IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. X, NO. X, MONTH DATE 2013 1 A Leaky Integrate-and-Fire Laser Neuron for Ultrafast Cognitive Computing Mitchell A. Nahmias, Bhavin J. Shastri, Member, IEEE, Alexander N. Tait Student Member, IEEE, Paul R. Prucnal Fellow, IEEE Abstract—We propose an original design for a neuron-inspired photonic computational primitive for a large-scale, ultrafast cognitive computing platform. The laser exhibits excitability and behaves analogously to a leaky integrate-and-fire (LIF) neuron. This model is both fast and scalable, operating up to a billion times faster than a biological equivalent and is realizable in a compact, vertical-cavity surface-emitting laser (VCSEL). We show that—under a certain set of conditions—the rate equations governing a laser with an embedded saturable absorber reduces to the behavior of LIF neurons. We simulate the laser using realistic rate equations governing a VCSEL cavity, and show behavior representative of cortical spiking algorithms simulated in small circuits of excitable lasers. Pairing this technology with ultrafast, neural learning algorithms would open up a new domain of processing. Index Terms—Cognitive computing, excitability, leaky integrate-and-fire (LIF) neuron, neuromorphic, neural networks, spike processing, mixed-signal, optoelectronics, photonic neuron, semiconductor lasers, ultrafast, vertical-cavity surface-emitting lasers (VCSELs). I. I NTRODUCTION I N AN EFFORT to break the limitations inherent in tra- ditional von Neumann architectures, some recent projects in computing have sought more effective signal processing techniques by leveraging the underlying physics of devices [1]–[6]. Cognitive computing platforms inspired by biolog- ical neural networks could solve unconventional computing problems and outperform current technology in both power efficiency and complexity [7]–[9]. These novel systems rely on an alternative set of computational principles, including hybrid analog-digital signal representations, co-location of memory and processing, unsupervised learning, and distributed representations of information. On the cellular level, the brain encodes information as events or spikes in time [10], a hybrid signal with both analog and digital properties as illustrated in Fig. 1. This Manuscript received December 4, 2012; revised Month Date, 201x; ac- cepted Month Date, 201x. This work was supported by Lockheed Martin Advanced Technology Laboratory through the IRAD program, as well as the Lockheed Martin Corporation through the Corporate University Research Program. The authors also acknowledge the support of the NSF MIRTHE Center at Princeton University, the Pyne Fund and Essig Enright Fund for Engineering in Neuroscience. The work of M. A. Nahmias and A. N. Tait was supported by the National Science Foundation Graduate Research Fellowship (NSF-GRF). The work of B. J. Shastri was supported by the National Sciences and Engineering Research Council of Canada (NSERC) Postdoctoral Fellowship (PDF). The authors are with the Lightwave Communications Laboratory, Depart- ment of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA (e-mail: mnahmias@princeton.edu). time time Digital System (coded in bits) Hybrid System (coded as events) Fig. 1. Spiking neural networks encode information as events in time rather than bits. Because the time at which a spike occurs is analog while its amplitude is digital, the signals use a mixed-signal or hybrid encoding scheme. encoding scheme is equivalent to analog pulse position mod- ulation (PPM) in optics, which has been utilized in various applications including the implementation of robust chaotic communication [11] and power efficient channel coding [12]. Spike processing has evolved in biological (nervous systems) and engineered (neuromorphic analog VLSI) systems as a means to exploit the efficiency of analog signals while over- coming the problem of noise accumulation inherent in analog computation [13]. Various technologies have emulated spike neural networks in electronics, including IBM’s neurosynaptic core as part of DARPA’s SyNAPSE program [1], [2] and Neurogrid as part of Stanford’s Brains in Silicon program [14]. Although these architectures have garnered success in various applications, they aim to target biological time scales rather than exceed them. Microelectronic neural networks that are both fast and highly interconnected are subject to a fundamental bandwidth fan-in tradeoff. Photonic platforms offer an alternative approach to mi- croelectronics. The high speeds, high bandwidth, and low cross-talk achievable in photonics are very well suited for an ultrafast spike-based information scheme. Because of this, photonic spike processors could access a computational do- main that is inaccessible by other technologies. This domain, which we describe as ultrafast cognitive computing, represents an unexplored processing paradigm that could have a wide range of applications in adaptive control, learning, perception, motion control, sensory processing (vision systems, auditory processors, and the olfactory system), autonomous robotics, and cognitive processing of the radio frequency spectrum. There has been a growing interest in photonic spike pro- cessing which has spawned a rich search for an appropriate computational primitive. The first category includes those based on discrete, fiber components [15]–[17]. However, the 0000–0000/00$00.00 c  2012 IEEE