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All-Optical Spiking Neuron Based on Passive Microresonator Jinlong Xiang , Axel Torchy, Xuhan Guo , and Yikai Su , Senior Member, IEEE

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All-Optical Spiking Neuron Based on Passive Microresonator Jinlong Xiang , Axel Torchy, Xuhan Guo , and Yikai Su , Senior Member, IEEE JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 38, NO. 15, AUGUST 1, 2020 4019 All-Optical Spiking Neuron Based on Passive Microresonator Jinlong Xiang , Axel Torchy, Xuhan Guo , and Yikai Su , Senior Member, IEEE Abstract—Neuromorphic photonics that aims to process and the neural network for a specific task and AI operating on store information simultaneously like human brains has emerged traditional computers consumes great power as well. In the as a promising alternative for next generation intelligent com- von Neumann computing architecture, the computing unit and puting systems. The implementation of hardware emulating the basic functionality of neurons and synapses is the fundamental the memory are physically separated from each other, thus the work in this field. However, previously proposed optical neurons machine instructions and data are serially transmitted between implemented with SOA-MZIs, modulators, lasers or phase change them. Consequently, the computational capacity is limited by materials are all dependent on active devices and pose challenges for the bandwidth and high energy consumption. Compared to the integration. Meanwhile, although the nonlinearity in nanocavities massively parallel processing of human brains, it’s undoubtedly has long been of interest, the previous theories are intended for specific situations, e.g., self-pulsation in microrings, and there is inefficient to train and simulate a neural network with software still a lack of systematic studies in the excitability behavior of on a von Neumann computer. the nanocavities including the silicon photonic crystal cavities. Neuromorphic computing takes inspiration from human Here, we report for the first time a universal coupled mode theory brains and aims to simultaneously process and store information model for all side-coupled passive microresonators. The excitabil- as fast as possible, which provides a promising alternative for ity of microresonators resulting from the subcritical Andronov- Hopf bifurcation is categorized as Class 2 neural excitability and next generation intelligent computing systems. It develops hard- can be used to mimic the Hodgkin-Huxley neuron model. We ware mimicking the basic functions of neurons and synapses, demonstrate that the microresonator-based neuron can exhibit the and then combines them into suitably scaled neural networks. typical characteristics of spiking neurons: excitability threshold, In the past few years, neuromorphic electronics, e.g., TrueNorth leaky integrating dynamics, refractory period, cascadability and at IBM [5], TPU at Google [6] and SpiNNaker at the University inhibitory spiking behavior, paving the way to realize all-optical spiking neural networks. of Manchester [7], have demonstrated impressive improvements in both energy efficiency and speed enhancement, allowing Index Terms—Coupled mode theory, microresonators, simultaneous operation of thousands of interconnected artificial nonlinearity, neuromorphic photonics, optical neurons. neurons. However, electronic architectures face fundamental limits as Moore’s law is slowing down [8]. Furthermore, the I. INTRODUCTION electronic communication links have intrinsic limitations on RTIFICIAL intelligence (AI) has attracted a lot of atten- speed, bandwidth and crosstalk. Distinct from those properties A tion lately because of its great potential to remarkably of electronics, silicon photonics naturally has the advantages of change almost every aspect of our daily life [1]. Applications low latency and low power consumption. Data is transmitted of AI such as face recognition [2], intelligent virtual assis- in silicon waveguides at the speed of light and the associated tant [3] and neural machine translation [4] have already been energy costs currently are just on the order of femtojoules per bit widely used and brought great convenience to us. However, [9]. Combined with the dense wavelength-division multiplexing it takes a considerable amount of computational time to train (WDM), mode division multiplexing (MDM) and polarization division multiplexing (PDM) technologies, the channel capacity Manuscript received December 24, 2019; revised March 7, 2020; accepted continues to increase. Consequently, neuromorphic photonic April 2, 2020. Date of publication April 8, 2020; date of current version systems could operate 6–8 orders-of-magnitude faster than neu- July 23, 2020. This work was supported in part by the National Key R&D romorphic electronics [10]. Program of China under Grant 