Excitability in a semiconductor laser with saturable absorber

Controllable non-uniformly distributed spiking cluster generation in broadband optoelectronic oscillator

An approach to achieve controllable non-uniformly distributed spiking cluster generation is proposed and demonstrated based on an externally-triggered broadband optoelectronic oscillator (OEO). The theory of controlling the distribution of the spiking pulses in a spiking cluster is established. Based on the theory, the dynamic and the distribution characteristics are analyzed and revealed in the stable spiking oscillation state under different externally-injected trigger signal voltages. The peak-voltage envelop of the cluster and the interval of the spiking pulses are demonstrated to have an approximate negative linearity relationship with the externally-injected trigger signal voltage in both the numerical simulation and the experiment, where a square waveform, a trapezoidal waveform, a parabola waveform, and a half-sinusoidal waveform are used as the externally-injected trigger signals. The results indicate that the spiking pulse distribution in the generated spiking cluster can be well controlled through tuning the externally-injected trigger signal voltage. The proposed scheme can be utilized in spiking encoding and reservoir computing.

Uniform spike trains in optically injected quantum cascade oscillators

It has been experimentally and theoretically analyzed that noise-induced excitability in quantum well and quantum dot semiconductor laser systems usually produces sharp spike patterns of non-uniform amplitude. In this paper, we experimentally record that a quantum cascade oscillator injected externally with a monochromatic laser beam exhibits a series of highly uniform spike trains, which occur in the proximity of the saddle-node bifurcation. Theoretical analysis based on a properly designed single-mode rate equation model endowed with quantum noise reveals that this high uniformity has its primary origin in the ultrashort carrier lifetime of the quantum cascade laser gain medium that is typically close to 1 ps.

Online spike-based recognition of digits with ultrafast microlaser neurons

Classification and recognition tasks performed on photonic hardware-based neural networks often require at least one offline computational step, such as in the increasingly popular reservoir computing paradigm. Removing this offline step can significantly improve the response time and energy efficiency of such systems. We present numerical simulations of different algorithms that utilize ultrafast photonic spiking neurons as receptive fields to allow for image recognition without an offline computing step. In particular, we discuss the merits of event, spike-time and rank-order based algorithms adapted to this system. These techniques have the potential to significantly improve the efficiency and effectiveness of optical classification systems, minimizing the number of spiking nodes required for a given task and leveraging the parallelism offered by photonic hardware.

Merging and disconnecting resonance tongues in a pulsing excitable microlaser with delayed optical feedback

Excitability, encountered in numerous fields from biology to neurosciences and optics, is a general phenomenon characterized by an all-or-none response of a system to an external perturbation of a given strength. When subject to delayed feedback, excitable systems can sustain multistable pulsing regimes, which are either regular or irregular time sequences of pulses reappearing every delay time. Here, we investigate an excitable microlaser subject to delayed optical feedback and study the emergence of complex pulsing dynamics, including periodic, quasiperiodic, and irregular pulsing regimes. This work is motivated by experimental observations showing these different types of pulsing dynamics. A suitable mathematical model, written as a system of delay differential equations, is investigated through an in-depth bifurcation analysis. We demonstrate that resonance tongues play a key role in the emergence of complex dynamics, including non-equidistant periodic pulsing solutions and chaotic pulsing. The structure of resonance tongues is shown to depend very sensitively on the pump parameter. Successive saddle transitions of bounding saddle-node bifurcations constitute a merging process that results in unexpectedly large regions of locked dynamics, which subsequently disconnect from the relevant torus bifurcation curve; the existence of such unconnected regions of periodic pulsing is in excellent agreement with experimental observations. As we show, the transition to unconnected resonance regions is due to a general mechanism: the interaction of resonance tongues locally at an extremum of the rotation number on a torus bifurcation curve. We present and illustrate the two generic cases of disconnecting and disappearing resonance tongues. Moreover, we show how a pair of a maximum and a minimum of the rotation number appears naturally when two curves of torus bifurcation undergo a saddle transition (where they connect differently).

