Excitability of a semiconductor laser by a two-mode homoclinic bifurcation

Photorefraction Simulates Well the Plasticity of Neural Synaptic Connections

In recent years, the need for systems capable of achieving the dynamic learning and information storage efficiency of the biological brain has led to the emergence of neuromorphic research. In particular, neuromorphic optics was born with the idea of reproducing the functional and structural properties of the biological brain. In this context, solitonic neuromorphic research has demonstrated the ability to reproduce dynamic and plastic structures capable of learning and storing through conformational changes in the network. In this paper, we demonstrate that solitonic neural networks are capable of mimicking the functional behaviour of biological neural tissue, in terms of synaptic formation procedures and dynamic reinforcement.

Inducing optical self-pulsation by electrically tuning graphene on a silicon microring

A mechanism for self-pulsation in a proposed graphene-on-silicon microring device is studied. The relevant nonlinear effects of two photon absorption, Kerr effect, saturable absorption, free carrier absorption, and dispersion are included in a coupled mode theory framework. We look at the electrical tunability of absorption and the Kerr effect in graphene. We show that the microring can switch from a stable rest state to a self-pulsation state by electrically tuning the graphene under constant illumination. This switching is indicative of a supercritical Hopf bifurcation since the frequency of the pulses is approximately constant at 7 GHz and the amplitudes initial grow with increasing Fermi level. The CMOS compatibility of graphene and the opto-electronic mechanism allows this to device to be fairly easily integrated with other silicon photonic devices.

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.

Excitable interplay between lasing quantum dot states

The optically injected semiconductor laser system has proven to be an excellent source of experimental nonlinear dynamics, particularly regarding the generation of excitable pulses. Typically for low-injection strengths, these pulses are the result of a small above-threshold perturbation of a stable steady state, the underlying physics is well described by the Adler phase equation, and each laser intensity pulse is accompanied by a 2π phase rotation. In this article, we show how, with a dual-state quantum dot laser, a variation of type I excitability is possible that cannot be described by the Adler model. The laser is operated so that emission is from the excited state only. The ground state can be activated and phase locked to the master laser via optical injection while the excited state is completely suppressed. Close to the phase-locking boundary, a region of ground-state emission dropouts correlated to excited-state pulses can be observed. We show that the phase of the ground state undergoes bounded rotations due to interactions with the excited state. We analyze the system both experimentally and numerically and find excellent agreement. Particular attention is devoted to the bifurcation conditions needed for an excitable pulse as well as its time evolution.

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.

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.

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.

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.

Manipulating coherence resonance in a quantum dot semiconductor laser via electrical pumping

Excitability and coherence resonance are studied in a semiconductor quantum dot laser under short optical self-feedback. For low pump levels, these are observed close to a homoclinic bifurcation, which is in correspondence with earlier observations in quantum well lasers. However, for high pump levels, we find excitability close to a boundary crisis of a chaotic attractor. We demonstrate that in contrast to the homoclinic bifurcation the crisis and thus the excitable regime is highly sensitive to the pump current. The excitability threshold increases with the pump current, which permits to adjust the sensitivity of the excitable unit to noise as well as to shift the optimal noise strength, at which maximum coherence is observed. The shift adds up to more than one order of magnitude, which strongly facilitates experimental realizations.

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.

Excitability in a semiconductor laser with saturable absorber

We show that a monolithic and compact vertical cavity laser with intracavity saturable absorber can emit short excitable pulses. These calibrated optical pulses can be excited as a response to an input perturbation whose amplitude is above a certain threshold. Subnanosecond excitable response is promising for applications to novel all-optical devices for information processing or logical gates.

Solitary and coupled semiconductor ring lasers as optical spiking neurons

We theoretically investigate the possibility of generating pulses in an excitable (asymmetric) semiconductor ring laser (SRL) using optical trigger pulses. We show that the phase difference between the injected field and the electric field inside the SRL determines the direction of the perturbation in phase space. Due to the folded shape of the excitability threshold, this has an important influence on the ability to cross it. A mechanism for exciting multiple consecutive pulses using a single trigger pulse (i.e., multipulse excitability) is revealed. We furthermore investigate the possibility of using asymmetric SRLs in a coupled configuration, which is a first step toward an all-optical neural network using SRLs as building blocks.

