tive radio. similarities with biological signal ......demand for data will continue to grow as smart...

Neuromorphic Photonics,Principles of

Bhavin J. Shastri, Alexander N. Tait,Thomas Ferreira de Lima, Mitchell A. Nahmias,Hsuan-Tung Peng and Paul R. PrucnalDepartment of Electrical Engineering, PrincetonUniversity, Princeton, NJ, USA

Article Outline

GlossaryDefinition of the SubjectIntroductionNeuromorphic Computing: Beyond von

Neumann and MooreTechnology PlatformsNeuromorphic PhotonicsPhotonic NeuronExcitable/Spiking LasersPhotonic Neural Network ArchitectureNeuromorphic Platform ComparisonFuture DirectionsSummary and ConclusionBibliography

Glossary

Benchmark A standardized task that can beperformed by disparate computing approaches,used to assess their relative processing merit inspecific cases.

Bifurcation A qualitative change in behavior ofa dynamical system in response to parametervariation. Examples include cusp (from mono-stable to bistable), Hopf (from stable to oscil-lating), and transcritical (exchange of stabilitybetween two steady states).

Brain-inspired computing (a.k.a. neuro-inspired computing) A biologically inspiredapproach to build processors, devices, andcomputing models for applications includingadaptive control, machine learning, and cogni-

tive radio. Similarities with biological signalprocessing include architectural, such as dis-tributed; representational, such as analog orspiking; or algorithmic, such as adaptation.

Broadcast and Weight A multiwavelength ana-log networking protocol in which multiple allphotonic neuron outputs are multiplexed anddistributed to all neuron inputs. Weights arereconfigured by tunable spectral filters.

Excitability A far-from-equilibrium nonlineardynamical mechanism underlying all-or-noneresponses to small perturbations.

Fan-in The number of inputs to a neuron.Layered network A network topology

consisting of a series of sets (i.e., layers) ofneurons. The neurons in each set project theiroutputs only to neurons in the subsequentlayer. Most commonly used type of networkused for machine learning.

Metric A quantity assessing performance of adevice in reference to a specific computingapproach.

Microring weight bank A silicon photonicimplementation of a reconfigurable spectralfilter capable of independently setting trans-mission at multiple carrier wavelengths.

Modulation The act of representing an abstractvariable in a physical quantity, such as photonrate (i.e., optical power), free carrier density(i.e., optical gain), and carrier drift (i.e., cur-rent). Electro-optic modulators are devices thatconvert from an electrical signal to the powerenvelope of an optical signal.

Moore’s law An observation that the number oftransistors in an integrated circuit doublesevery 18 to 24 months, doubling itsperformance.

Multiply-accumulate (MAC) A common oper-ation that represents a single multiplicationfollowed by an addition: a a + (b � c).

Neural networks A wide class of computingmodels consisting of a distributed set ofnodes, called neurons, interconnected withconfigurable or adaptable strengths, calledweights. Overall neural network behavior can

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be extremely complex relative to single neuronbehavior.

Neuromorphic computing Computingapproaches based on specialized hardwarethat formally adheres to one or more neuralnetwork models. Algorithms, metrics, andbenchmarks can be shared between disparateneuromorphic computers that adhere to a com-mon mathematical model.

Neuromorphic photonics An emerging field atthe nexus of photonics and neural networkprocessing models, which combines the com-plementary advantages of optics and electron-ics to build systems with high efficiency, highinterconnectivity, and extremely highbandwidth.

Optoelectronics A technology of electronicdevices and systems (semiconductor lasers,photodetectors, modulators, photonic inte-grated circuits) that interact (source, detect,and control).

Photonic integrated circuits (PICs) A chip thatintegrates many photonic components (lasers,modulators, filters, detectors) connected byoptical waveguides that guide light; similar toan electronic integrated circuit that consists oftransistors, diodes, resistors, capacitors, andinductors, connected by conductive wires.

Physical cascadability The ability of one neu-ron to produce an output with the same repre-sentational properties as its inputs. Forexample, photonic-electronicphotonic or32bit-analog-32bit.

Recurrent network A network topology inwhich each neuron output can reach everyother neuron, including itself. Every networkis a subset of a recurrent network.

Reservoir computing A computationalapproach in which a complex, nonlinear sub-strate performs a diversity of functions, fromwhich linear classifiers extract the most usefulinformation to perform a given algorithm. Thereservoir can be implemented by a recurrentneural network or a wide variety of other sys-tems, such as time-delayed feedback.

Semiconductor lasers Lasers based on semicon-ductor gain media, where optical gain isachieved by stimulated emission at an

interband transition under conditions of ahigh carrier density in the conduction band.

Signal cascadability The ability of one neuronto elicit an equivalent or greater response whendriving multiple other neurons. The number oftarget neurons is called fan-out.

Silicon photonics A chip-scale, silicon-on-insulator (SOI) platform for monolithic inte-gration of optics and microelectronics for guid-ing, modulating, amplifying, and detectinglight.

Spiking neural networks (SNNs) A biologi-cally realistic neural network model that pro-cesses information with spikes or pulses thatencode information temporally.

Wavelength-division multiplexing (WDM)One of the most common multiplexing tech-niques used in optics where different wave-lengths (colors) of light are combined,transmitted, and separated again.

WDM weighted addition A simultaneous sum-mation of power modulated signals and trans-duction from multiple optical carriers to oneelectronic carrier. Occurs when multiplexedoptical signals impinge on a standardphotodetector.

Weight matrix A way to describe all networkconnection strengths between neuronsarranged such that rows are input neuron indi-ces and columns are output neuron indices.The weight matrix can be constrained to besymmetric, block off-diagonal, sparse, etc. torepresent particular kinds of neural networks.

Weighted addition The operation describinghow multiple inputs to a neuron are combinedinto one variable. Can be implemented in thedigital domain by multiply-accumulate (MAC)operations or in the analog domain by variousphysical processes (e.g., current summing,total optical power detection).

Definition of the Subject

In an age overrun with information, the ability toprocess reams of data has become crucial. Thedemand for data will continue to grow as smartgadgets multiply and become increasingly

2 Neuromorphic Photonics, Principles of

integrated into our daily lives. Next-generationindustries in artificial intelligence services andhigh-performance computing are so far supportedby microelectronic platforms. These data-intensive enterprises rely on continual improve-ments in hardware. Their prospects are running upagainst a stark reality: conventional one-size-fits-all solutions offered by digital electronics can nolonger satisfy this need, as Moore’s law(exponential hardware scaling), interconnectiondensity, and the von Neumann architecture reachtheir limits.

With its superior speed and reconfigurability,analog photonics can provide some relief to theseproblems; however, complex applications of ana-log photonics have remained largely unexploreddue to the absence of a robust photonic integrationindustry. Recently, the landscape for commer-cially manufacturable photonic chips has beenchanging rapidly and now promises to achieve

economies of scale previously enjoyed solely bymicroelectronics.

Despite the advent of commercially viablephotonic integration platforms, significant chal-lenges still remain before scalable analog pho-tonic processors can be realized. A centralchallenge is the development of mathematicalbridges linking photonic device physics to modelsof complex analog information processing.Among such models, those of neural networksare perhaps the most widely studied and used bymachine learning and engineering fields.

Recently, the scientific community has set outto build bridges between the domains of photonicdevice physics and neural networks, giving rise tothe field of neuromorphic photonics (Fig. 1). Thisentry reviews the recent progress in integratedneuromorphic photonics. We provide an overviewof neuromorphic computing, discuss the associ-ated technology (microelectronic and photonic)platforms, and compare their metric performance.

Neuromorphic Photonics, Principles of, Fig. 1 Theadvent of neuromorphic photonics is due to the conver-gence of recent advances in photonic integration

technology, resurgence of scalable computing models(e.g., spiking, deep neural networks), and a large-scalesilicon industrial ecosystem

Neuromorphic Photonics, Principles of 3

We discuss photonic neural network approachesand challenges for integrated neuromorphic pho-tonic processors while providing an in-depthdescription of photonic neurons and a candidateinterconnection architecture. We conclude with afuture outlook of neuro-inspired photonicprocessing.

Introduction

Complexity manifests in our world in countlessways (Strogatz 2001; Vicsek 2002) ranging fromintracellular processes (Crescenzi et al. 1998) andhuman brain area function (Markram et al. 2011)to climate dynamics (Donges et al. 2009) andworld economy (Hidalgo et al. 2007). An under-standing of complex systems is a fundamentalchallenge facing the scientific community. Under-standing complexity could impact the progress ofour society as a whole, for instance, in fightingdiseases, mitigating climate change, or creatingeconomic benefits.

Current approaches to complex systems andbig data analysis are based on software, executedon serialized and centralized von Neumannmachines. However, the interconnected structureof complex systems (i.e., many elementsinteracting strongly and with variation (Bhallaand Iyengar 1999)) makes them challenging toreproduce in this conventional computing frame-work. Memory and data interaction bandwidthsconstrain the types of informatic systems that arefeasible to simulate. The conventional computingapproach has persisted thus far due to an expo-nential performance scaling in digital electronics,most famously embodied in Moore’s law. Formost of the past 60 years, the density of transis-tors, clock speed, and power efficiency in micro-processors have approximately doubled every18 months. These empirical laws are fundamen-tally unsustainable. The last decade has witnesseda statistically significant (>99.95% likelihood(Marr et al. 2013)) plateau in processor energyefficiency.

This situation suggests that the time is ripe forradically new approaches to information pro-cessing, one being neuromorphic photonics. An

emerging field at the nexus of photonics and neu-roscience, neuromorphic photonics combines thecomplementary advantages of optics and electron-ics to build systems with high efficiency, highinterconnectivity, and extremely high bandwidth.This entry reviews the recent progress in inte-grated neuromorphic photonic research. First, weintroduce neuromorphic computing and give anoverview of current technology platforms inmicroelectronics and photonics. Next, we discussthe evolution of neuromorphic photonics, the pre-sent photonic neural network approaches, andchallenges for emerging integrated neuromorphicphotonic processors. We introduce the concept ofa “photonic neuron” followed by a discussion onits feasibility. We summarize recent research onoptical devices that could be used as network-compatible photonic neurons. We discuss a net-working architecture that efficiently channelizesthe transmission window of an integrated wave-guide. We also compare metrics betweenneuromorphic electronics and neuromorphic pho-tonics. Finally, we offer a glimpse at the futureoutlook for neuro-inspired photonic processingand discuss potential applications.

Neuromorphic Computing: Beyond vonNeumann and Moore

Conventional digital computers are based on thevon Neumann architecture (von Neumann 1993).It consists of a memory that stores both data andinstructions, a central processing unit (CPU), andinputs and outputs (Fig. 2 (left)). Instructions anddata stored in the memory unit are separated fromthe CPU by a shared digital bus. This is known asthe von Neumann bottleneck (Backus 1978)which fundamentally limits the performance ofthe system – a problem that is aggravated asCPUs become faster and memory units larger.This computing paradigm has dominated forover 60 years driven in part by the continualprogress dictated by Moore’s law (Moore 2000)for CPU scaling and Koomey’s law (Koomeyet al. 2011) for energy efficiency (in multiply-accumulate (MAC) operations per joule) compen-sating the bottleneck. Over the last several years,


such scaling has not followed suit, approaching anasymptote. The computation efficiency levels offbelow 10 GMAC/s/Wor 100 pJ per MAC (HaslerandMarr 2013). The reasons behind this trend canbe traced to both the representation of informationat the physical level and the interaction of pro-cessing with memory at the architectural level(Marr et al. 2013).

Breaching the energy efficiency wall of digitalcomputation by orders of magnitude is not funda-mentally impossible. In fact, the human brain,believed to be the most complex system in theuniverse, is estimated to execute an amazing 1018

MAC/s using only 20 W of power (Hasler andMarr 2013; Merkle 1989). It does this with 1011

neurons with an average of 104 inputs each. Thisleads to an estimated total of 1015 synaptic con-nections, all conveying signals up to 1 kHz band-width. The calculated computational efficiencyfor the brain (< aJ/MAC) is therefore eight ordersof magnitude beyond that of current supercom-puters (100pJ/MAC). The brain is a natural stan-dard for information processing, one that has beencompared to artificial processing systems sincetheir earliest inception. Nevertheless, the brain asa processor differs radically from computerstoday, both at the physical level and at the archi-tectural level. Its exceptional performance is, atleast partly, due to the neuron biochemistry, itsunderlying architecture, and the biophysics ofneuronal computation algorithms.