Time-Multiplexed Spiking Convolutional Neural Network Based on VCSELs for Unsupervised Image Classification

In this work, we present numerical results concerning a multilayer “deep” photonic spiking convolutional neural network, arranged so as to tackle a 2D image classification task. The spiking neurons used are typical two-section quantum-well vertical-cavity surface-emitting lasers that exhibit isomorphic behavior to biological neurons, such as integrate-and-fire excitability and timing encoding. The isomorphism of the proposed scheme to biological networks is extended by replicating the retina ganglion cell for contrast detection in the photonic domain and by utilizing unsupervised spike dependent plasticity as the main training technique. Finally, in this work we also investigate the possibility of exploiting the fast carrier dynamics of lasers so as to time-multiplex spatial information and reduce the number of physical neurons used in the convolutional layers by orders of magnitude. This last feature unlocks new possibilities, where neuron count and processing speed can be interchanged so as to meet the constraints of different applications.

Asymmetric excitable phase triggering in an optically injected semiconductor laser

One of the defining characteristics of excitability is the existence of an excitable threshold: the minimum perturbation amplitude necessary to produce an excitable response. We analyze an optically injected dual state quantum dot laser, previously shown to display a dual state stochastic excitable dynamic. We show that deterministic triggering of this dynamic can be achieved via optical phase perturbations. Further, we demonstrate that there are in fact two asymmetric excitable thresholds in this system corresponding to the two possible directions of optical phase perturbations. For fast enough perturbations, an excitable interval arises, and there is a limit to the perturbation amplitude, above which excitations no longer arise, a phenomenon heretofore unobserved in studies of excitability.

Pulse-timing symmetry breaking in an excitable optical system with delay

Excitable systems with delayed feedback are important in areas from biology to neuroscience and optics. They sustain multistable pulsing regimes with different numbers of equidistant pulses in the feedback loop. Experimentally and theoretically, we report on the pulse-timing symmetry breaking of these regimes in an optical system. A bifurcation analysis unveils that this originates in a resonance phenomenon and that symmetry-broken states are stable in large regions of the parameter space. These results have impact in photonics for, e.g., optical computing and versatile sources of optical pulses.

Image edge detection with a photonic spiking VCSEL-neuron

We report both experimentally and in theory on the detection of edge features in digital images with an artificial optical spiking neuron based on a vertical-cavity surface-emitting laser (VCSEL). The latter delivers fast (< 100 ps) neuron-like optical spikes in response to optical inputs pre-processed using convolution techniques; hence representing image feature information with a spiking data output directly in the optical domain. The proposed technique is able to detect target edges of different directionalities in digital images by applying individual kernel operators and can achieve complete image edge detection using gradient magnitude. Importantly, the neuromorphic (brain-like) spiking edge detection of this work uses commercially sourced VCSELs exhibiting responses at sub-nanosecond rates (many orders of magnitude faster than biological neurons) and operating at the important telecom wavelength of 1300 nm; hence making our approach compatible with optical communication and data-centre technologies.

The limits of sustained self-excitation and stable periodic pulse trains in the Yamada model with delayed optical feedback

We consider the Yamada model for an excitable or self-pulsating laser with saturable absorber and study the effects of delayed optical self-feedback in the excitable case. More specifically, we are concerned with the generation of stable periodic pulse trains via repeated self-excitation after passage through the delayed feedback loop and their bifurcations. We show that onset and termination of such pulse trains correspond to the simultaneous bifurcation of countably many fold periodic orbits with infinite period in this delay differential equation. We employ numerical continuation and the concept of reappearance of periodic solutions to show that these bifurcations coincide with codimension-two points along families of connecting orbits and fold periodic orbits in a related advanced differential equation. These points include heteroclinic connections between steady states and homoclinic bifurcations with non-hyperbolic equilibria. Tracking these codimension-two points in parameter space reveals the critical parameter values for the existence of periodic pulse trains. We use the recently developed theory of temporal dissipative solitons to infer necessary conditions for the stability of such pulse trains.

Pulse propagation in a 1D array of excitable semiconductor lasers

Nonlinear pulse propagation is a major feature in continuously extended excitable systems. The persistence of this phenomenon in coupled excitable systems is expected. Here, we investigate theoretically the propagation of nonlinear pulses in a 1D array of evanescently coupled excitable semiconductor lasers. We show that the propagation of pulses is characterized by a hopping dynamics. The average pulse speed and bifurcation diagram are characterized as a function of the coupling strength between the lasers. Several instabilities are analyzed such as the onset and disappearance of pulse propagation and a spontaneous breaking of the translation symmetry. The pulse propagation modes evidenced are specific to the discrete nature of the 1D array of excitable lasers.

