolution SNN with residual connection, using the surrogate gradient direct training technique. Classification is performed by a fully-connected network. We also suggest a hybrid photonic DCRSNN, in which photonic SNNs are used for classification with a converted training method. The accuracy of hard and soft reset methods, as well as three different surrogate functions, were evaluated and compared across four different datasets. Results indicated a maximum accuracy of 76.36% for MR, 91.03% for AG News, 88.06% for IMDB and 93.99% for Yelp review polarity. Soft reset methods used in the deep convolutional SNN yielded slightly better accuracy than their hard reset counterparts. We also considered the effects of different pooling methods and observation time windows and found that the convergence accuracy achieved by convolutional SNNs was comparable to that of convolutional neural networks under the same conditions. Moreover, the hybrid photonic DCRSNN also shows comparable testing accuracy. This work provides new insights into extending the SNN applications in the field of text classification and natural language processing, which is interesting for the resources-restrained scenarios.

Optical cascaded reservoir computing for realization of dual-channel high-speed OTDM chaotic secure communication via four optically pumped VCSEL

In this work, we propose a chaotic secure communication system with optical time division multiplexing (OTDM), using two cascaded reservoir computing systems based on multi beams of chaotic polarization components emitted by four optically pumped VCSELs. Here, each level of reservoir layer includes four parallel reservoirs, and each parallel reservoir contains two sub-reservoirs. When the reservoirs in the first-level reservoir layer are well trained and the training errors are far less than 0.1, each group of chaotic masking signals can be effectively separated. When the reservoirs in the second reservoir layer are effectively trained and the training errors are far less than 0.1, the output for each reservoir can be well synchronized with the corresponding original delay chaotic carrier-wave. Here, the synchronization quality between them can be characterized by the correlation coefficients of more than 0.97 in different parameter spaces of the system. Under these high-quality synchronization conditions, we further discuss the performances of dual-channel OTDM with a rate of 4×60 Gb/s. By observing the eye diagram, bit error rate and time-waveform of each decoded message in detail, we find that there is a large eye-openings in the eye diagrams, low bit error rate and higher quality time-waveform for each decoded message. Except that the bit error rate of one decoded message is lower than 7 × 10^-3 in different parameter spaces, and those of the other decoded messages are close to 0, indicating that high-quality data transmissions are expected to be realized in the system. The research results show that the multi-cascaded reservoir computing systems based on multiple optically pumped VCSELs provide an effective method for the realization of multi-channel OTDM chaotic secure communications with high-speed.

Pulmonary Nodule Detection and Classification Using All-Optical Deep Diffractive Neural Network

A deep diffractive neural network (D2NN) is a fast optical computing structure that has been widely used in image classification, logical operations, and other fields. Computed tomography (CT) imaging is a reliable method for detecting and analyzing pulmonary nodules. In this paper, we propose using an all-optical D2NN for pulmonary nodule detection and classification based on CT imaging for lung cancer. The network was trained based on the LIDC-IDRI dataset, and the performance was evaluated on a test set. For pulmonary nodule detection, the existence of nodules scanned from CT images were estimated with two-class classification based on the network, achieving a recall rate of 91.08% from the test set. For pulmonary nodule classification, benign and malignant nodules were also classified with two-class classification with an accuracy of 76.77% and an area under the curve (AUC) value of 0.8292. Our numerical simulations show the possibility of using optical neural networks for fast medical image processing and aided diagnosis.

BP-based supervised learning algorithm for multilayer photonic spiking neural network and hardware implementation

We introduce a supervised learning algorithm for photonic spiking neural network (SNN) based on back propagation. For the supervised learning algorithm, the information is encoded into spike trains with different strength, and the SNN is trained according to different patterns composed of different spike numbers of the output neurons. Furthermore, the classification task is performed numerically and experimentally based on the supervised learning algorithm in the SNN. The SNN is composed of photonic spiking neuron based on vertical-cavity surface-emitting laser which is functionally similar to leaky-integrate and fire neuron. The results prove the demonstration of the algorithm implementation on hardware. To seek ultra-low power consumption and ultra-low delay, it is great significance to design and implement a hardware-friendly learning algorithm of photonic neural networks and realize hardware-algorithm collaborative computing.

Stochastic photonic spiking neuron for Bayesian inference with unsupervised learning

Stochasticity is an inherent feature of biological neural activities. We propose a noise-injection scheme to implement a GHz-rate stochastic photonic spiking neuron (S-PSN). The firing-probability encoding is experimentally demonstrated and exploited for Bayesian inference with unsupervised learning. In a breast diagnosis task, the stochastic photonic spiking neural network (S-PSNN) can not only achieve a classification accuracy of 96.6%, but can also evaluate the diagnosis uncertainty with prediction entropies. As a result, the misdiagnosis rate is reduced by 80% compared to that of a conventional deterministic photonic spiking neural network (D-PSNN) for the same task. The GHz-rate S-PSN endows the neuromorphic photonics with high-speed Bayesian inference for reliable information processing in error-critical scenarios.