Neuromorphic computing offers hope to build-ing large-scale “bio-inspired” hardware whose

computational efficiencies move toward those ofa human brain. In doing so, neuromorphic plat-forms (Fig. 2 (middle)) could break performancelimitations inherent in traditional von Neumannarchitectures in solving particular classes of prob-lems. Their distributed hardware architectures canmost efficiently evaluate models with high datainterconnection, among which are real-time com-plex system assurance and big data awareness.

At the device level, digital CMOS is reachingphysical limits (Mathur 2002; Taur et al. 1997).As the CMOS feature sizes scale down below90 nm to 65 nm, the voltage, capacitance, anddelay no longer scale according to a well-definedrate by Dennard’s law (Dennard et al. 1974). Thisleads to a trade-off between performance (whentransistor is on) and subthreshold leakage (when itis off). For example, as the gate oxide (whichserves as an insulator between the gate and chan-nel) is made as thin as possible (1.2 nm, aroundfive atoms thick Si) to increase the channel con-ductivity, a quantum mechanical phenomenon ofelectron tunneling (Taur 2002; Lee and Hu 2001)occurs between the gate and channel leading toincreased power

consumption. The recent shift to multi-corescaling alleviated these constraints, but the break-down of Dennard scaling has limited the numberof cores than can simultaneously be powered onwith a fixed power budget and heat extraction rate.Fixed power budgets have necessitated so-calleddark silicon strategies (Esmaeilzadeh et al. 2012).Projections for the 8 nm node indicate that over

Neuromorphic Photonics, Principles of, Fig. 2 Neuralnets: The photonic edge. Von Neumann architectures (left),relying on sequential input-output through a central pro-cessor, differ fundamentally from more decentralized

neural network architectures (middle). Photonic neuralnets (right) can solve the interconnect bottleneck by usingone waveguide to carry signals from many connections(easily N2�10, 000) simultaneously


50% of the chip will be dark (Esmaeilzadeh et al.2012), meaning unused at a given time. This hasled to a widening rift between conventional com-puting capabilities and contemporary computingneeds, particularly for the analysis of complexsystems.

Computational tools have been revolutionaryin hypothesis testing and simulation. They haveled to the discovery of innumerable theories inscience, and they will be an indispensable aspectof a holistic approach to problems in big data andmany body physics; however, huge gaps betweeninformation structures in observed systems andstandard computing architectures motivate aneed for alternative paradigms if computationalabilities are to be brought to the growing class ofproblems associated with complex systems.Brain-inspired computing approaches share theinterconnected causal structures and dynamicsanalogous to the complex systems present in ourworld. This is in contrast to conventionalapproaches, where these structures are virtualizedat considerable detriment to energy efficiency.From a usual constraint of a fixed power budget,energy efficiency caps overall simulation scale.

Over the years, there has been a deeply com-mitted exploration of unconventional computingtechniques (Hasler and Marr 2013; Keyes 1985;Jaeger and Haas 2004;Merolla et al. 2014; Modhaet al. 2011; Tucker 2010; Caulfield and Dolev2010; Woods and Naughton 2012; Benjaminet al. 2014; Pfeil et al. 2013; Furber et al. 2014;Snider 2007; Eliasmith et al. 2012; Indiveri et al.2011; Brunner et al. 2013a; Tait et al. 2017; Shenet al. 2017; Shainline et al. 2017; Prucnal et al.2016; Prucnal and Shastri 2017) to alleviate thedevice level and system/architectural level chal-lenges faced by conventional computing plat-forms. Specifically, neuromorphic computing isgoing through an exciting period as it promisesto make processors that use low energies whileintegrating massive amounts of information.Neuromorphic engineering aims to buildmachines employing basic nervous systems oper-ations by bridging the physics of biology withengineering platforms enhancing performancefor applications interacting with natural environ-ments such as vision and speech (Hasler and Marr

2013). These neural-inspired systems are exem-plified by a set of computational principles,including hybrid analog-digital signal representa-tions (discussed next), co-location of memory andprocessing, unsupervised statistical learning, anddistributed representations of information.

Technology Platforms

Information representation can have a profoundeffect on information processing. The spikingmodel found in biology is a sparse coding schemerecognized by the neuroscience community as aneural encoding strategy for information pro-cessing (Ostojic 2014; Paugam-Moisy and Bohte2012; Kumar et al. 2010; Izhikevich 2003;Diesmann et al. 1999; Borst and Theunissen1999) and has code-theoretic justifications(Sarpeshkar 1998; Thorpe et al. 2001; Maasset al. 2002). Spiking approaches promise extremeimprovements in computational power efficiency(Hasler and Marr 2013) because they directlyexploit the underlying physics of biology (Jaegerand Haas 2004; Sarpeshkar 1998; Maass 1997;Izhikivich 2007), analog electronics, or, in thepresent case, optoelectronics. Digital in amplitudebut temporally analog, spiking naturally inter-leaves robust, discrete representations for commu-nication with precise, continuous representationsfor computation in order to reap the benefits ofboth digital and analog. Spiking has two primaryadvantages over synchronous analog: (1) its ana-log variable (time) is less noisy than its digitalvariable (amplitude), and (2) it is asynchronous,without a global clock. Clock synchronizationallows for time-division multiplexing (TDM);however, it is a significant practical problem inmany-core systems (Mundy et al. 2015). Theseadvantages may account for the ubiquity of spik-ing in natural processing systems (Thorpe et al.2001). It is natural to deepen this distinction toinclude physical representational aspects, with theimportant result that optical carrier noise does notaccumulate. As will be discussed, when an opticalpulse is generated, it is transmitted and routedthrough a linear optical network with the help ofits wavelength identifier (Fig. 3).


Neuromorphic MicroelectronicsSpiking primitives have been built in CMOS ana-log circuits, digital neurosynaptic cores, and non-CMOS devices. Various technologies (Fig. 4)have demonstrated large-scale spiking neural net-works in electronics, including notably Neurogridas part of Stanford University’s Brains in Siliconprogram (Benjamin et al. 2014), IBM’s TrueNorthas part of DARPA’s SyNAPSE program (Merollaet al. 2014), HICANN as part of HeidelbergUniversity’s FACETS/BrainScaleS project(Schemmel et al. 2010), and University ofManchester’s neuromorphic chip as part of theSpiNNaker project (Furber et al. 2014); the lattertwo are under the flagship of the European Com-mission’s Human Brain Project (The HBP Report2012). These spiking platforms promise potentadvantages in efficiency, fault tolerance, andadaptability over von Neumann architectures tobetter interact with natural environments byapplying the circuit and system principles of neu-ronal computation, including robust analog sig-naling, physics-based dynamics, distributedcomplexity, and learning. Using thisneuromorphic hardware to process faster signals(e.g., radio waveforms) is, however, not a simplematter of accelerating the clock. These systemsrely on slow timescale operation to accomplishdense interconnection.

Whereas von Neumann processors rely onpoint-to-point memory processor communication,a neuromorphic processor typically requires alarge number of interconnects (i.e., �100 s ofmany-to-one fan-in per processor) (Hasler andMarr 2013). This requires a significant amountof multicasting, which creates a communicationburden. This, in turn, introduces fundamental per-formance challenges that result from RC and radi-ative physics in electronic links, in addition to thetypical bandwidth-distance-energy limits ofpoint-to-point connections (Miller 2000). Whilesome incorporate a dense mesh of wires overlay-ing the semiconductor substrate as crossbararrays, large-scale systems are ultimately forcedto adopt some form of TDM or packet switching,notably, address-event representation (AER),which introduces the overhead of representingspike as digital codes instead of physical pulses.This abstraction at the architectural level allowsvirtual interconnectivities to exceed wire densityby a factor related to the sacrificed bandwidth,which can be orders of magnitude (Boahen2000). Spiking neural networks (SNNs) basedon AER are thus effective at targeting biologicaltimescales and the associated application space:real-time applications (object recognition) in thekHz regime (Merolla et al. 2014; Furber et al.2014) and accelerated simulation in the lowMHz regime (Schemmel et al. 2010). However,

Analog Signal

timetime

Digital Signal (coded as bits)

time

Hybrid Signal (coded as events)

NeuromorphicPhotonics, Principles of,Fig. 3 Spiking neuralnetworks encodeinformation as events intime rather than bits.Because the time at which aspike occurs is analog whileits amplitude is digital, thesignals use a mixed-signalor hybrid encoding scheme(Reproduced from Tait et al.2014a). With permission ofSpringer)


neuromorphic processing for high-bandwidthapplications in the GHz regime (such as sensingand manipulating the radio spectrum and forhypersonic aircraft control) must take a funda-mentally different approach to interconnection.

Toward Neuromorphic PhotonicsJust as optics and photonics are being employedfor interconnection in conventional CPU systems,optical networking principles can be applied to theneuromorphic domain (Fig. 2 (right)). Mapping aprocessing paradigm to its underlying dynamics,than abstracting the physics away entirely, cansignificantly streamline efficiency and perfor-mance, and mapping a laser’s behavior to a neu-ron’s behavior relies on discovering formalmathematical analogies (i.e., isomorphisms) intheir respective governing dynamics. Many ofthe physical processes underlying photonicdevices have been shown to have a strong analogywith biological processing models, which canboth be described within the framework of non-linear dynamics. Large-scale integrated photonicplatforms (see Fig. 5) offer an opportunity for

ultrafast neuromorphic processing that comple-ments neuromorphic microelectronics aimed atbiological timescales. The high switching speeds,high communication bandwidth, and low crosstalk achievable in photonics are very well-suitedfor an ultrafast spike-based information schemewith high interconnection densities (Prucnal et al.2016; Tait et al. 2014b). The efforts in this bud-ding research field aims to synergistically inte-grate the underlying physics of photonics withspiking neuron-based processing. Neuromorphicphotonics represents a broad domain of applica-tions where quick, temporally precise, and robustsystems are necessary.

Later in this entry, we compare metricsbetween neuromorphic electronics andneuromorphic photonics.

Neuromorphic Photonics

Photonics has revolutionized information trans-mission (communication and interconnects),while electronics, in parallel, has dominated

Neuromorphic Photonics, Principles of,Fig. 4 Selected pictures of five different neuromorphichardware discussed here. They include TrueNorth

(Merolla et al. 2014), HICANN (Schemmel et al. 2010),SpiNNaker (Furber et al. 2014), Neurogrid (Benjaminet al. 2014)


information transformation (computations). Thisleads naturally to the following question: how canthe unifying of the boundaries between the two bemade as effective as possible? (Keyes 1985;Tucker 2010; Caulfield and Dolev 2010). CMOSgates only draw energy from the rail when andwhere called upon; however, the energy requiredto drive an interconnect from one gate to the nextdominates CMOS circuit energy use. Relaying asignal from gate to gate, especially using aclocked scheme, induces penalties in latency andbandwidth compared to an optical waveguide pas-sively carrying multiplexed signals.

This suggests that starting up a new architec-ture from a photonic interconnection fabricsupporting nonlinear optoelectronic devices canbe uniquely advantageous in terms of energy effi-ciency, bandwidth, and latency, sidesteppingmany of the fundamental trade-offs in digital andanalog electronics. It may be one of the few prac-tical ways to achieve ultrafast, complex on-chipprocessing without consuming impracticalamounts of power (Prucnal and Shastri 2017).

Complex photonic systems have been largelyunexplored due to the absence of a robust pho-tonic integration industry. Recently, however, the

landscape for manufacturable photonic chips hasbeen changing rapidly and now promises toachieve economies of scale previously enjoyedsolely by microelectronics. In particular, a newphotonic manufacturing hybrid platform thatcombines in the same chip both active (e.g., lasersand detectors) and passive elements (e.g., wave-guides, resonators, modulators) is emerging (Fanget al. 2007; Liang et al. 2010; Liang and Bowers2010a; Roelkens et al. 2010; Heck et al. 2013).A neuromorphic photonic approach based on thisplatform could potentially operate six to eightorders of magnitude faster than neuromorphicelectronics when accounting for the bandwidthreduction of virtualizing interconnects (Prucnaland Shastri 2017) (cf. Fig. 6; also see Table 1and related discussion).

In the past, the communication potentials ofoptical interconnects have received attention forneural networking; however, attempts to realizeholographic or matrix-vector multiplication sys-tems have failed to outperform mainstream elec-tronics at relevant problems in computing, whichcan perhaps be attributed to the immaturity oflarge-scale integration technologies andmanufacturing economics.