Ultrafast optical integration and pattern classification for neuromorphic photonics based on spiking VCSEL neurons

In today’s data-driven world, the ability to process large data volumes is crucial. Key tasks, such as pattern recognition and image classification, are well suited for artificial neural networks (ANNs) inspired by the brain. Neuromorphic computing approaches aimed towards physical realizations of ANNs have been traditionally supported by micro-electronic platforms, but recently, photonic techniques for neuronal emulation have emerged given their unique properties (e.g. ultrafast operation, large bandwidths, low cross-talk). Yet, hardware-friendly systems of photonic spiking neurons able to perform processing tasks at high speeds and with continuous operation remain elusive. This work provides a first experimental report of Vertical-Cavity Surface-Emitting Laser-based spiking neurons demonstrating different functional processing tasks, including coincidence detection and pattern recognition, at ultrafast rates. Furthermore, our approach relies on simple hardware implementations using off-the-shelf components. These results therefore hold exciting prospects for novel, compact and high-speed neuromorphic photonic platforms for future computing and Artificial Intelligence systems.

All-optical neuromorphic XOR operation with inhibitory dynamics of a single photonic spiking neuron based on a VCSEL-SA

We propose a simple hardware architecture for solving exclusive OR (XOR) tasks in a single step by using a single photonic spiking neuron based on vertical-cavity surface-emitting lasers with an embedded saturable absorber (VCSEL-SA) subject to dual-polarized pulsed optical injection. We model the inhibitory photonic spiking neuron by extending the Yamada model and spin-flip model to incorporate the two polarization-resolved modes and the saturable absorber. It is shown that, by carefully adjusting the temporal difference according to the inhibitory window, the XOR operation can be realized in a single photonic spiking neuron, which is interesting and valuable for the photonic neuromorphic computing and information processing.

Mode Locking of the Hermite-Gaussian Modes of a Nanolaser

Mode locking is predicted in a nanolaser cavity forming an effective photonic harmonic potential. The cavity is substantially more compact than a Fabry-Perot resonator with a comparable pulsing period, which is here controlled by the potential. In the limit of instantaneous gain and absorption saturation, mode locking corresponds to a stable dissipative soliton, which is very well approximated by the coherent state of a quantum mechanical harmonic oscillator. This property is robust against noninstantaneous material response and nonzero phase-intensity coupling.

All-optical inhibitory dynamics in photonic neuron based on polarization mode competition in a VCSEL with an embedded saturable absorber

An all-optical spike inhibition scheme based on polarization-mode competition (PMC) in a vertical-cavity surface-emitting laser (VCSEL) with an embedded saturable absorber is proposed and investigated numerically. The inhibitory dynamics is characterized by spike amplitude and first-spike latency (FSL) for the first time, to the best of our knowledge. The effects of time differences between inhibitory and excitatory inputs, inputs strengths, bias current, as well as noise on the spike amplitude and FSL are examined. The results show that a spike can be triggered in the y-polarization mode by excitatory input and can be inhibited in the presence of inhibitory input due to PMC.

Square wave excitability in quantum dot lasers under optical injection

Quantum dot lasers display many unique dynamic phenomena when optically injected. Bistability has been predicted in a region of high injection strength. Experimentally, we show that a square wave phenomenon, rather than a phase-locked bistability, is observed in this region. The squares can manifest as a periodic train but also as noise-driven Type II excitable events. We interpret the appearance of the square waves as a thermally induced breaking of the bistability. Indeed, we find experimentally that over the duration of a square, the relative detuning between the master and the slave evolves deterministically. A relatively simple, physically motivated, rate equation model is presented and displays excellent agreement with the experiment.

Polarization-resolved and polarization- multiplexed spike encoding properties in photonic neuron based on VCSEL-SA

The spike encoding properties of two polarization-resolved modes in vertical-cavity surface-emitting laser with an embedded saturable absorber (VCSEL-SA) are investigated numerically, based on the spin-flip model combined with the Yamada model. The results show that the external input optical pulse (EIOP) can be encoded into spikes in X-polarization (XP) mode, Y-polarization (YP) mode, or both XP and YP modes. Furthermore, the numerical bifurcation diagrams show that a lower (higher) strength of EIOP is beneficial for generating tonic (phasic) spikes; a small amplitude anisotropy contributes to wide (narrow) tonic spiking range in XP (YP) mode; a large current leads to low thresholds of EIOP strength for both XP and YP modes. However, the spike encoding properties are hardly affected by the phase anisotropy. The encoding rate is shown to be improved by increasing EIOP strength. Moreover, dual-channel polarization-multiplexed spike encoding can also be achieved in a single VCSEL-SA. To the best of our knowledge, such single channel polarization-resolved and dual-channel polarization-multiplexed spike encoding schemes have not yet been reported. Hence, this work is valuable for ultrafast photonic neuromorphic systems and brain-inspired information processing.