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.

Analog-to-spike encoding and time-efficient RF signal processing with photonic neurons

The radio-frequency (RF) signal processing in real time is indispensable for advanced information systems, such as radar and communications. However, the latency performance of conventional processing paradigm is worsened by high-speed analog-to-digital conversion (ADC) generating massive data, and computation-intensive digital processing. Here, we propose to encode and process RF signals harnessing photonic spiking response in fully-analog domain. The dependence of photonic analog-to-spike encoding on threshold level and time constant is theoretically and experimentally investigated. For two classes of waveforms from real RF devices, the photonic spiking neuron exhibits distinct distributions of encoded spike numbers. In a waveform classification task, the photonic-spiking-based scheme achieves an accuracy of 92%, comparable to the K-nearest neighbor (KNN) digital algorithm for 94%, and the processing latency is reduced approximately from 0.7 s (code running time on a CPU platform) to 80 ns (light transmission delay) by more than one million times. It is anticipated that the asynchronous-encoding, and binary-output nature of photonic spiking response could pave the way to real-time RF signal processing.

Accurate separation of mixed high-dimension optical-chaotic signals using optical reservoir computing based on optically pumped VCSELs

In this work, with the mixing fractions being known in advance or unknown, the schemes and theories for the separations of two groups of the mixed optical chaotic signals are proposed in detail, using the VCSEL-based reservoir computing (RC) systems. Here, two groups of the mixed optical chaotic signals are linearly combined with many beams of the chaotic x-polarization components (X-PCs) and Y-PCs emitted by the optically pumped spin-VCSELs operation alone. Two parallel reservoirs are performed by using the chaotic X-PC and Y-PC output by the optically pumped spin-VCSEL with both optical feedback and optical injection. Moreover, we further demonstrate the separation performances of the mixed chaotic signal linearly combined with no more than three beams of the chaotic X-PC or Y-PC. We find that two groups of the mixed optical chaos signals can be effectively separated by using two reservoirs in single RC system based on optically pumped Spin-VCSEL and their corresponding separated errors characterized by the training errors are no more than 0.093, when the mixing fractions are known as a certain value in advance. If the mixing fractions are unknown, we utilize two cascaded RC systems based on optically pumped Spin-VCSELs to separate each group of the mixed optical signals. The mixing fractions can be accurate predicted by using two parallel reservoirs in the first RC system. Based on the values of the predictive mixing fractions, two groups of the mixed optical chaos signals can be effectively separated by utilizing two parallel reservoirs in the second RC system, and their separated errors also are no more than 0.093. In the same way, the mixed optical chaos signal linearly superimposed with more than three beams of optical chaotic signals can be effectively separated. The method and idea for separation of complex optical chaos signals proposed by this paper may provide an impact to development of novel principles of multiple access and demultiplexing in multi-channel chaotic cryptography communication.

Defect corrections for coherent optical information processing of grayscale images in a DMD-based 4f-system using a collimated light source

Digital micromirror device (DMD)-based 4f-systems, a type of coherent optical information processing system, have become a powerful tool for optical convolutional neural networks taking advantage of their fast modulation speed and high-resolution capability. However, proper high bit-depth image information processing remains challenging due to the optical diffractions that arise from the binary nature of DMD operation. In this paper, we first characterize the diffraction phenomena that cause irradiance defects, namely the nonlinear grayscale and unintended dark lines. Then to resolve the issues, we propose a DMD operation method and a modified structure of the 4f-system based on blazed diffraction grating theory and numerical calculation of the Rayleigh-Sommerfeld propagation model. As a demonstration, we implement high bit-depth image information processing with an optimized optical 4f-system using DMDs and a collimated coherent light source.

Detections of the position-vectors of the multi targets located in a circular space based on an asymmetric coupling semiconductor lasers network

We present a novel scheme for the detections of the position-vectors of the multi targets distributed in a circular space using multi channels of the probe chaotic waves emitted by the asymmetric coupling semiconductor lasers network (ACSLN), where these probe waves possess the attractive features of the time-space uncorrelation and wide bandwidth. Using these features, the accurate measurement for the position-vectors of the multi targets can be achieved by correlating the multi channels of the probe waves with their corresponding reference waves. The further research results show that the detections for the position-vectors of the multi targets possess very low relative errors that are no more than 0.22%. The ranging-resolutions for the multi targets located in a circular space can be achieved as high as 3 mm by optimizing some key parameters, such as injection current and injection strength. In addition, the ranging-resolutions exhibit excellent strong anti-noise performance even when the signal-to-noise ratio and relative noise intensity appear obvious enhancement. The detections for the position-vectors of the multi targets based on the ACSLN offers interesting perspectives for the potential applications in the driverless cars and the object tracking system with omnidirectional vision.