Bonded III-V layer• DFB excitable lasers

Off-chip pins• Analog electronic I/O• Programming interface• PowerSOI layer

• Silicon waveguides, filters

Module backbonering

NetworkStage

IMAssembly

LIF

• Electro-optic modulators

Neuromorphic Photonics, Principles of,Fig. 5 Conceptual rendering of a photonic neuromorphicprocessor. Laser arrays (orange layer) implement pulsed(spiking) dynamics with electro-optic physics, and a

photonic network on-chip (blue and gray) supports com-plex structures of virtual interconnection among these ele-ments, while electronic circuitry (yellow) controls stability,self-healing, and learning


Computational Speed (MMAC/s/cm2)

Eff

icie

ncy

(G

MA

C/s

/W)

10210–210–1

102103104105106107108109

110

104 106 108 1010 10111

TrueNorth

NeuroGrid HICANN

Neuromorphic Electronics

Silicon photonics

Digital Electronics

Digital Efficiency Wall

State-of-the-Art

SpiNNaker Microwave Electronics

Neuromorphic Photonics

Nanophotonics

Neuromorphic Photonics, Principles of,Fig. 6 Comparison of neuromorphic hardware platforms.Neuromorphic photonic architectures potentially sport bet-ter speed-to-efficiency characteristics than state-of-the-artelectronic neural nets (such as IBM’s TrueNorth, StanfordUniversity’s Neurogrid, Heidelberg University’s HICANN),as well as advanced digital electronic systems (such as the

University of Manchester’s SpiNNaker). On the top right:the photonic neuron platforms studied in Prucnal and Shastri(2017). The regions highlighted in the graph are approxi-mate, based on qualitative trade-offs of each technology(Adapted from Ferreira de Lima et al. 2017). Licensedunder Creative Commons Attribution-NonCommercial-NoDerivatives License (CC BY-NC-ND))

Neuromorphic Photonics, Principles of, Table 1 Comparison between different neuromorphic processors

ChipMAC rate/processora

Energy/MAC(pJ)b

Processorfan-in

Area/MAC(mm2)c

Synapseprecision (bit)

Photonic hybrid III-V/Sid 20 GHz 0.26 108 205 5.1

Sub-l photonics e (futuretrend)

200 GHz 0.0007 �200 20 8

HICANN (Schemmelet al. 2010)

22.4 MHz 198.4 224 780 4

TrueNorth (Merolla et al.2014)

2.5 kHz 0.27 256 4.9 5

Neurogrid (Benjaminet al. 2014)

40.1 kHz 119 4096 7.1 13

SpiNNakerf (Furber et al.2014)

3.2 kHz 6 � 105 320 217 16

aA MAC event occurs each time a spike is integrated by the neuron. Neuron fan-in refers to the number of possibleconnections to a single neuronbThe energy per MAC for HICANN, TrueNorth, Neurogrid, and SpiNNaker were estimated by dividing wall-plug powerto number of neurons and to operational MAC rate per processorcThe area per MAC was estimated by dividing the chip/board size to the number of MAC units (neuron count times fan-in).All numbers therefore include overheads in terms of footprint and areadIII–V/Si hybrid stands for estimated metrics of a spiking neural network in a photonic integrated circuit in a III–V/Sihybrid platformeSub-l stands for estimated metrics for a platform using optimized sub-wavelength structures, such as photonic crystalsfNeurons, synapses, and spikes are digitally encoded in event headers that travel around co-integrated processor cores. Soall numbers here are based on a typical application example


Techniques in silicon photonic integrated cir-cuit (PIC) fabrication are driven by a tremendousdemand for optical interconnects within conven-tional digital computing systems (Smit et al. 2012;Jalali and Fathpour 2006), which means platformsfor systems integration of active photonics arebecoming commercial reality (Liang et al. 2010;Roelkens et al. 2010; Heck et al. 2013; Liang andBowers 2010b; Marpaung et al. 2013). The poten-tial of recent advances in integrated photonics toenable unconventional computing has not yetbeen investigated. The theme of current researchhas been on howmodern PIC platforms can topplehistoric technological barriers between large-scaleanalog networks and photonic neural systems. Inthis context, there are two complementary areas ofinvestigation by the research community, namely,photonic spike processing and photonic reservoircomputing.While the scope of this entry is limitedto the former, we briefly introduce both.

Photonic Spike ProcessingAn investigation of photonics for information pro-cessing based on spikes has taken place alongsidethe development of electronic spiking architec-tures. Since the first demonstration of photonicspike processing by Rosenbluth et al.(Rosenbluth et al. 2009), there has been a surgein research related to aspects of spike processingin various photonic devices with a recent bloom ofproposed forms of spiking dynamics (Tait et al.

2014b; Kelleher et al. 2010; Kravtsov et al. 2011;Fok et al. 2011; Coomans et al. 2011; Brunsteinet al. 2012; Nahmias et al. 2013; Van Vaerenberghet al. 2013; Aragoneses et al. 2014; Selmi et al.2014; Hurtado and Javaloyes 2015; Garbin et al.2015; Shastri et al. 2016; Romeira et al. 2016) – astrategy that could lead to combined computationand communication in the same substrate.

We recently (Prucnal et al. 2016; Prucnal andShastri 2017) reviewed the recent surge of interest(Tait et al. 2014a; Kelleher et al. 2010; Coomanset al. 2011; Brunstein et al. 2012; Nahmias et al.2013, 2015; Van Vaerenbergh et al. 2012, 2013;Aragoneses et al. 2014; Selmi et al. 2014; Hurtadoand Javaloyes 2015; Garbin et al. 2015; Shastriet al. 2016; Yacomotti et al. 2006a; Goulding et al.2007; Hurtado et al. 2010, 2012; Coomans 2012;Romeira et al. 2013, 2016; Sorrentino et al. 2015)in the information processing abilities of semicon-ductor devices that exploit the dynamical isomor-phism between semiconductor photocarriers andneuron biophysics. Many of these proposals for“photonic neurons” or “laser neurons” or “opticalneurons” for spike processing are based on lasersoperating in an excitable regime (Fig. 7). Excit-ability (Hodgkin and Huxley 1952; Krauskopfet al. 2003) is a dynamical system property under-lying all-or-none responses.

The difference in physical timescales allowsthese laser systems to exhibit these properties,except many orders of magnitude faster than

Spiking Excitability

Isomorphism between physics and

computation

PHOTONIC SPIKE PROCESSOR

COMPUTATIONAL MODEL UNDERLYING PHYSICSNeuromorphicPhotonics, Principles of,Fig. 7 Analogies betweenspike processing andphotonics can be exploitedto create a computationalparadigm that performsbeyond the sum of its parts.By reducing the abstractionbetween process (spiking)and physics (excitability),there could be a significantadvantage on speed, energyusage, scalability (Adaptedwith permission fromPrucnal et al. 2016).Copyright 2016 OpticalSociety of America)


their biological counterparts (Nahmias et al.2013); the temporal resolution (tied to spikewidths) and processing speed (tied to refractoryperiod) are accelerated by factors nearing 100 mil-lion (Fig. 8). A network of photonic neurons couldopen computational domains that demand unprec-edented temporal precision, power efficiency, andfunctional complexity, potentially includingapplications in wideband radio-frequency(RF) processing, adaptive control of multi-antenna systems, and high-performance scientificcomputing.

Photonic Reservoir ComputingReservoir computing (RC) is another promisingapproach for neuro-inspired computing. A centraltenet of RC is that complex processes are gener-ated in a medium whose behavior is not necessar-ily understood theoretically. Instead, the“reservoir” (a fixed, recurrent network of non-linear nodes; see Fig. 9) generates a large numberof complex processes, and linear combinations ofreservoir signals are trained to approximate a

desired task (Verstraeten et al. 2007). To arrive ata user-defined behavior, reservoirs do not need tomodel or program and instead rely on supervisedmachine learning techniques for simple linearclassifiers. This is advantageous in systemswhose overall behavior is complex, yet difficultto model or correspond to a theoretical behavior.There are a wide class of physical systems that fitthat description, and the reservoir concept makesthem highly likely to apply to widespread infor-mation processing tasks (Soriano et al. 2015).

Over the past several years, reservoir com-puters have been constructed that exploit theincredible bandwidths and speeds available tophotonic signals. These “photonic reservoirs” uti-lize optical multiplexing strategies to form highlycomplex virtual networks. Photonic RC particu-larly is attractive when the information to be pro-cessed is already in the optical domain, forexample, applications in telecommunicationsand image processing. Recently, there has been asignificant development in the hardware realiza-tion of RC. Optical reservoirs have been

Neuromorphic Photonics, Principles of,Fig. 8 Difference in spike processing timescales (pulsewidth and refractory period) between biological neurons

(left), electronic spiking neurons (middle), and photonicneurons (right) (Reproduced with permission from Prucnalet al. (2016). Copyright 2016 Optical Society of America)

NeuromorphicPhotonics, Principles of,Fig. 9 Comparison of thearchitectures of afeedforward (left-hand side)with a recurrent neuralnetwork (right-hand side);the gray arrows sketch thepossible direction ofcomputation (Adapted fromBurgsteiner (2005))


demonstrated with various schemes such asbenchtop demonstrations with a fiber with a singlenonlinear dynamical node (Brunner et al. 2013a,b; Paquot et al. 2012; Martinenghi et al. 2012;Larger et al. 2012; Duport et al. 2012, 2016;Hicke et al. 2013; Soriano et al. 2013; Ortínet al. 2015), and integrated solutions includingmicroring resonators (Mesaritakis et al. 2013), anetwork of coupled semiconductor optical ampli-fiers (SOAs) (Vandoorne et al. 2011), and a pas-sive silicon photonic chip (Vandoorne et al. 2014).

It has been experimentally demonstrated andverified that some of these photonic RC solutionsachieve highly competitive figures of merit atunprecedented data rates often outperformingsoftware-based machine learning techniques forcomputationally hard tasks such as spoken digitand speaker recognition, chaotic time series pre-diction, signal classification, or dynamical systemmodeling. Another significant advantage ofphotonic-based approaches, as pointed out byVandoorne et al. (Vandoorne et al. 2014), is thestraightforward use of coherent light to exploitboth the phase and amplitude of light. The simul-taneous exploitation of two physical quantitiesresults in a notable improvement over real-valuednetworks that are traditionally used in software-based RC – a reservoir operating on complexnumbers in essence doubles the internal degreesof freedom in the system, leading to a reservoirsize that is roughly twice as large as the samedevice operated with incoherent light.

Neuromorphic spike processing and reservoirapproaches differ fundamentally and possesscomplementary advantages. Both derive a broadrepertoire of behaviors (often referred to as com-plexity) from a large number of physical degreesof freedom (e.g., intensities) coupled throughinteraction parameters (e.g., transmissions). Bothoffer means of selecting a specific, desired behav-ior from this repertoire using controllable param-eters. In neuromorphic systems, network weightsare both the interaction and controllable parame-ters, whereas, in reservoir computers, these twogroups of parameters are separate. This distinctionhas two major implications. Firstly, the interactionparameters of a reservoir do not need to be observ-able or even repeatable from system to system.

Reservoirs can thus derive complexity from phys-ical processes that are difficult to model or repro-duce. Furthermore, they do not require significanthardware to control the state of the reservoir.Neuromorphic hardware has a burden to corre-spond physical parameters (e.g., drive voltages)to model parameters (e.g., weights). Secondly,reservoir computers can only be made to elicit adesired behavior through instance-specific super-vised training, whereas neuromorphic computerscan be programmed a priori using a known set ofweights. Because neuromorphic behavior is deter-mined only by controllable parameters, theseparameters can be mapped directly between dif-ferent system instances, different types ofneuromorphic systems, and simulations.Neuromorphic hardware can leverage existingalgorithms (e.g., Neural Engineering Framework(NEF) (Stewart and Eliasmith 2014)), map virtualtraining results to hardware, and particular behav-iors are guaranteed to occur. Photonic RCs can ofcourse be simulated; however, they have nocorresponding guarantee that a particular hard-ware instance will reproduce a simulated behavioror that training will be able to converge to thisbehavior.

Challenges for Integrated NeuromorphicPhotonicsKey criteria for nonlinear elements to enable ascalable computing platform includethresholding, fan-in, and cascadability (Keyes1985; Tucker 2010; Caulfield and Dolev 2010).Past approaches to optical computing have metchallenges realizing these criteria. A variety ofdigital logic gates in photonics that suppressamplitude noise accumulation have been claimed,but many proposed optical logic devices do notmeet necessary conditions of cascadability. Ana-log photonic processing has found application inhigh-bandwidth filtering of microwave signals(Capmany et al. 2006), but the accumulation ofphase noise, in addition to amplitude noise, limitsthe ultimate size and complexity of such systems.

Recent investigations (Prucnal and Shastri2017; Tait et al. 2014b; Coomans et al. 2011;Brunstein et al. 2012; Nahmias et al. 2013, 2015;Van Vaerenbergh et al. 2013; Aragoneses et al.