Experimental and numerical characterization of an all-fiber laser with a saturable absorber

We experimentally characterize the pulsing dynamics of a short all-fiber laser consisting of separate gain and absorber sections. Systematically varying the optical pump power for different lengths of the absorber section (ranging from 0.21 to 1.48 m) allows us to map out the qualitative behavior of the system. This identifies three main operational regions: nonlasing, stable Q-switching, and irregular pulsing. When interpreted in terms of the bifurcation structure of the Yamada model, the experimental results are in good qualitative agreement.

Pulse train interaction and control in a microcavity laser with delayed optical feedback

We report experimental and theoretical results on the pulse train dynamics in an excitable semiconductor microcavity laser with an integrated saturable absorber and delayed optical feedback. We show how short optical control pulses can trigger, erase, or retime regenerative pulse trains in the external cavity. Both repulsive and attractive interactions between pulses are observed, and are explained in terms of the internal dynamics of the carriers. A bifurcation analysis of a model consisting of a system of nonlinear delay differential equations shows that arbitrary sequences of coexisting pulse trains are very long transients towards weakly stable periodic solutions with equidistant pulses in the external cavity.

Two distinct excitable responses for a laser with a saturable absorber

Excitable lasers with saturable absorbers are currently investigated as potential candidates for low level spike processing tasks in integrated optical platforms. Following a small perturbation of a stable equilibrium, a single and intense laser pulse can be generated before returning to rest. Motivated by recent experiments [Selmi et al., Phys. Rev. E 94, 042219 (2016)10.1103/PhysRevE.94.042219], we consider the rate equations for a laser containing a saturable absorber (LSA) and analyze the effects of different initial perturbations. With its three steady states and following Hodgkin classification, the LSA is a Type I excitable system. By contrast to perturbations on the intensity leading to the same intensity pulse, perturbations on the gain generate pulses of different amplitudes. We explain these distinct behaviors by analyzing the slow-fast dynamics of the laser in each case. We first consider a two-variable LSA model for which the conditions of excitability can be explored in the phase plane in a transparent manner. We then concentrate on the full three variable LSA equations and analyze its solutions near a degenerate steady bifurcation point. This analysis generalizes previous results [Dubbeldam et al., Phys. Rev. E 60, 6580 (1999)1063-651X10.1103/PhysRevE.60.6580] for unequal carrier density rates. Last, we discuss a fundamental difference between neuron and laser models.

Delay dynamics of neuromorphic optoelectronic nanoscale resonators: Perspectives and applications

With the recent exponential growth of applications using artificial intelligence (AI), the development of efficient and ultrafast brain-like (neuromorphic) systems is crucial for future information and communication technologies. While the implementation of AI systems using computer algorithms of neural networks is emerging rapidly, scientists are just taking the very first steps in the development of the hardware elements of an artificial brain, specifically neuromorphic microchips. In this review article, we present the current state of the art of neuromorphic photonic circuits based on solid-state optoelectronic oscillators formed by nanoscale double barrier quantum well resonant tunneling diodes. We address, both experimentally and theoretically, the key dynamic properties of recently developed artificial solid-state neuron microchips with delayed perturbations and describe their role in the study of neural activity and regenerative memory. This review covers our recent research work on excitable and delay dynamic characteristics of both single and autaptic (delayed) artificial neurons including all-or-none response, spike-based data encoding, storage, signal regeneration and signal healing. Furthermore, the neural responses of these neuromorphic microchips display all the signatures of extended spatio-temporal localized structures (LSs) of light, which are reviewed here in detail. By taking advantage of the dissipative nature of LSs, we demonstrate potential applications in optical data reconfiguration and clock and timing at high-speeds and with short transients. The results reviewed in this article are a key enabler for the development of high-performance optoelectronic devices in future high-speed brain-inspired optical memories and neuromorphic computing.