Hierarchical-dependent cluster synchronization in directed networks with semiconductor lasers

Cluster synchronization in complex networks with mutually coupled semiconductor lasers (SLs) has recently been extensively studied. However, most of the previous works on cluster synchronization patterns have concentrated on undirected networks. Here, we numerically study the complete cluster synchronization patterns in directed networks composed of SLs, and demonstrate that the values of the SLs parameter and network parameter play a prominent role on the formation and stability of cluster synchronization patterns. Moreover, it is shown that there is a hierarchical dependency between the synchronization stability of different clusters in directed networks. The stability of one cluster can be affected by another cluster, but not vice versa. Without loss of generality, the results are validated in another SLs network with more complex topology.

Motion detection and direction recognition in a photonic spiking neural network consisting of VCSELs-SA

Motion detection and direction recognition are two important fundamental visual functions among the many cognitive functions performed by the human visual system. The retina and visual cortex are indispensable for composing the visual nervous system. The retina is responsible for transmitting electrical signals converted from light signals to the visual cortex of the brain. We propose a photonic spiking neural network (SNN) based on vertical-cavity surface-emitting lasers with an embedding saturable absorber (VCSELs-SA) with temporal integration effects, and demonstrate that the motion detection and direction recognition tasks can be solved by mimicking the visual nervous system. Simulation results reveal that the proposed photonic SNN with a modified supervised algorithm combining the tempotron and the STDP rule can correctly detect the motion and recognize the direction angles, and is robust to time jitter and the current difference between VCSEL-SAs. The proposed approach adopts a low-power photonic neuromorphic system for real-time information processing, which provides theoretical support for the large-scale application of hardware photonic SNN in the future.

Strong cluster synchronization in complex semiconductor laser networks with time delay signature suppression

Cluster synchronization is a state where clusters of nodes inside the network exhibit isochronous synchronization. Here, we present a mechanism to realize the strong cluster synchronization in semiconductor laser (SL) networks with complex topology, where stable cluster synchronization is achieved with decreased correlation between dynamics of different clusters and time delay signature concealment. We elucidate that, with the removal of intra-coupling within clusters, the stability of cluster synchronization could be enhanced effectively, while the statistical correlation among dynamics of each cluster decreases. Moreover, it is demonstrated that the correlation between clusters can be further reduced with the introduction of dual-path injection and frequency detuning. The robustness of strong cluster synchronization on operation parameters is discussed systematically. Time delay signature in chaotic outputs of SL network is concealed simultaneously with heterogeneous inter-coupling among different clusters. Our results suggest a new approach to control the cluster synchronization in complex SL networks and may potentially lead to new network solutions for communication schemes and encryption key distribution.

Spiking VGG7: Deep Convolutional Spiking Neural Network with Direct Training for Object Recognition

We propose a deep convolutional spiking neural network (DCSNN) with direct training to classify concrete bridge damage in a real engineering environment. The leaky-integrate-and-fire (LIF) neuron model is employed in our DCSNN that is similar to VGG. Poisson encoding and convolution encoding strategies are considered. The gradient surrogate method is introduced to realize the supervised training for the DCSNN. In addition, we have examined the effect of observation time step on the network performance. The testing performance for two different spike encoding strategies are compared. The results show that the DCSNN using gradient surrogate method can achieve a performance of 97.83%, which is comparable to traditional CNN. We also present a comparison with STDP-based unsupervised learning and a converted algorithm, and the proposed DCSNN is proved to have the best performance. To demonstrate the generalization performance of the model, we also use a public dataset for comparison. This work paves the way for the practical engineering applications of the deep SNNs.

Experimental implementation of spike-based neuromorphic XOR operation based on polarization-mode competition in a single VCSOA

We experimentally and numerically propose an approach for implementing spike-based neuromorphic exclusive OR (XOR) operation using a single vertical-cavity semiconductor optical amplifier (VCSOA). XOR operation is realized based on the neuron-like inhibitory dynamics of the VCSOA subject to dual-polarized pulsed optical injections. The inhibitory dynamics based on the polarization-mode competition effect are analyzed, and the inhibitory response can be obtained in a suitable range of wavelength detuning. Here, all input and output bits are represented by spikes that are compatible with the photonic spiking neural network. The experimental and numerical results show that XOR operation can be realized in two polarization modes by adjusting the time offset in the inhibitory window and setting defined reference thresholds. In addition, the influences of delay time and input intensity ratio on XOR operation are studied experimentally. This scheme is energy efficient because VCSOA neuromorphic photonics computing and information processing.