2014; Selmi et al. 2014; Hurtado and Javaloyes2015; Garbin et al. 2015; Shastri et al. 2016;Romeira et al. 2016) have suggested that an alter-native approach to exploit the high bandwidth ofphotonic devices for computing lies not inincreasing device performance or fabrication, butinstead in examining models of computation thathybridize techniques from analog and digital pro-cessing. These investigations have concluded thata photonic neuromorphic processor could satisfythem by implementing a model of a neuron, i.e., aphotonic neuron, as opposed to the model of alogic gate. Early work in neuromorphic photonicsinvolved fiber-based spiking approaches for learn-ing, pattern recognition, and feedback (Rosenbluthet al. 2009; Kravtsov et al. 2011; Fok et al. 2011).Spiking behavior resulted from a combination ofSOA together with a highly nonlinear fiberthresholder, but they were neither excitable norasynchronous and therefore not suitable for scal-able, distributed processing in networks.

“Neuromorphism” implies a strict isomor-phism between artificial neural networks andoptoelectronic devices. There are two researchchallenges necessary to establish this isomor-phism: the nonlinearity (equivalent tothresholding) in individual neurons and the syn-aptic interconnection (related to fan-in andcascadability) between different neurons, as willbe discussed in the proceeding sections. Once theisomorphism is established and large networks arefabricated, we anticipate that the computationalneuroscience and software engineering will havea new optimized processor for which they canadapt their methods and algorithms.

Photonic neurons address the traditional prob-lem of noise accumulation by interleaving physi-cal representations of information.Representational interleaving, in which a signalis repeatedly transformed between codingschemes (digital-analog) and physical variables(electronic-optical), can grant many advantagesto computation and noise properties. From anengineering standpoint, the logical function of anonlinear neuron can be thought of as increasingsignal-to-noise ratio (SNR) that tends to degradein linear systems, whether that means a continu-ous nonlinear transfer function suppressing

analog noise or spiking dynamics curtailingpulse attenuation and spreading. As a result, weneglect purely linear PNNs as they do not offermechanisms to maintain signal fidelity in a largenetwork in the presence of noise.

The optical channel is highly expressive andcorrespondingly very sensitive to phase and fre-quency noise. For example, the networking archi-tecture proposed in Tait et al. (2014b) relies onwavelength-division multiplexing (WDM) forinterconnecting many points in a photonic sub-strate together. Any proposal for networking com-putational primitives must address the issue ofpractical cascadability: transferring informationand energy in the optical domain from one neuronto many others and exciting them with the samestrength without being sensitive to noise. This isnotably achieved, for example, by encoding infor-mation in energy pulses that can trigger stereotyp-ical excitation in other neurons regardless of theiranalog amplitude. In addition, as will be discussednext, schemes which exhibit limitations withregard to wavelength channels may require alarge number of wavelength conversion steps,which can be costly, noisy, and inefficient.

Photonic Neuron

What Is an Artificial Neuron?Neuroscientists research artificial neural networksas an attempt to mimic the natural processingcapabilities of the brain. These networks of simplenonlinear nodes can be taught (rather than pro-grammed) and reconfigured to best execute adesired task; this is called learning. Today, neuralnets offer state-of-the-art algorithms for machineintelligence such as speech recognition, naturallanguage processing, and machine vision(Bengio et al. 2013).

Three elements constitute a neural network: aset of nonlinear nodes (neurons), configurableinterconnection (network), and information repre-sentation (coding scheme). An elementary illus-tration of a neuron is shown in Fig. 10. Thenetwork consists of a weighted directed graph, inwhich connections are called synapses. The inputof a neuron is a linear combination (or weighted


addition) of the outputs of the neurons connectedto it. Then, the particular neuron integrates thecombined signal and produces a nonlinearresponse, represented by an activation function,usually monotonic and bounded.

Three generations of neural networks were his-torically studied in computational neuroscience(Maass 1997). The first was based on theMcCulloch-Pitts neural model, which consists ofa linear combiner followed by a steplike activa-tion function (binary output). These neural net-works are Boolean complete – i.e., they have theability of simulating any Boolean circuit and aresaid to be universal for digital computations. Thesecond generation implemented analog outputs,with a continuous activation function instead ofa hard thresholder. Neural networks of the secondgeneration are universal for analog computationsin the sense they can uniformly approximate arbi-trarily well any continuous function with a com-pact domain (Maass 1997). When augmentedwith the notion of “time,” recurrent connectionscan be created and be exploited to create attractorstates (Eliasmith 2005) and associative memory(Hopfield 1982) in the network.

Physiological neurons communicate with eachother using pulses called action potentials orspikes. In traditional neural network models, ananalog variable is used to represent the firing rateof these spikes. This coding scheme called ratecoding was believed to be a major, if not the only,

coding scheme used in biology. Surprisingly,there are some fast analog computations in thevisual cortex that cannot possibly be explainedby rate coding. For example, neuroscientists dem-onstrated in the 1990s that a single cortical area inmacaque monkey is capable of analyzing andclassifying visual patterns in just 30 ms, in spiteof the fact that these neurons’ firing rates areusually below 100 Hz – i.e., less than three spikesin 30 ms (Thorpe et al. 2001; Maass 1997; Perrettet al. 1982) which directly challenges the assump-tions of rate coding. In parallel, more evidencewas found that biological neurons use the precisetiming of these spikes to encode information,which led to the investigation of a third generationof neural networks based on a spiking neuron.

The simplicity of the models of the previousgenerations precluded the investigation of thepossibilities of using time as resource for compu-tation and communication. If the timing of indi-vidual spikes itself carry analog information(temporal coding), then the energy necessary tocreate such spike is optimally employed to expressinformation. Furthermore, Maass et al. showed thatthis third generation is a generalization of the firsttwo and, for several concrete examples, can emu-late real-valued neural network models while beingmore robust to noise (Maass 1997).

For example, one of the simplest models of aspiking neuron is called leaky integrate-and-fire(LIF), described in Eq. 1. It represents a simplified

Neuromorphic Photonics, Principles of,Fig. 10 Nonlinear model of a neuron. Note the threeparts: (i) a set of synapses, or connecting links; (ii) anadder, or linear combiner, performing weighted addition;

and (iii) a nonlinear activation function (Reproduced withpermission from Prucnal et al. (2016). Copyright 2016Optical Society of America)


circuit model of the membrane potential of a bio-logical spiking neuron.

CmdVm tð Þdt

¼ 1

RmVm tð Þ � VLð Þ þ Iapp tð Þ;

if Vm tð Þ� > Vthresh

then releaseaspike andset Vm tð Þ� ! Vreset,

(1)

where Vm(t) is the membrane voltage, Rm themembrane resistance, VL the equilibrium poten-tial, and Iapp the applied current (input). More bio-realistic models, such as the Hodgkin-Huxleymodel, involve several ordinary differential equa-tions and nonlinear functions.

However, simply simulating neural networkson a conventional computer, be it of any genera-tion, is costly because of the fundamentally serialnature of CPU architectures. Bio-realistic SNNpresent a particular challenge because of theneed for fine-grained time discretization(Izhikevich 2004). Engineers circumvent thischallenge by employing an event-driven simula-tion model which resolves this issue by storing thetime and shape of the events expanded in a suit-able basis in a simulation queue. Although sim-plified models do not faithfully reproduce keyproperties of cortical spiking neurons, it allowsfor large-scale simulations of SNNs, from whichkey networking properties can be extracted.

Alternatively, one can build an unconven-tional, distributed network of nonlinear nodes,which directly use the physics of nonlineardevices or excitable dynamical systems, signifi-cantly dropping energetic cost per bit.

Here, we discuss recent advances inneuromorphic photonic hardware and the con-straints to which particular implementationsmust subject, including accuracy, noise,cascadability, and thresholding. A successfularchitecture must tolerate eventual inaccuraciesand noise, indefinite propagation of signals, andprovide mechanisms to counteract noise accumu-lation as the signal traverses across the network.

Basic Requirements for a Photonic NeuronAn artificial neuron described in Fig. 10 mustperform three basic mathematical operations:array multiplication (weighting), summation, anda nonlinear transformation (activation function).Moreover, the inputs to be weighted in the firststage must be of the same nature of the output – inthe case considered here, photons.

As the size of the network grows, additionalmechanisms are required at the hardware level toensure the integrity of the signals. The neuronmust have a scalable number of inputs, referredto as maximum fan-in (Nf), which will determinethe degree of connectivity of the network. Eachneuron’s output power must be strong enough todrive at least Nf others (cascadability). This con-cept is tied closely with that of thresholding: theSNR at the output must be higher than at its input.Cascadability, thresholding, and fan-in are partic-ularly challenging to optical systems due to quan-tum efficiency (photons have finite supply) andamplified spontaneous emission (ASE) noise,which degrades SNR.

The Processing Network NodeA networkable photonic device with optical I/O,provided that it is capable of emulating an artifi-cial neuron, is named a processing network node(PNN) (Tait et al. 2014b). Formulations of a pho-tonic PNN can be divided into two main catego-ries: all-optical and optical-electrical-optical(O/E/O), respectively, classified according towhether the information is always embedded inthe optical domain or switches from optical toelectrical and back. We note that the term all-optical is sometimes very loosely defined in engi-neering articles. Physicists reserve it for devicesthat rely on parametric nonlinear processes, suchas four-wave mixing. Here, our definitionincludes devices that undergo nonparametric pro-cesses as well, such as semiconductor lasers withoptical feedback, in which optical pulses directlyperturb the carrier population, triggering quickenergy exchanges with the cavity field that resultsin the release of another optical pulse.

Silicon waveguides have a relatively enormoustransparency window of 7.5 THz (Agrawal 2002)over which they can guide lightwaves with very


low attenuation and cross talk, in contrast withelectrical wires or radio-frequency transmissionlines. With WDM, each input signal exists at adifferent wavelength but is superimposed withother signals onto the same waveguide. For exam-ple, to maximize the information throughput, asingle waveguide could carry hundreds of wide-band signals (�20 GHz) simultaneously. As such,it is highly desirable and crucial to design a PNNthat is compatible with WDM. All-optical ver-sions of a PNN must have some way to summultiwavelength signals, and this requires a pop-ulation of charge carriers. On the other hand, O/E/O versions could make use of photodetectors(PD) to provide a spatial sum of WDM signals.The PD output could drive an E/O converter,involving a laser or a modulator, whose opticaloutput is a nonlinear result of the electrical input.Instances of both techniques are presented in thenext section.

All-Optical PNNsCoherent injection models are characterized byinput signals directly interacting with cavitymodes, such that outputs are at the same wave-length as inputs (Fig. 11a). Since coherent opticalsystems operate at a single wavelength l, the

signals lack distinguishability from one anotherin a WDM-encoded framework. As demonstratedin Alexander et al. (2013), the effective weight ofcoherently injected inputs is also strongly phasedependent. Global optical phase control presents achallenge in synchronized laser systems but alsoaffords an extra degree of freedom to configureweight values.

Incoherent injection models inject light in awavelength lj to selectively modulate anintracavity property that then triggers excitableoutput pulses in an output wavelength li(Fig. 11b). A number of approaches (Nahmiaset al. 2013; Selmi et al. 2014, 2015; Hurtado andJavaloyes 2015) – including those based on opti-cal pumping – fall under this category. Whiledistinct, the output wavelength often has a strin-gent relationship with the input wavelength. Forexample, excitable micropillar lasers (Selmi et al.2014; Barbay et al. 2011) are carefully designed tosupport one input mode with a node coincidentwith an antinode of the lasing mode. In caseswhere the input is also used as a pump (Shastriet al. 2016), the input wavelength must be shorterthan that of the output in order to achieve carrierpopulation inversion.

WDM networking introduces wavelength con-straints that conflict with the ones inherent tooptical injection. One approach for networkingoptically injected devices is to attempt to separatethese wavelength constraints. In early work onneuromorphic photonics in fiber, this was accom-plished with charge-carrier-mediated cross-gainmodulation (XGM) in an SOA (Rosenbluth et al.2009; Kravtsov et al. 2011; Fok et al. 2011).

O/E/O PNNsIn this kind of PNN, the O/E subcircuit is respon-sible for the weighted addition functionality,whereas the E/O is responsible for the non-linearity (Fig. 11c). Each subcircuit can thereforebe analyzed independently. The analysis of anO/E WDM weighted addition circuit is deferredto a later section (photonic neural networks).