Controlled inhibition of spiking dynamics in VCSELs for neuromorphic photonics: theory and experiments

We report experimentally and theoretically on the controllable inhibition of spiking regimes in a 1300 nm wavelength vertical-cavity surface-emitting laser. Reproducible suppression of spiking dynamics is demonstrated at fast operation speeds (up to sub-ns rates) and with total control on the temporal duration of the spiking inhibition windows. This Letter opens new paths toward a photonic inhibitory neuronal model system for use in future neuromorphic photonic information processing modules and which are able to operate at speeds up to 8 orders of magnitude faster than biological neurons.

Direct measurements of multi-photon induced nonlinear lattice dynamics in semiconductors via time-resolved x-ray scattering

Nonlinear optical phenomena in semiconductors present several fundamental problems in modern optics that are of great importance for the development of optoelectronic devices. In particular, the details of photo-induced lattice dynamics at early time-scales prior to carrier recombination remain poorly understood. We demonstrate the first integrated measurements of both optical and structural, material-dependent quantities while also inferring the bulk impulsive strain profile by using high spatial-resolution time-resolved x-ray scattering (TRXS) on bulk crystalline gallium arsenide. Our findings reveal distinctive laser-fluence dependent crystal lattice responses, which are not described by previous TRXS experiments or models. The initial linear expansion of the crystal upon laser excitation stagnates at a laser fluence corresponding to the saturation of the free carrier density before resuming expansion in a third regime at higher fluences where two-photon absorption becomes dominant. Our interpretations of the lattice dynamics as nonlinear optical effects are confirmed by numerical simulations and by additional measurements in an n-type semiconductor that allows higher-order nonlinear optical processes to be directly observed as modulations of x-ray diffraction lineshapes.

Artificial Neuron Based on Integrated Semiconductor Quantum Dot Mode-Locked Lasers

Neuro-inspired implementations have attracted strong interest as a power efficient and robust alternative to the digital model of computation with a broad range of applications. Especially, neuro-mimetic systems able to produce and process spike-encoding schemes can offer merits like high noise-resiliency and increased computational efficiency. Towards this direction, integrated photonics can be an auspicious platform due to its multi-GHz bandwidth, its high wall-plug efficiency and the strong similarity of its dynamics under excitation with biological spiking neurons. Here, we propose an integrated all-optical neuron based on an InAs/InGaAs semiconductor quantum-dot passively mode-locked laser. The multi-band emission capabilities of these lasers allows, through waveband switching, the emulation of the excitation and inhibition modes of operation. Frequency-response effects, similar to biological neural circuits, are observed just as in a typical two-section excitable laser. The demonstrated optical building block can pave the way for high-speed photonic integrated systems able to address tasks ranging from pattern recognition to cognitive spectrum management and multi-sensory data processing.

Spike latency and response properties of an excitable micropillar laser

We present experimental measurements concerning the response of an excitable micropillar laser with saturable absorber to incoherent as well as coherent perturbations. The excitable response is similar to the behavior of spiking neurons but with much faster time scales. It is accompanied by a subnanosecond nonlinear delay that is measured for different bias pump values. This mechanism provides a natural scheme for encoding the strength of an ultrafast stimulus in the response delay of excitable spikes (temporal coding). Moreover, we demonstrate coherent and incoherent perturbations techniques applied to the micropillar with perturbation thresholds in the range of a few femtojoules. Responses to coherent perturbations assess the cascadability of the system. We discuss the physical origin of the responses to single and double perturbations with the help of numerical simulations of the Yamada model and, in particular, unveil possibilities to control the relative refractory period that we recently evidenced in this system. Experimental measurements are compared to both numerical simulations of the Yamada model and analytic expressions obtained in the framework of singular perturbation techniques. This system is thus a good candidate to perform photonic spike processing tasks in the framework of novel neuroinspired computing systems.

Regenerative memory in time-delayed neuromorphic photonic resonators

We investigate a photonic regenerative memory based upon a neuromorphic oscillator with a delayed self-feedback (autaptic) connection. We disclose the existence of a unique temporal response characteristic of localized structures enabling an ideal support for bits in an optical buffer memory for storage and reshaping of data information. We link our experimental implementation, based upon a nanoscale nonlinear resonant tunneling diode driving a laser, to the paradigm of neuronal activity, the FitzHugh-Nagumo model with delayed feedback. This proof-of-concept photonic regenerative memory might constitute a building block for a new class of neuron-inspired photonic memories that can handle high bit-rate optical signals.