2019YFB2203101, in part by the Natural Science Foundation of China under Grant 61805137 and Grant 61835008, in part by the Synapses and neurons are the basic building blocks of human Natural Science Foundation of Shanghai under Grant 19ZR1475400, in part by brains, which perform the linear weight-and-sum operation and Shanghai Sailing Program under Grant 18YF1411900, and in part by the Open the nonlinear activation operation. To obtain a complicated Project Program of Wuhan National Laboratory for Optoelectronics under Grant 2018WNLOKF012. (Corresponding author: Xuhan Guo.) brain-inspired optical chip, the hardware implementation of The authors are with the State Key Laboratory of Advanced the fundamental function units is essential. Recently, a number Optical Communication Systems and Networks Department of Elec- of different concepts for neuromorphic computing have been tronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China (e-mail: [email protected]; [email protected]; proposed, including the reservoir computing [11]–[17], artificial [email protected]; [email protected]). neural networks (ANN) [18]–[25] and spiking neural networks Color versions of one or more of the figures in this article are available online (SNN) [26]–[44]. Utilizing the linear optics offered by the native at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2020.2986233 interference properties of light makes it possible to implement 0733-8724 © 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: Shanghai Jiaotong University. Downloaded on July 28,2020 at 03:22:41 UTC from IEEE Xplore. Restrictions apply. 4020 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 38, NO. 15, AUGUST 1, 2020 II. COUPLED MODE THEORY OF MICRORESONATOR The nonlinearity of microresonators has long been of interest as a simple mechanism to manipulate light with light. The nonlinear phenomena have already been widely observed and carefully studied in different material platforms and various types of integrated resonators. All the self-pulsation, bistabil- ity and excitability behavior have been experimentally demon- strated in microrings [45]–[49], microdisks [50], [51] and two- Fig. 1. The passive microresonator couples with only one waveguide and the dimensional photonic crystal (PhC) cavities in InP platform [52], trigger pulse is applied in the opposite direction of the input pump light. [53]. The silicon two-dimensional PhC cavities can also exhibit bistability [54]–[56] and self-pulsation [57]–[60] behaviors. Besides, bistability has been observed in racetrack resonator [61] and silicon one-dimensional PhC cavity [62], [63]. While completely passive optical matrix multiplication units for neu- excitability behavior hasn’t been demonstrated in silicon PhC ral network applications in both free-space [21], [25] and the nanocavities. waveguide-based coherent circuitry [18]. Modulators combined The basic principle of nonlinear behaviors for Silicon-On- with photodetectors [23], [24], SOA-MZIs [19], [38] and laser- Insulator (SOI) microresonators is [48]: two-photon absorption cooled atoms with electro-magnetically induced transparency (TPA) effect first generates free carriers, which are then able to [25] are used to realize the nonlinear activation function in ANN. absorb light by free carrier absorption (FCA) effect. Besides, Meanwhile, lasers, e.g., micro-pillar lasers [36], two-section the presence of free carriers leads to a blueshift in the resonance lasers with saturable absorber regions [26], [27], [43], vertical- wavelength by free carrier dispersion (FCD) effect. Moreover, cavity surface-emitting lasers (VCSELs) [34], [35], [37], [40]– surface state absorption takes place everywhere at the silicon- [42], [44] and quantum dot (QD) lasers [39] are typically used to silica interface, and meanwhile some light is lost due to the implement the functionality of spiking neurons in SNN. Owing surface scattering and radiation loss. Therefore, the absorbed to its unique optical properties in different states, phase change optical energy is mainly lost in the form of heat. Owing to the material (PCM) has emerged as an attractive alternative to pro- thermo-optic effect, the heat induces a redshift in the resonance vide in hardware both the basic integrate-and-fire functionality wavelength. Typically, the free carriers relax at least one order of neurons and the plastic weighting operation of synapses of magnitude faster than the heat. Consequently, this difference [28]–[31]. Moreover, the broadcast-and-weight architecture [33] between the timescale of the fast free carrier dynamics and the has been proposed to unite well-defined neurons and synapses slow heating effects results in the self-pulsation, bistability and on the mainstream silicon photonics platform. However, the excitability phenomena in microresonators. optical neurons proposed so
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