The E/O subcircuit of the PNN must take anelectronic input representing the complementaryweighted sum of optical inputs, perform somedynamical or nonlinear process, and generate a

Neuromorphic Photonics, Principles of,Fig. 11 General classification of semiconductor excitablelasers based on (a) coherent optical injection, (b) non-coherent optical injection, and (c) full electrical injection.Each of these lasers can be pumped either electrically oroptically (Reproduced from Ferreira de Lima et al. (2017).Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives License. (CCBY-NC-ND))


clean optical output on a single wavelength. Fig-ure 12 classifies six different ways nonlinearitiescan be implemented in an E/O circuit. The type ofnonlinearity, corresponding to different neuralmodels, is separated into dynamical systems andcontinuous nonlinearities, both of which have asingle input u and output y. A continuous non-linearity is described by a differential equation_y ¼ f y, uð Þ. This includes continuous-time recur-rent neural networks (CTRNNs) such as Hopfieldnetworks. The derivative of y introduces a senseof time, which is required to consider recurrentnetworking, although it does not excludefeedforward models where time plays no role,such as perceptron models. A dynamical systemhas an internal state x

!and is described by

_x ¼ g x!, u

� �; _y ¼ h x

!, y, u

� �, where the second

differential equation represents the mappingbetween the internal state x

!and the output y.

There are a wide variety of spiking models basedon excitability, threshold behavior, relaxationoscillations, etc. covered, for example, inIzhikivich (2007).

Physical implementations of these nonlinear-ities can arise from devices falling into roughlythree categories: pure electronics, electro-opticphysics in modulators, and active laser behavior(Fig. 12). Figure 12a illustrates spiking lasers,which are detailed in the next section and offerperhaps the most promise in terms of garneringthe full advantage of recent theoretical results onspike processing efficiency and expressiveness.Figure 12b is a spiking modulator. The work inVan Vaerenbergh et al. (2012) might be adapted tofit this classification; however, to the authors’knowledge, an ultrafast spiking modulatorremains to be experimentally demonstrated.Figure 12c illustrates a purely electronic approachto nonlinear neural behavior. Linear E/O could bedone by either a modulator or directly driven laser.This class could encompass interesting intersec-tions with efficient analog electronic neurons insilicon (Indiveri et al. 2011; Pickett et al. 2013).A limitation of these approaches is the need tooperate slow enough to digitize outputs into aform suitable for electronic TDM and/or AERrouting.

Figure 12d describes a laser with continuousnonlinearity, an instantiation of which wasrecently demonstrated in Nahmias et al. (2016).Figure 12e shows a modulator with continuousnonlinearity; the first demonstration of which in aPNN and recurrent network is presented in Taitet al. (2017). The pros and cons between theschemes in Fig. 12d, e are the same ones broughtup by the on-chip versus off-chip light sourcedebate, currently underway in the silicon photoniccommunity. On-chip sources could provideadvantageous energy scaling (Heck and Bowers2014), but they require the introduction of exoticmaterials to the silicon photonic process to pro-vide optical gain. Active research in this area hasthe goal of making source co-integration feasible(Liang and Bowers 2010a; Roelkens et al. 2010).An opposing school of thought argues thaton-chip sources are still a nascent technology(Vlasov 2012). While fiber-to-chip coupling pre-sents practical issues (Barwicz et al. 2016), dis-crete laser sources are cheap and well understood.Furthermore, on-chip lasers dissipate largeamounts of power (Sysak et al. 2011), the fullimplications of which may complicate systemdesign (Vlasov 2012). In either case, the concep-tion of a PNN module, consisting of a photonicweight bank, detector, and E/O converter, as aparticipant in a broadcast-and-weight network,could be applied to a broad array of neuronmodels and technological implementations.

Both discussed all-optical and O/E/O PNNapproaches depend on charge-carrier dynamics,whose lifetime eventually limits the bandwidthof the summation operation. The O/E/O strategy,however, has a few advantages: it can be modu-larized; it uses more standard optoelectronic com-ponents; and it is more amenable to integration.Therefore here we give more attention to thisstrategy. Moreover, although the E/O part of thePNN can involve any kind of nonlinearity(Fig. 12), not necessarily spiking, we are focusingon spiking behavior because of its interestingnoise resistance and richness of representation.As such, we study here excitable semiconductorlaser physics with the objective of directly pro-ducing optical spikes.


In this light, the PNN could be separated intothree parts, just like the artificial neuron:weighting, addition, and neural behavior.Weighting and adding define how nonlinearnodes can be networked together, whereas theneural behavior dictates the activation functionshown in Fig. 10. In the next section, we reviewrecent developments of semiconductor excitablelasers that emulate spiking neural behavior, and,following that, we discuss a scalable WDM net-working scheme.

Excitable/Spiking Lasers

In the past few years, there has been a bloom ofoptoelectronic devices exhibiting excitabledynamics isomorphic to a physiological neuron.Excitable systems can be roughly defined by threecriteria: (a) there is only one stable state at whichthe system can indefinitely stay at rest; (b) whenexcited above a certain threshold, the systemundergoes a stereotypical excursion, emitting aspike; and (c) after the excursion, the systemdecays back to rest in the course of a refractoryperiod during which it is temporarily less likely toemit another spike.

Analogy to Leaky Integrate-and-Fire ModelExcitable behavior can be realized near the thresh-old of a passively Q-switched two-section laserwith saturable absorber (SA). Figure 13a, b showsan example of integrated design in a hybrid pho-tonic platform. This device comprises a III–Vepitaxial structure with multiple quantum well(MQW) region (the gain region) bonded to alow-loss silicon rib waveguide that rests on asilicon-on-insulator (SOI) substrate withsandwiched layers of graphene acting as a satura-ble absorber region. The laser emits light along thewaveguide structure into a passive silicon net-work. Figure 13c–e shows experimental datafrom a fiber ring laser prototype, demonstratingkey properties of excitability.

In general, the dynamics of a two-section lasercomposed of a gain section and a saturableabsorber (SA) can be described by the Yamadamodel (Eqs. 2, 3, and 4) (Yamada 1993). This 3Ddynamical system, in its simplest form, can bedescribed with the following undimensionalizedequations (Nahmias et al. 2013; Barbay et al.2011):

No

nlin

ear

Dyn

amic

s(S

pik

ing

)

dbias/pump

input

outputLinear E/O

Modulator Nonlinearity Electronic Nonlinearity

pump

output

input

bias

output

input

Laser Nonlinearity

pump

output

input

bias

output

input

bias/pump

input

outputLinear E/O

e f

a b c

Co

ntin

uous

No

nlin

eari

ty

Neuromorphic Photonics, Principles of,Fig. 12 Classification of O/E/O PNN nonlinearities andpossible implementations. (a) Spiking laser neuron. (b)Spiking modulator. (c) Spiking or arbitrary electronic sys-tem driving a linear electro-optic (E/O) transducer – eithermodulator or laser. (d) Overdriven continuous laser neu-ron, as demonstrated in Nahmias et al. (2016). (e)

Continuous modulator neuron, as demonstrated in Taitet al. (2017). (f) Continuous purely electronic nonlinearitywith optical output (Reproduced from Ferreira de Limaet al. 2017). Licensed under Creative CommonsAttribution-NonCommercial-NoDerivatives License.(CC BY-NC-ND)


InGaAsP

SCR

MQW

Si

SiO2

-1.5 -1 -0.5 0.5 1 1.5

1

00

x Distance ( mµ )

yD

ista

nce

(m

µ)

-0.5

0.5

0

Graphene + BN

InGaAsP

Si

SiO2

MQW

Contacts

1.5

1

y D

ista

nce

(nm

)

0.5

0

Graphene (0.335nm)

Boron Nitride (1nm)

Graphene (0.335nm)

a

b

Fig. 13 (continued)


dG tð Þdt¼ gG A� G tð Þ � G tð ÞI tð Þ½ � þ y tð Þ (2)

dQ tð Þdt¼ gQ B� Q tð Þ � aQ tð ÞI tð Þ½ (3)

dI tð Þdt¼ gI G tð Þ � Q tð Þ � 1½ �I tð Þ þ ef Gð Þ, (4)

whereG(t) models the gain,Q(t) is the absorption,I(t) is the laser intensity, A is the bias current of thegain region, B is the level of absorption,a describes the differential absorption relative tothe differential gain, gG is the relaxation rate of thegain, gQ is the relaxation rate of the absorber, gI isthe inverse photon lifetime, y(t) is the time-dependent input perturbations, and ∊f (G) is thespontaneous noise contribution to intensity; ∊ is asmall coefficient.

In simple terms, if we assume electricalpumping at the gain section, the input perturba-tions are integrated by the gain section accordingto Eq. 2. An SA effectively becomes transparentas the light intensity builds up in the cavity andbleaches its carriers. It was shown in Nahmiaset al. (2013) that the near-threshold dynamics ofthe laser described can be approximated to Eq. 5:

dG tð Þdt¼ �gG G tð Þ � Að Þ þ y tð Þ;

ifG tð Þ > Gthreshℤreleaseapulse, andset G tð Þ ! Greset,

(5)

where G(t) models the gain, gG is the gain carrierrelaxation rate, and A is the gain bias current. Theinput y(t) can include spike inputs of the formy(t) = �idi(t � ti) for spike firing times ti, Gthresh

is the gain threshold, and Greset � 0 is the gain attransparency.

One can note the striking similarity to the LIFmodel in Eq. 1: setting the variables gG= 1/RmCm,A = VL, y(t) = Iapp (t)/Rm Cm, and G(t) = Vm (t)shows their algebraic equivalence. Thus, the gainof the laser G(t) can be thought of as a virtualmembrane voltage, the input current A as a virtualequilibrium voltage, etc.

A remarkable difference can be observedbetween the two systems though: whereas in theneural cell membrane the timescales are governedby an RmCm constant of the order of ms, the carrierdynamics in lasers are as fast as ns. Although thisform of excitability was found in two-sectionlasers, other device morphologies have alsoshown excitable dynamics. The advantage ofconstructing a clear abstraction to the LIF modelis that it allows engineers to reuse the samemethods developed in the computational neuro-science community for programming aneuromorphic processor.

In the next section, we present recent opticaldevices with excitable dynamics.

Semiconductor Excitable LasersOptical excitability in semiconductor devices arebeing widely studied, both theoretically andexperimentally. These devices include multi-section lasers, ring lasers, photonic crystal nano-cavities, tunneling diode attached to laser diodes,and semiconductor lasers with feedback, summa-rized in Table 2. We group them under the termi-nology excitable lasers for convenience, butexceptions are described in the caption of thetable.

��

Neuromorphic Photonics, Principles of,Fig. 13 Excitable dynamics of the graphene excitablelaser. Blue and red curves correspond to input and outputpulses, respectively. (a) Cutaway architecture of a hybridInGaAsP-graphene-silicon evanescent laser (not to scale)showing a terraced view of the center. (b) Cross-sectionalprofile of the excitable laser with an overlaid electric field

(E-field) intensity E!��2

profile. (c–e) Excitable dynamics of

the graphene fiber laser. (c) Excitatory activity (temporal

integration of nearby pulses) can push the gain above thethreshold, releasing spikes. Depending on the input signal,the system can have a suppressed response due to thepresence of either subthreshold input energies (integratedpower

Ð|y(t)|2dt or (d) a refractory period during which the

laser is unable to pulse (regardless of excitation strength).(e) Restorative properties: repeatable pulse shape evenwhen inputs have different energies (Reproduced fromShastri et al. (2016). Licensed under Creative CommonsAttribution License (CC BY))


Generally speaking, these lasers use III–Vquantum wells or quantum dots for efficient lightgeneration. However, they fall into one of threeinjection categories (illustrated in Fig. 11) andpossess very diverse excitability mechanisms. Itis difficult to group the rich dynamics of differentlasers – which often requires a system of severalcoupled ordinary differential equations to repre-sent it – using classification keywords. We focuson two fundamental characteristics: the way eachlaser can be modulated (injection scheme col-umn), and on the physical effect that directlyshapes the optical pulse (excitable dynamicscolumn).

The injection scheme of the laser will deter-mine whether it is compatible to all-optical PNNsor O/E/O PNNs. Some of them (B, C, H) operate

free of electrical injection, meaning that bits ofinformation remain elegantly encoded in opticalcarriers. However, as we have pointed out,avoiding the E/O conversion is much more diffi-cult when you are trying to build a weight-and-sum device compatible with WDM, which is anessential building block for scalable photonic neu-ral networks.