Adaptive time-delayed photonic reservoir computing based on Kalman-filter training

We propose an adaptive time-delayed photonic reservoir computing (RC) structure by utilizing the Kalman filter (KF) algorithm as training approach. Two benchmark tasks, namely the Santa Fe time-series prediction and the nonlinear channel equalization, are adopted to evaluate the performance of the proposed RC structure. The simulation results indicate that with the contribution of adaptive KF training, the prediction and equalization performance for the benchmark tasks can be significantly enhanced, with respect to the conventional RC using a training approach based on the least-squares (LS). Moreover, by introducing a complex mask derived from a bandwidth and complexity enhanced chaotic signal into the proposed RC, the performance of prediction and equalization can be further improved. In addition, it is demonstrated that the proposed RC system can provide a better equalization performance for the parameter-variant wireless channel equalization task, compared with the conventional RC based on LS training. The work presents a potential way to realize adaptive photonic computing.

Multilayer Photonic Spiking Neural Networks: Generalized Supervised Learning Algorithm and Network Optimization

We propose a generalized supervised learning algorithm for multilayer photonic spiking neural networks (SNNs) by combining the spike-timing dependent plasticity (STDP) rule and the gradient descent mechanism. A vertical-cavity surface-emitting laser with an embedded saturable absorber (VCSEL-SA) is employed as a photonic leaky-integrate-and-fire (LIF) neuron. The temporal coding strategy is employed to transform information into the precise firing time. With the modified supervised learning algorithm, the trained multilayer photonic SNN successfully solves the XOR problem and performs well on the Iris and Wisconsin breast cancer datasets. This indicates that a generalized supervised learning algorithm is realized for multilayer photonic SNN. In addition, network optimization is performed by considering different network sizes.

An All-MRR-Based Photonic Spiking Neural Network for Spike Sequence Learning

Photonic spiking neural networks (SNN) have the advantages of high power efficiency, high bandwidth and low delay, but limitations are encountered in large-scale integration. The silicon photonics platform is a promising candidate for realizing large-scale photonic SNN because it is compatible with the current mature CMOS platforms. Here, we present an architecture of photonic SNN which consists of photonic neuron, photonic spike timing dependent plasticity (STDP) and weight configuration that are all based on silicon micro-ring resonators (MRRs), via taking advantage of the nonlinear effects in silicon. The photonic spiking neuron based on the add-drop MRR is proposed, and a system-level computational model of all-MRR-based photonic SNN is presented. The proposed architecture could exploit the properties of small area, high integration and flexible structure of MRR, but also faces challenges caused by the high sensitivity of MRR. The spike sequence learning problem is addressed based on the proposed all-MRR-based photonic SNN architecture via adopting supervised training algorithms. We show the importance of algorithms when hardware devices are limited.

Photonic decision-making for arbitrary-number-armed bandit problem utilizing parallel chaos generation

In this paper, we propose and experimentally demonstrate a novel scheme that helps to solve an any-number-armed bandit problem by utilizing two parallel simultaneously-generated chaotic signals and the epsilon (ɛ)-greedy strategy. In the proposed scheme, two chaotic signals are experimentally generated, and then processed by an 8-bit analog-to-digital conversion (ADC) with 4 least significant bits (LSBs), to generate two amplitude-distribution-uniform sequences for decision-making. The correspondence between these two random sequences and different arms is established by a mapping rule designed in virtue of the ɛ-greedy-strategy. Based on this, decision-making for an exemplary 5-armed bandit problem is successfully performed, and moreover, the influences of the mapping rule and unknown reward probabilities on the correction decision rate (CDR) performance for the 4-armed to 7-armed bandit problems are investigated. This work provides a novel way for solving the arbitrary-number-armed bandit problem.

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.

Chaotic synchronization of a distant star-type laser network with multiple optical injections

A novel multi-injection module (MIM) is introduced into a typical distant star-type laser network, which is composed of a hub semiconductor laser node (H-SLN), star semiconductor laser nodes (S-SLNs) and tens of kilometers of fiber links. The chaotic synchronization of this distant network is investigated both experimentally and theoretically. As a result of using the MIM, a significantly low correlation (about 0.2) is successfully achieved between the H-SLN and S-SLNs in different clusters. This correlation is much lower than in previously reported results. Even when the fiber length is extended to 80 kilometers a low correlation (about 0.18) between the H-SLN and S-SLNs in different clusters is also obtained. Moreover, the dependence of chaotic synchronization on the operating conditions, such as the injection power, frequency detuning, and frequency mismatch between arbitrary nodes are examined. Lastly, using a theoretical model, we discuss the broad conditions for achieving chaotic synchronization among S-SLNs in the same cluster, and analyze the effect of the MIM branch number on chaotic synchronization.