Spike processing with a graphene excitable laser

Novel materials and devices in photonics have the potential to revolutionize optical information processing, beyond conventional binary-logic approaches. Laser systems offer a rich repertoire of useful dynamical behaviors, including the excitable dynamics also found in the time-resolved "spiking" of neurons. Spiking reconciles the expressiveness and efficiency of analog processing with the robustness and scalability of digital processing. We demonstrate a unified platform for spike processing with a graphene-coupled laser system. We show that this platform can simultaneously exhibit logic-level restoration, cascadability and input-output isolation--fundamental challenges in optical information processing. We also implement low-level spike-processing tasks that are critical for higher level processing: temporal pattern detection and stable recurrent memory. We study these properties in the context of a fiber laser system and also propose and simulate an analogous integrated device. The addition of graphene leads to a number of advantages which stem from its unique properties, including high absorption and fast carrier relaxation. These could lead to significant speed and efficiency improvements in unconventional laser processing devices, and ongoing research on graphene microfabrication promises compatibility with integrated laser platforms.

Spatiotemporal Chaos Induces Extreme Events in an Extended Microcavity Laser

Extreme events such as rogue waves in optics and fluids are often associated with the merging dynamics of coherent structures. We present experimental and numerical results on the physics of extreme event appearance in a spatially extended semiconductor microcavity laser with an intracavity saturable absorber. This system can display deterministic irregular dynamics only, thanks to spatial coupling through diffraction of light. We have identified parameter regions where extreme events are encountered and established the origin of this dynamics in the emergence of deterministic spatiotemporal chaos, through the correspondence between the proportion of extreme events and the dimension of the strange attractor.

Temporal summation in a neuromimetic micropillar laser

Neuromimetic systems are systems mimicking the functionalities or architecture of biological neurons and may present an alternative path for efficient computing and information processing. We demonstrate here experimentally temporal summation in a neuromimetic micropillar laser with an integrated saturable absorber. Temporal summation is the property of neurons to integrate delayed input stimuli and to respond by an all-or-none kind of response if the inputs arrive in a sufficiently small time window. Our system alone may act as a fast optical coincidence detector and paves the way to fast photonic spike-processing networks.

Optical spike-timing-dependent plasticity with weight-dependent learning window and reward modulation

Optical spike-timing-dependent plasticity (STDP) synapses form the basis of learning in photonic neuromorphic system. In biological neural systems, STDP synapses generally have multiplicative boundary mechanisms, and can be modulated by a third factor such as dopamine. Analogously, we introduce a third factor into optical STDP: The current-injection of semiconductor optical amplifiers can be modified in an adaptive way according to local or global feedback signals. The local one is present synaptic weight, which elicits an optical weight-dependent STDP, while the global one is a reward signal. We demonstrate that the optical weight-dependent STDP can emulate the behavior of biological STDP synapses more closely, and can be seen as an intermediate configuration between additive and multiplicative STDP, which balances stability and competition among synapses. Simulation studies with scalable photonic neurons further show that optical STDP with reward modulation enables reward-based reinforcement learning.

SIMPEL: circuit model for photonic spike processing laser neurons

We propose an equivalent circuit model for photonic spike processing laser neurons with an embedded saturable absorber—a simulation model for photonic excitable lasers (SIMPEL). We show that by mapping the laser neuron rate equations into a circuit model, SPICE analysis can be used as an efficient and accurate engine for numerical calculations, capable of generalization to a variety of different types of laser neurons with saturable absorber found in literature. The development of this model parallels the Hodgkin-Huxley model of neuron biophysics, a circuit framework which brought efficiency, modularity, and generalizability to the study of neural dynamics. We employ the model to study various signal-processing effects such as excitability with excitatory and inhibitory pulses, binary all-or-nothing response, and bistable dynamics.

Effects of periodic forcing on the temporally correlated spikes of a semiconductor laser with feedback

Optical excitable devices that mimic neuronal behavior can be building-blocks of novel, brain-inspired information processing systems. A relevant issue is to understand how such systems represent, via correlated spikes, the information of a weak external input. Semiconductor lasers with optical feedback operating in the low frequency fluctuations regime have been shown to display optical spikes with intrinsic temporal correlations similar to those of biological neurons. Here we investigate how the spiking laser output represents a weak periodic input that is implemented via direct modulation of the laser pump current. We focus on understanding the influence of the modulation frequency. Experimental sequences of inter-spike-intervals (ISIs) are recorded and analyzed by using the ordinal symbolic methodology that identifies and characterizes serial correlations in datasets. The change in the statistics of the various symbols with the modulation frequency is empirically shown to be related to specific changes in the ISI distribution, which arise due to different phase-locking regimes. A good qualitative agreement is also found between simulations of the Lang and Kobayashi model and observations. This methodology is an efficient way to detect subtle changes in noisy correlated ISI sequences and may be applied to investigate other optical excitable devices.