The excitable dynamics determines importantproperties such as energy efficiency, switchingspeed, and bandwidth of the nonlinear node. The“optical interference”mechanism typically meansthat there are two competing modes with a certainphase relationship that can undergo a 2p topolog-ical excursion and generating an optical pulse inamplitude at the output port. This mechanism isnotably different than the others in which it does

Neuromorphic Photonics, Principles of,Table 2 Characteristics of recent excitable laser devices.Note that this table does not have a one-to-one correspon-dence to Fig. 12, because some of them are not E/O

devices. However, we observe that devices A, D, andF belong to the category Fig. 12a and device E resemblesmore closely to the category Fig. 12c

DeviceInjectionscheme Pump

Excitabledynamics References

A. Two-section gain andSA

Electrical Electrical Stimulatedemission

(Nahmias et al. 2013, 2015; Selmi et al. 2014,2015; Shastri et al. 2014, 2015, 2016; Barbayet al. 2011; Spühler et al. 1999; Dubbeldam andKrauskopf 1999; Dubbeldam et al. 1999;Larotonda et al. 2002; Elsass et al. 2010)

B. Semiconductor ringlaser

Coherentoptical

Electrical Opticalinterference

(Coomans et al. 2010, 2011, 2013; VanVaerenbergh et al. 2012; Gelens et al. 2010)

C. Microdisk laser Coherentoptical

Electrical Opticalinterference

(Van Vaerenbergh et al. 2013; Alexander et al.2013)

D. 2D photonic crystalnanocavitya

Electrical Electrical Thermal (Brunstein et al. 2012; Yacomotti et al. 2006a, b)

E. Resonant tunnelingdiode photodetector andlaser diodeb

Electrical orincoherentoptical

Electrical Electricaltunneling

(Romeira et al. 2013; 2016)

F. Injection-lockedsemiconductor laser withdelayed feedback

Electrical Electrical Opticalinterference

(Kelleher et al. 2010, 2011; Garbin et al. 2014,2015; Goulding et al. 2007; Wieczorek et al.1999, 2002, 2005; Barland et al. 2003; Marinoand Balle 2005; Turconi et al. 2013)

G. Semiconductor laserswith optical feedback

Incoherentoptical

Electrical Stimulatedemission

(Aragoneses et al. 2014; Sorrentino et al. 2015;Giudici et al. 1997; Yacomotti et al. 1999;Giacomelli et al. 2000; Heil et al. 2001;Wünscheet al. 2001)

H. Polarization switchingVCSELs

Coherentoptical

Optical Opticalinterference

(Hurtado and Javaloyes 2015; Hurtado et al.2010, 2012)

aTechnically this device is not an excitable laser, but an excitable cavity connected to a waveguidebThe authors call it excitable optoelectronic device, because the excitability mechanism lies entirely in an electroniccircuit, rather than the laser itself


not require exchange of energy between chargecarriers populations and the cavity field. As aresult, systems based on this effect are not limitedby carrier lifetimes, yet are vulnerable to phasenoise accumulation. Other mechanisms includephoton absorption, stimulated emission, thermo-optic effect, and electron tunneling. There, theelectronic dynamics of the device governs thepopulation of charge carriers available for stimu-lated emission, thereby dominating the timescaleof the generated pulses. Models of these mecha-nisms and how they elicit excitability are compre-hensively detailed in Prucnal et al. (2016), but aquantitative comparison between performancemetrics of lasers in Table 2 is still called for.Qualitatively, however, excitable lasers can simul-taneously borrow key properties of electronictransistors, such as thresholding and cascadability.

In addition to individual laser excitability, therehave been several demonstrations of simple pro-cessing circuits. Temporal pattern recognition(Shastri et al. 2016) and stable recurrent memory(Shastri et al. 2016; Romeira et al. 2016; Garbinet al. 2014) are essential toy circuits that demon-strate basic aspects of network compatibility.

Photonic Neural Network Architecture

Isomorphism to Biological Spiking NeuronNeurons only have computational capabilities ifthey are in a network. Therefore, an excitable laser(or spiking laser) can only be viewed as a neuroncandidate if it is contained in a PNN (Fig. 14). Theconfigurable analog connection strengths betweenneurons, called weights, are as important to thetask of network processing as the dynamicalbehavior of individual elements. Earlier, we havediscussed several proposed excitable lasersexhibiting neural behavior and cascadabilitybetween these lasers. In this section, we discussthe challenges involving the creation of a networkof neurons using photonic hardware, in particular,the creation of a weighted addition scheme forevery PNN. Tait et al. (2014b) proposed an inte-grated photonic neural networking scheme calledbroadcast-and-weight that uses WDM to support

a large number of reconfigurable analog connec-tions using silicon photonic device technology.

A spiking and/or analog photonic network con-sists of three aspects: a protocol, a node thatabides by that protocol (the PNN), and a networkmedium that supports multiple connectionsbetween these nodes. This section will beginwith broadcast-and-weight as a WDM protocolin which many signals can coexist in a singlewaveguide and all nodes have access to all thesignals. Configurable analog connections aresupported by a novel device called a microringresonator (MRR) weight bank (Fig. 15). We willsummarize experimental investigations of MRRweight banks.

Broadcast-and-Weight ProtocolWDM channelization of the spectrum is one wayto efficiently use the full capacity of a waveguide,which can have usable transmission windows upto 60 nm (7.5 THz bandwidth) (Preston et al.2011). In fiber communication networks, aWDM protocol called broadcast-and-select hasbeen used for decades to create many potentialconnections between communication nodes(Ramaswami 1993). In broadcast-and-select, theactive connection is selected, not by altering theintervening medium, but rather by tuning a filter atthe receiver to drop the desired wavelength.Broadcast-and-weight is similar but differs bydirecting multiple inputs simultaneously intoeach detector (Fig. 15b) and with a continuousrange of effective drop strengths between �1and +1, corresponding to an analog weightingfunction.

The ability to control each connection, eachweight, independently is a crucial aspect of neuralnetwork models. Weighting in a broadcast-and-weight network is accomplished by a tunablespectral filter bank at each node, an operationanalogous to a neural weight. The local state ofthe filters defines the interconnectivity pattern ofthe network.

A great variety of possible weight profilesallows a group of functionally similar units toinstantiate a tremendous variety of neural net-works. A reconfigurable filter can be implementedby a MRR – in simple words, a waveguide bent


back on itself to create an interference condition.The MRR resonance wavelength can be tunedthermally (as in Fig. 15c) or electronically ontimescales much slower than signal bandwidth.Practical, accurate, and scalable MRR controltechniques are a critical step toward large-scaleanalog processing networks based on MRRweight banks.

Controlling Photonic Weight BanksSensitivity to fabrication variations, thermal fluc-tuations, and thermal cross talk has made MRRcontrol an important topic for WDM demulti-plexers (Klein et al. 2005), high-order filters

(Mak et al. 2015), modulators (Cox et al. 2014),and delay lines (Cardenas et al. 2010). Com-monly, the goal of MRR control is to track aparticular point in the resonance relative to thesignal carrier wavelength, such as its center ormaximum slope point. On the other hand, anMRR weight must be biased at arbitrary pointsin the filter roll-off region in order to multiply anoptical signal by a continuous range of weightvalues. Feedback control approaches are well-suited to MRR demultiplexer and modulator con-trol (DeRose et al. 2010; Jayatilleka et al. 2015),but these approaches rely on having a referencesignal with consistent average power. In analog

s(t)wiwixi(t)xi(t)

xj(t)

Weighted Inputs

Summation

LIF model

output

Integrate Threshold

Reset

x1(t)

xN(t)

xi(t) = n (t- n)

t

Processing Network Node

Model

WDM Waveguide

+V

-V

P P

P

1 i N

excitatory weight bank

inhibitoryweight bank

Spectral Filter Bank

Current pump

Excitable Laser

j

Balanced PD

Output cross-couplerLaser

Photonic Neuron Architecture

Synaptic variable

Σ ∫

Biological Spiking Neuron Model

wN

w1

Neuromorphic Photonics, Principles of,Fig. 14 Isomorphism between photonic neuron module(i.e., a PNN) to a biological spiking neuron model. Top:depiction of a single unit neural network model. Inputs xiare weighted and summed. The result�iwixi experiences anonlinear function. Bottom: Possible physical implemen-tation of a PNN. A WDM signal is incident on a bank offilters (excitatory and inhibitory) which are created using aseries of microring filters that apply a series of weights.

The resulting signal is incident on a balanced photodetectorwhich applies a summation operation and drives an excit-able laser with a current signal. The resulting laser outputsat a specified wavelength which is subsequently coupledback into the broadcast interconnect (see Fig. 15) (Adaptedwith permission from Tait et al. J. Lightwave Technol. 32,4029–4041 (2014) (Tait et al. 2014). Copyright 2014 Opti-cal Society of America)


networks, signal activity can depend strongly onthe weight values, so these signals cannot be usedas references to estimate weight values. These

reasons dictate a feedforward control approachfor MRR weight banks.

Single Channel Control Accuracy and PrecisionHow accurate can a weight be? The resolutionrequired for effective weighting is a topic ofdebate within the neuromorphic electronics com-munity, with IBM’s TrueNorth selecting four dig-ital bits plus one sign bit (Akopyan et al. 2015). InTait et al. (2016b), continuous weight control ofanMRRweight bank channel was shown using aninterpolation-based calibration approach. Thegoal of the calibration is to have a model ofapplied current/voltage versus effective weightcommand. The calibration can be performedonce per MRR, and its parameters can be storedin memory. Once calibration is complete, the con-troller can navigate the MRR transfer function toapply the correct weight value for a given com-mand. However, errors in the calibration, environ-mental fluctuations, or imprecise actuators causethe weight command to be inaccurate. It is neces-sary to quantify that accuracy.

Analog weight control accuracy can be char-acterized in terms of the ratio of weight range(normalized to 1.0) to worst-case weight inaccu-racy over a sweep and stated in terms of bits or adynamic range. The initial demonstration reportedin Tait et al. (2016b) indicates a dynamic range ofthe weight controller of 9.2 dB, in other words, anequivalent digital resolution of 3.1 bits.

Multichannel Control Accuracy and PrecisionAnother crucial feature of an MRR weight bank issimultaneous control of all channels. Whensources of cross talk between one weight andanother are considered, it is impossible to interpo-late the transfer function of each channel indepen-dently. Simply extending the single-channelinterpolation-based approach of measuring a setof weights over the full range would require anumber of calibration measurements that scalesexponentially with the channel count, since thedimension of the range grows with channel count.Simultaneous control in the presence of cross talktherefore motivates model-based calibrationapproaches.

. . . . . .λ-M

UX

E/O Converter(Laser neuron)

1

2

3

N

Tunable Spectral Filter

PowerDetector

Broadcast Interconnect

. . .

. . .

a)

DROP

THRUIN

WDMinput

s

RF output

MRR weight bank Balanced PD

WDM Weighted Addition

b)

c)

20 mm

100 mm

Neuromorphic Photonics, Principles of, Fig. 15 (a)Broadcast-and-weight network. An array of source lasersoutputs distinct wavelengths (represented by solid color).These channels are wavelength multiplexed (WDM) in asingle waveguide (multicolor). Independent weightingfunctions are realized by tunable spectral filters at theinput of each unit. Demultiplexing does not occur in thenetwork. Instead, the total optical power of each spectrallyweighted signal is detected, yielding the sum of the inputchannels. The electronic signal is transduced to an opticalsignal after nonlinear transformation. (b) Tunable spectralfilter constructed using microring resonator (MRR) weightbank. Tuning MRRs between on- and off-resonanceswitches a continuous fraction of optical power betweendrop and through ports. A balanced photodetector(PD) yields the sum and difference of weighted signals.(c) Left: optical micrograph of a silicon MRR weight bank,showing a bank of four thermally tunedMRRs. Right:widearea micrograph, showing fiber-to-chip grating couplers(Reproduced with permission from Tait et al. (2016a).Copyright 2016 Optical Society of America)


Model-based, as opposed to interpolation-based, calibration involves parameterized modelsfor cross talk inducing effects. The predominantsources of cross talk are thermal leakage betweennearby integrated heaters and, in a lab setup,interchannel cross-gain saturation in fiber ampli-fiers, although optical amplifiers are not a concernfor fully integrated systems that do not have fiber-to-chip coupling losses. Thermal cross talk occurswhen heat generated at a particular heater affectsthe temperature of neighboring devices (seeFig. 15c). In principle, the neighboring channelcould counter this effect by slightly reducing theamount of heat its heater generates. A calibrationmodel for thermal effects provides two basic func-tions: forward modeling (given a vector of appliedcurrents, what will the vector of resultant temper-atures be?) and reverse modeling (given a desiredvector of temperatures, what currents should beapplied?). Models such as this must be calibratedto physical devices by fitting parameters to mea-surements. Calibrating a parameterized modelrequires at least as many measurements as freeparameters. Tait et al. (2016a) describes a methodfor fitting parameters withO(N) spectral and oscil-loscope measurements, where N is the number ofMRRs. As an example, whereas an interpolation-only approach with 20-point resolution wouldrequire 204= 160, 000 calibration measurements,the presented calibration routine takes roughly4 � [10(heater) + 20(filter) + 4(amplifier)] = 136total calibration measurements. Initial demonstra-tions achieved simultaneous four-channel MRRweight control with an accuracy of 3.8 bits andprecision of 4.0 bits (plus 1.0 sign bit) on eachchannel. While optimal weight resolution is still atopic of discussion in the neuromorphic electron-ics community (Hasler and Marr 2013), severalstate-of-the-art architectures with dedicatedweight hardware have settled on 4-bit resolution(Akopyan et al. 2015; Friedmann et al. 2013).

Scalability with Photonic Weight BanksEngineering analysis and design relies on quanti-fiable descriptions of performance called metrics.The natural questions of “how many channels arepossible” and, subsequently, “how many more orfewer channels are garnered by a different design”

are typically resolved by studying trade-offs.Increasing the channel count performance metricwill eventually degrade some other aspect of per-formance until the minimum specification isviolated.

Studying trade-offs between these metrics areimportant for better designing the network andunderstanding its limitations. Just as was thecase with control methodologies, it was foundthat quantitative analysis for MRR weight banksmust follow an approach significantly differentfrom those developed for MRR demultiplexersand modulators (Tait et al. 2016c).

In conventional analyses of MRR devices formultiplexing, demultiplexing, and modulatingWDM signals, the trade-off that limits channelspacing is interchannel cross talk (Preston et al.2011; Jayatilleka et al. 2016). However, unlikeMRR demultiplexers where each channel iscoupled to a distinct waveguide output (Kleinet al. 2005), MRR weight banks have only twooutputs with some portion of every channelcoupled to each. All channels are meant to besent to both detectors in some proportion, so thenotion of cross talk between signals breaks down(Fig. 15b). Instead, for dense channel spacing,different filter peaks viewed from the commondrop port begin to merge together. This has theeffect of reducing the weight bank’s ability toweight neighboring signals independently. Asdetailed in Tait et al. (2016c), Tait et al. (1) quan-tify this effect as a power penalty by including anotion of tuning range with the cross-weight pen-alty metric and (2) perform a channel densityanalysis by deriving the scalability of weightbanks that use microresonators of a particularfinesse.

In summary, WDM channel spacing, do, canbe used to determine the maximum channel countgiven a resonator finesse. While finesse can varysignificantly with the resonator type, normalizedspacing is a property of the circuit (i.e., multi-plexer vs. modulators vs. weight bank). Makingan assumption that a 3 dB cross-weight penalty isallowed, we find that the minimum channel spac-ing falls between 3.41 and 4.61 linewidthsdepending on bus length. High finesse siliconMRRs, such as shown in Xu et al. (2008)


(finesse = 368) and (Biberman et al. 2012)(finesse = 540), could support 108 and 148 chan-nels, respectively. Other types of resonators insilicon, such as elliptical microdisks (Xionget al. 2011) (finesse = 440) and traveling-wavemicroresonators (Soltani et al. 2010)(finesse = 1140) could reach up to 129 and334 channels, respectively.

MRR weight banks are an important compo-nent of neuromorphic photonics – regardless ofPNN implementation because they control theconfiguration of analog network linking photonicneurons together. In Tait et al. (2016a), it wasconcluded that ADC resolution, sensitivized bybiasing conditions, limited the attainable weightaccuracy. Controller accuracy is expected to

improve by reducing the mismatch betweentuning range of interest and driver range. Taitet al. (2016c) arrived at a scaling limit of 148 chan-nels for a MRR weight bank, which is notimpressive in.

the context of neural networks. However, thenumber of neurons could be extended beyond thislimit using spectrum reuse strategies (Fig. 16)proposed in Tait et al. (2014b), by tailoring inter-ference within MRR weight banks as discussed inTait et al. (2016c), or by packing more dimensionsof multiplexing within silicon waveguides, suchas mode-division multiplexing. As the modelingrequirements for controlling MRR weight banksbecome more computationally intensive, a feed-back control technique would be transformative

Fully interconnectedneuron cluster

Local Connection Between Clusters

A

C

E

G

Logical

IN OUT

Broadcast LoopLevel 1(BL:1)

BL:1 BL:1 BL:1

BL:2 BL:2

BL:3

BL:1

Recurrent Broadcast Loop:Neuron Cluster

B

D

F

H

Functional Physical

I

Neuromorphic Photonics, Principles of,Fig. 16 Spectrum reuse strategy. Panels are organizedinto rows at different scales (core, cluster, chip, and multi-chip) and into columns at three different views (logical,functional, and physical). (a, b) Depicts the model andphotonic implementation of a neuron as a processing net-work node (PNN) as detailed in Fig. 14. (c, d) Fullyinterconnected network by attaching PNNs to a broadcast

loop (BL) waveguide. (e, f) A slightly modified PNN cantransfer information from one BL to another. (g, h) Hier-archical organization of the waveguide broadcast architec-ture showing a scalable modular structure. (i) Using thisscheme, neuron count in one chip is only limited by foot-print, but photonic integrated circuits (PICs) can be furtherinterconnected in an optical fiber network


for both precision and modeling demands.Despite the special requirements of photonicweight bank devices making them different fromcommunication-related MRR devices, futureresearch could enable schemes for feedbackcontrol.

Neuromorphic Platform Comparison

As stated earlier, the neuromorphic computingcommunity has been making vigorous effortstoward large-scale spiking neuromorphic hard-ware, e.g., Heidelberg HICANN chip via theFACETS/BrainScaleS projects (Schemmel et al.2010), IBMTrueNorth via the DARPA SyNAPSEprogram (Merolla et al. 2014), StanfordUniversity’s Neurogrid (Benjamin et al. 2014),and SpiNNaker (Furber et al. 2014) (Fig. 4).Many researchers are concentrating their effortstoward the long-term technical potential and func-tional capability of the hardware compared tostandard digital computers. One of the maindrivers for the community is computationalpower efficiency (Hasler and Marr 2013): digitalCPUs are reaching a power efficiency wall withthe current von Neumann architecture, but hard-ware neural networks, in which memory andinstructions are simplified and colocated, offer toovercome this barrier.

These projects also aimed at simulating large-scale spiking neural networks, with the goal ofsimulating subcircuits of the human cortex, at abiological timescale (<1 kHz). The HICANNchip, exceptionally, is designed to be acceleratedat about 10,000 times respective to biologicaltimescales and features analog synapses and real-istic neural spiking behaviors (Schemmel et al.2010). It pays the price of huge power consump-tion: 800 W for a wafer-scale system containing180,000 neurons (Benjamin et al. 2014). In con-trast, TrueNorth aimed for large-scale, efficientnetworks optimized for biologically plausibletasks, such as machine vision, but with a simpli-fied neural model (Merolla et al. 2014). Indeed, itcontained a total of 1 M neurons and 256 Msynapses per chip, consuming only 63 mW ofpower (Merolla et al. 2014). The Neurogrid

board also aimed for scalability and efficiency,consuming 5 W.

also with 1 M neurons and about four billionsynapses, but it kept greater biological fidelity tothe mammalian cortex. The SpiNNaker computeris designed to simulate scalably large and versatilenetworks using arrays of chips with 18 ARM968processing cores each: unlike the other three tech-nologies, the number of synapses per neuron, oreven the number of neurons, is not fixed and canbe dynamically reprogrammed (Furber et al.2014). The demonstrated system has 48 chipsinterconnected in a PCB, but it can be scaled upto 1200 interconnected PCBs, totalling a 72 kWpeak power consumption.

We have recently produced a quantitative com-parison between the aforementioned electronicand photonic neuromorphic hardware architec-tures (Prucnal and Shastri 2017). In order to com-pare these processors with one another, wereintroduce the multiply-accumulate (MAC) oper-ation that typically bottlenecks complexcomputations.

The MAC operation takes the following form:a a + (w � x). It includes both a product (i.e.,x is multiplied by the “weight” w) and an addition(the result is accumulated to variable a). In neuralnetwork models, inputs are combined via aweighted sum of the form S wixi. The result isthen input into some nonlinear scalar functionf{x} which can range from a simple sigmoid func-tion to a complex nonlinear dynamical systemwith hysteresis, depending on the complexity ofthe neuron being modeled. The weighted sum canbe broken down into a series of MAC operationsof the form ai = ai � 1 + wixi for i = 1. . .M. Eachneuron requires M parallel MAC operations pertime stepDt (in a given bit period t, determined bythe signal bandwidth capacity) or one operationper synapse, where M refers to the number ofinputs for a given node. Thus, a hardware neuralnetwork can be characterized with M � N MACoperations per time step Dt (i.e., quadratic scalingof MAC operations), where N is the number ofneurons in the network.

The nonlinear function f {x} also takes upcomputational resources, but since this operationscales with N rather than M � N, it does not


represent the most costly operation. Therefore, asthe size of the network N grows large, MACs –i.e., “synaptic computations” – become the mostburdensome hardware bottlenecks in neural net-works (Hasler and Marr 2013).

For consistency, we compare architectures thathave similar functionality: we limit ourselves tofully reconfigurable systems of spiking neuralnetworks. For the photonically enhanced system,we studied an optoelectronic neural network withPNNs instantiated within the hybrid silicon/III–Vplatform (Nahmias et al. 2015; Ferreira de Limaet al. 2016). We also consider a future photoniccrystal instantiation, based on fundamental phys-ical considerations. Calculated metrics are basedon realistic device parameters, derived from theliterature. We also refer the reader to a moredetailed discussion of spiking electronicneuromorphic hardware in Liu et al. (2015) andan overview of current spiking and nonspikinghardware in Nawrocki et al. (2016).

Results are summarized in Table 1. The moststriking figure is the number of operations persecond, which exceeds electronic platforms bythree orders of magnitude, compared to the ana-log/digital accelerated HICANN and six orders ofmagnitude compared to the others which arepurely digital implementations. This stems fromboth the high bandwidths and low latencies pos-sible with photonic signals. The optoelectronicapproach is able to achieve such energy efficiencyat high speeds because power is mainly consumedstatically by the lasers, while the passive filtershave low leakage current. This contrasts withCMOS digital switches, whose power consump-tion increases dynamically with clock speed. Pro-cessor fan-in is similar in both platforms, despitevery differing technologies. The area per MAC ismore stringent in a photonically enhanced system,since photonic elements cannot be shrunk beyondthe diffraction limit of light. This is because eachdata channel requires a weighting filter in thePNN, such as anMRR pair, which adds a footprintpenalty. However, this is compensated by the factthat a single waveguide can carry many widebandchannels simultaneously, unlike electronic wires.Nonetheless, even though photonically enhancedsystems cannot compete with the miniaturization

of future nanoelectronics, the estimated footprintof such a system is currently on par with some ofthe electronics systems presented here.

Future Directions

After half a century of continuous investment andcommercial success, digital CMOS electronicsdominates the industry of general-purpose com-puting. However, with growing demand for con-nectivity, there is an urgent need for ultrafastcoprocessors that could relieve the stress in digitalprocessing circuits. Here, we have presented ele-ments of a reconfigurable photonic hardware thatcan emulate spiking neural networks operating abillion times faster than the brain. As we identifyproper metrics for a neuromorphic photonic pro-cessor, research efforts are incipiently trans-itioning from individual devices to systemsdesign. We are witnessing a fast maturation ofstandardized photonic foundries in several plat-forms. Chrostowski and Hochberg say(Chrostowski and Hochberg 2015) we are enter-ing a nascent era of fabless photonics, where userscan create computer-assisted chip designs andhave it fabricated by these foundries using qualitycontrolled, repeatable processes. It is reasonableto expect that neuromorphic photonic coproces-sors (Fig. 17) can be fabricated and packagedusing fabless services for near-term research andlong-term volume production.

Applications for neuromorphic photonic pro-cessors can be grouped into two categories: (1) afront-end stage for RF systems and data centersand (2) ultrafast processing for specialized fastapplications (Prucnal and Shastri 2017). The firstcategory utilizes the low-latency, parallelism, andenergy efficiency properties of photonics to alle-viate the throughput of RF systems, e.g., by exe-cuting dimensionality reduction tasks such asprincipal component analysis or blind-source sep-aration. The second category takes advantage ofthe raw speed (bandwidth and latency) of thephotonic processor to execute iterative algorithmsmapped to recurrent neural networks.

Neuromorphic photonic processors join a classof photonic hardware accelerators designed to


assist in acquisition, feature extraction, and stor-age of wideband waveforms (Jalali andMahjoubfar 2015). These accelerators manipulatethe spectrotemporal of a wideband signal, a taskdifficult to accomplish in analog electronics overbroad bandwidth and with low loss.