Response of laser-localized structures to external perturbations in coupled semiconductor microcavities

Laser-localized structures have been observed in several experiments based on broad-area semiconductor lasers. They appear as bounded regions of laser light emission which can exist independently of each other and are expected to be commuted via external optical perturbations. In this work, we perform a statistical analysis of time-resolved commutation experiments in a system of coupled lasers and show the role of wavelength, polarization and pulse energy in the switching process. Furthermore, we also analyse the response of the system outside of the stability region of laser-localized states in search of an excitable response. We observe not only a threshold separating two types of responses, but also a strong variability in the system's trajectory when returning to the initial stable fixed point.

Relative refractory period in an excitable semiconductor laser

We report on experimental evidence of neuronlike excitable behavior in a micropillar laser with saturable absorber. We show that under a single pulsed perturbation the system exhibits subnanosecond response pulses and analyze the role of the laser bias pumping. Under a double pulsed excitation we study the absolute and relative refractory periods, similarly to what can be found in neural excitability, and interpret the results in terms of a dynamical inhibition mediated by the carrier dynamics. These measurements shed light on the analogy between optical and biological neurons and pave the way to fast spike-time coding based optical systems with a speed several orders of magnitude faster than their biological or electronic counterparts.

Drift-induced excitable localized states

Excitable localized states, spatial structures which possess both the features of temporal excitable pulses and of transverse cavity solitons, have been theoretically predicted in model systems as single pulses of light localized in space with a finite and deterministic duration. We study experimentally the nucleation of laser localized structures on a device defect and its motion along a spatial gradient. We demonstrate that in the reference frame of the drifting localized structure, the resulting dynamics presents the typical features of excitable systems. In particular, for specific parameter values, we observe that the nucleation of laser localized structures is triggered by noise, while the drift of the localized structure up to a spatial region where it vanishes provides the deterministic orbit which brings the system back to its initial rest state. The control of such structures may open the way to novel applications of localized structures beyond that of simple stationary bits.

Excitation transfer between optically injected microdisk lasers

Recently, we have theoretically demonstrated that optically injected microdisk lasers can be tuned in a class I excitable regime, where they are sensitive to both inhibitory and excitatory external input pulses. In this paper, we propose, using simulations, a topology that allows the disks to react on excitations from other disks. Phase tuning of the intermediate connections allows to control the disk response. Additionally, we investigate the sensitivity of the disk circuit to deviations in driving current and locking signal wavelength detuning. Using state-of-the-art fabrication techniques for microdisk laser, the standard deviation of the lasing wavelength is still about one order of magnitude too large. Therefore, compensation techniques, such as wavelength tuning by heating, are necessary.

Excitability and optical pulse generation in semiconductor lasers driven by resonant tunneling diode photo-detectors

We demonstrate, experimentally and theoretically, excitable nanosecond optical pulses in optoelectronic integrated circuits operating at telecommunication wavelengths (1550 nm) comprising a nanoscale double barrier quantum well resonant tunneling diode (RTD) photo-detector driving a laser diode (LD). When perturbed either electrically or optically by an input signal above a certain threshold, the optoelectronic circuit generates short electrical and optical excitable pulses mimicking the spiking behavior of biological neurons. Interestingly, the asymmetric nonlinear characteristic of the RTD-LD allows for two different regimes where one obtain either single pulses or a burst of multiple pulses. The high-speed excitable response capabilities are promising for neurally inspired information applications in photonics.

Control of excitable pulses in an injection-locked semiconductor laser

In spite of numerous theoretical and experimental reports of excitability in lasers with injected signal based on the locking-unlocking transition, the response of the system to controlled external perturbations (which is at the basis of the definition of excitable systems) has not been experimentally studied yet. In the following, we analyze the response of an injection-locked semiconductor laser to different external perturbations. We demonstrate the existence of a perturbation threshold beyond which the response of the system is independent of the strength of the stimulation and, thus, demonstrate its excitable character. We show that optically perturbing such an excitable system via the control of the phase of the injection beam can be useful for optical pulse generation.