Real-Time Radio-Frequency ProcessingHigh-volume data applications, including stream-ing video and cloud services, will continue to pushthe telecommunications industry to build better,high-bandwidth systems. Data traffic on somemobile networks alone has increased by over6000% (Index 2015). This has motivated theexploration of more efficient usage of spectralresources (Akyildiz et al. 2006). Although RFintegrated circuits (RFICs) have been researchedfor applications such as duplex processing (Lee2003; Razavi 2000) or control of beamformingantennas (Yu et al. 2011; Razavi 2009), therequirement for impedance-matched transmissionlines greatly increases device and interconnectfootprint, limiting the overall complexity of eachchip. Photonics provides a solution to these

fundamental limitations: optical waveguides cansupport large bandwidths (�100 s of THz) withhigh information density and low cross talkbetween multiplexed channels. By using tech-niques such as WDM, a large number of multi-GHz channels can exist within the same opticalwaveguide. As a result, the number of virtualchannels can greatly exceed the number of phys-ical waveguides, allowing for the formation ofcomplex processing circuits without a significanthardware overhead.

After some initial front-end processing (i.e.,heterodyning and amplification), most radio trans-ceiver systems are processed by either digital sig-nal processors (DSP) or field programmable gatearrays (FGPAs) for more complex signal opera-tions. However, the speeds of these processors(i.e., �500 MHz) limit the overall throughput ofRF carrier signals, which can easily be in the�GHz. Clever sampling and parallelization canhelp alleviate this bottleneck but at the cost ofmuch higher latency and a significant resource/energy overhead. Specialized RF application-specific integrated circuits (ASICs) are anotheroption but are expensive, require significantdevelopment time, and have limitedre-configurability. Future imagined multiple-inmultiple-out (MIMO) systems – which, in thecase of massive MIMO, can be on the order of�100 s of input and output channels (Larssonet al. 2014; Gesbert et al. 2003) – are especiallysusceptible to this bottleneck and may require aradically new solution.

Adding a photonic processing chip to the frontof a radio transceiver would allow very complexoperations to be performed in real time, which cansignificantly offload electronic post-processingand provide a technology to make faster, morerelevant RF decisions on the fly. Massive MIMOsystems based on beamforming in phased arrayantennas require a processor that can distinguishand operate on hundreds of high-bandwidth sig-nals simultaneously, a feat that is currently speedlimited by current electronic processors (Larssonet al. 2014; Hansen 2009). A photonic neuralnetwork model is a perfect fit for addressing thiskind of technological challenge: efficient MIMObeamforming relies on MAC operations that are

SNN

Weight controlcircuit

2N*Nf wires

Supervised learningcircuit

FPGA/CPU

OUTIN

Low latency

Digital

N neurons

Neuromorphic Photonics, Principles of,Fig. 17 Diagram description of a fully packagedneuromorphic processor. While two layers of electronicsprovide reconfigurability, the photonic spiking neural net-work permits low-latency functionality. Nf: fan-in of eachneuron (Reproduced from Ferreira de Lima et al. 2017).Licensed under Creative CommonsAttributionNonCommercial-NoDerivatives License.(CC BY-NC-ND))


already applied in neural network models viaweighted addition. In addition, classification algo-rithms can be built efficiently using the neuralnetwork approach, allowing for RF fingerprintingand signal identification.

As spread spectrum, adaptive RF transceiversbecome more widespread in future telecommuni-cation systems, the scalability of the photonicapproach could provide significant processingadvantages. Its high bandwidth, low latency, andhigh throughput would be especially useful in anultra-wideband (UWB) radio system, in which itcould sample from many frequencies and direc-tions simultaneously to scan for spectral opportu-nities and make a decision quickly and efficiently.Pairing this technology with an FPGA or elec-tronic ASIC controller would enable the imple-mentation of adaptive optimization and learningalgorithms in real time for ultrafast cognitive radioapplications.

Nonlinear ProgrammingAnother way of taking advantage of raw speed isvia an iterative approach. Iterative algorithms findsuccessfully better approximations to a problemof interest and often require many time steps toreach a desired solution. Since one of the mostsalient advantages of a photonic approach is itslow time of flight (�ps) between communicatingprocessors, the convergence rates can be signifi-cantly improved by implementing them on a pho-tonic platform. A large class of problems that canbe solved iteratively includes linear and non-linear programming problems. These methodsseek to minimize some objective function

E x!� �

of real variables in x!

subject to a series

of constraints represented by equalities or inequal-ities, i.e.,g x

!� �� 0 andh x

!� �¼ 0. Applications

in telecommunications, aerospace, and financialindustries can be described in this basic frame-work, including optimal portfolio trading strate-gies, control of machinery/actuators, andallocation of resources and jobs in online servers.Using a photonic approach, 100-variable prob-lems could converge in less than �100 ns, whichcould be useful in the control of very fast dynam-ical systems (i.e., actuators) or in the creation of

low-latency optimization routines in data-intensive environments.

Mathematical optimization problems can begrouped into linear and nonlinear optimizationproblems. Nonlinear optimization problems areoften difficult to solve and sometimes involveexotic techniques such as genetic algorithms orparticle swarm optimization. Nonlinear optimiza-tion problems, however, are nonetheless qua-dratic to second order around the local vicinityof the optimum. Therefore, quadratic program-ming (QP) – which finds the minima/maximaquadratic functions of variables subject to linearconstraints (Lendaris et al. 1999) – becomes aneffective first pass at such problems and can beapplied to a wide array of applications. For exam-ple, many machine learning problems, such assupport vector machine (SVM) training andleast-squares regression, can be reformulated interms of a QP problem. In addition, computationalproblems such as model predictive control(MPC), an optimal nonlinear control algorithm,or compressive sampling, a method for samplingat rates below the Nyquist without loss of infor-mation via the characterization of sparsity inincoming data, are examples of QP problems.Together, these applications represent some ofthe most effective yet generalized tools for acquir-ing and processing information and using theresults to control systems. QP is an NP hard prob-lem in the number of variables, which means thatconventional digital computers must either belimited to solving quadratic programs of veryfew variables or to applications where computa-tion time is noncritical. This is reflected in indus-trial applications of QP solvers. MPC is used inthe chemical industry to control chemical pro-cessing plants, where reaction timescales can bemade very long, and in the finance industry tocontrol long-term portfolio optimization. Theapplication of MPC to faster systems, therefore,relies on new ways of finding faster solutions toQP problems (Jerez et al. 2011). In machine learn-ing, many algorithms (such as SVM) requireoffline training because of the computationalcomplexity of QP but would be much more effec-tive if they could be trained online (Fig. 18).


While Hopfield showed that Hopfield net-works are able to solve quadratic optimizationproblems quickly over 25 years ago (Tank andHopfield 1986), Hopfield quadratic optimizersare uncommon today. This is largely due to thehigh connectivity between neurons that neuralnetworks require (n2 connections for n neurons).In an electronic circuit, as the number of connec-tions increases, the bandwidth at which the systemcan operate without being subject to cross talkbetween connections and other issues decreases(Tait et al. 2014b). This creates an undesirabletrade-off between neuron speed and neural net-work size. Photonic neural networks have severaladvantages over their electrical counterparts.Most importantly, the connectivity concerns prev-alent in electronic neurons are significantly ame-liorated by using light as a communicationmedium (Tait et al. 2014b). WDM allows forhundreds of high-bandwidth signals to flowthrough a single optical waveguide. Moreover,the analog computational bandwidth of a photonicneuron (as designed in Tait et al. (2016b)) lies inthe picosecond to femtosecond timescale(Nahmias et al. 2015). For a Hopfield quadraticoptimizer, this means that a photonic

implementation (Fig. 19) can simultaneouslyhave large dimensionality and a fast convergencetime to the minimum. These processors representsome of the most effective yet generalized toolsfor acquiring and processing information and con-trolling highly mobile systems, such as a hyper-sonic aircraft (Keviczky and Balas 2006).

Summary and Conclusion

Photonics has revolutionized information com-munication, while electronics, in parallel, hasdominated information processing. Recently,there has been a determined exploration of theunifying boundaries between photonics and elec-tronics on the same substrate, driven in part byMoore’s law approaching its long-anticipated end.For example, the computational efficiency fordigital processing has leveled off around 100 pJper MAC. As a result, there has been a wideninggap between today’s computational efficiency andthe next-generation needs, such as big data appli-cations which require advanced pattern matchingand real-time analysis. This, in turn, has led toexpeditious advances in (1) emerging devices that

Sound byte Spatio-temporal spike encoding Word recognition

Complex RF signal Laser pulse encoding

Neuromorphic Photonics, Principles of, Fig. 18 Avision for a brain-inspired laser neural network forenhanced RF communication. Top: spoken words aretransformed into spatiotemporal “spike” (event) patternsby biological neurons. A pattern recognition neuron issensitive to a specific spike fingerprint and releases itsown spike only if it occurs, shown in “target output.”Bottom: in analogy with audio waveforms, a much faster

system (�GHz) based on excitable lasers could operatedirectly on RF waveforms. Applying operations at thefront-end of RF transceivers could offload complex signalprocessing operations to a photonic chip and address band-width and latency limitations of current FPGA and DSPsolutions (The spike-coded pattern is reproduced fromTapson et al. 2013). Licensed under Creative CommonsAttribution License (CC BY))


are called “beyond CMOS” or “More-than-Moore”; (2) novel processing or unconventionalcomputing architectures called “beyond von Neu-mann” that are brain-inspired, i.e., neuromorphic;and (3) CMOS-compatible photonic interconnecttechnologies. Collectively, these researchendeavors have given rise to the field ofneuromorphic photonics (Fig. 1). Emerging pho-tonic hardware platforms have the potential tovastly exceed the capabilities of electronics bycombining ultrafast operation, moderate complex-ity, and full programmability, extending thebounds of computing for applications such asnavigation control on hypersonic aircrafts andreal-time analysis of the RF spectrum.

In this entry, we discussed the current progressand requirements of such a platform. In a photonicspike processor, information is encoded as eventsin the temporal and spatial domains of spikes(or optical pulses). This hybrid coding scheme isdigital in amplitude but analog in time and bene-fits from the bandwidth efficiency of analog pro-cessing and the robustness to noise of digitalcommunication. Optical pulses are received, pro-cessed, and generated by certain class of semicon-ductor devices that exhibit excitability – anonlinear dynamical mechanism underlying all-or-none responses to small perturbations. Opto-electronic devices operating in the excitableregime are dynamically analogous to a biophysi-cal neuron, but roughly eight orders of magnitudefaster. We dubbed these devices as “photonic neu-rons” or “laser neurons.” The field is now

reaching a critical juncture where there is a shiftfrom studying single photonic neurons to study-ing interconnected networks of such devices.A recently proposed on-chip networking architec-ture called broadcast-and-weight could supportmassively parallel (all-to-all) interconnectionbetween excitable devices using wavelength divi-sion multiplexing.

A hybrid III–V/Si photonic platform is a can-didate for an integrated hardware platform. III–Vcompound semiconductor technology, such asindium phosphide (InP) and gallium arsenide(GaAs), is at the forefront of providing activeelements like lasers, amplifiers, and detectors.Silicon, in parallel, brings compatibility withCMOS fabrication processes and low-loss passivecomponents like waveguides and resonators.Scalable and fully reconfigurable networks ofexcitable lasers can be implemented in the siliconphotonic layer of modern hybrid integration plat-forms, in which spiking lasers in a bonded InPlayer are densely interconnected through a siliconlayer. Such a photonic spike processor will poten-tially be able to support several thousandinterconnected devices. It is predicted that such achip would have a computational efficiency of260 fJ per MAC, which surpasses the energyefficiency wall by two orders of magnitude whileoperating at high speeds (i.e., signal bandwidths10 GHz). The emerging field of photonic spikeprocessors has received tremendous interest andcontinues to develop as photonic integrated cir-cuits increase in performance and scale. As novelapplications requiring real-time, ultrafastprocessing – such as the exploitation of the RFspectrum – become more demanding, we expectthat these systems will find use in a variety ofhigh-performance, time-critical environments.

Moving forward, we envision a tremendousinterest in designing, building, and understandingphotonic networks of excitable elements for ultra-fast information processing, guided by the latestcomputational models of the brain. Successfulimplementation of a small-scale photonic spikeprocessor could, in principle, provide the funda-mental technology to build and study larger-scale

Model predictive control (MPC)

Quadratic programming

problem

Photonic Hopfield network

Sensors Actuators

Mapped to

Mapped to

Neuromorphic Photonics, Principles of,Fig. 19 Employing a photonic neural network for amodel predictive control problem by solving a quadraticprogramming problem with a Hopfield network


brain-inspired networks based on laser excitabil-ity. Neuromorphic photonics is poised to usher inexciting new fields of inquiry and impactful enter-prises of application.

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