Dimensional signature on noise-induced excitable statistics in an optically injected semiconductor laser

Noise-induced excitability is a prevalent feature in many nonlinear dynamical systems. The optically injected semiconductor laser is one of the simplest such systems and is readily amenable to both experimental and theoretical analysis. We show that the dimensionality of this system may be tuned experimentally and that this has a strong signature on the interspike statistics. The phase of the slave laser is resolved experimentally in the frame of the master laser, allowing an examination of the dynamics at extremely low injection strengths where intensity measurements alone cannot determine the dynamics fully. Generic phase equations are found for the different dimensional scenarios. When the dimensionality is greater than 1, we show that a precursor of a homoclinic bifurcation generates a noise-induced frequency and that the homoclinic bifurcation admits a bistability in the system.

Excitability in optically injected semiconductor lasers: contrasting quantum-well- and quantum-dot-based devices

Excitability is a generic prediction for an optically injected semiconductor laser. However, the details of the phenomenon differ depending on the type of device in question. For quantum-well lasers very complicated multipulse trajectories can be found, while for quantum-dot lasers the situation is much simpler. Experimental observations show the marked differences in the pulse shapes while theoretical considerations reveal the underlying mechanism responsible for the contrast, identifying the increased stability of quantum-dot lasers to perturbations as the root.

Excitability in ramped systems: the compost-bomb instability

The paper studies a novel excitability type where a large excitable response appears when a system’s parameter is varied gradually, or ramped, above some critical rate. This occurs even though there is a (unique) stable quiescent state for any fixed setting of the ramped parameter. We give a necessary and a sufficient condition for the existence of a critical ramping rate in a general class of slow–fast systems with folded slow (critical) manifold. Additionally, we derive an analytical condition for the critical rate by relating the excitability threshold to a canard trajectory through a folded saddle singularity. The general framework is used to explain a potential climate tipping point termed the ‘compost-bomb instability’—an explosive release of soil carbon from peatlands into the atmosphere occurs above some critical rate of global warming even though there is a unique asymptotically stable soil carbon equilibrium for any fixed atmospheric temperature.

Excitable phase slips in an injection-locked single-mode quantum-dot laser

An experimental study of the dynamics of a single-mode quantum-dot semiconductor laser undergoing optical injection is described for the first time, to our knowledge. In particular, the first observation of excitable pulses near the locking boundaries for both positive and negative detuning is reported, indicating locking via a saddle-node bifurcation for both signs of the detuning. The phase evolution of the slave electric-field during pulsing was measured and confirmed that the pulses result from 2pi phase slips. The interpulse-time statistics were analyzed, and a Kramers-like distribution was obtained.

Excitability in a quantum dot semiconductor laser with optical injection

We experimentally analyze the dynamics of a quantum dot semiconductor laser operating under optical injection. We observe the appearance of single- and double-pulse excitability at one boundary of the locking region. Theoretical considerations show that these pulses are related to a saddle-node bifurcation on a limit cycle as in the Adler equation. The double pulses are related to a period-doubling bifurcation and occur on the same homoclinic curve as the single pulses.

Fast thermo-optical excitability in a two-dimensional photonic crystal

We experimentally demonstrate excitability in a semiconductor two-dimensional photonic crystal. Excitability is a nonlinear dynamical mechanism underlying pulselike responses to small perturbations in systems possessing one stable state. We show that a band-edge photonic crystal resonator exhibits class II excitability, resulting from the nonlinear coupling between the high-Q optical mode, the charge-carrier density, and the fast (sub-micros) thermal dynamics. In this context, the critical slowing down of the electro-optical dynamics close to the excitable threshold can delay the optical response by an amount comparable to the duration of the output pulse (5 ns). The latter results from a short thermal dynamical excursion along a high local intensity manifold of the phase space.

Noise induced complexity: from subthreshold oscillations to spiking in coupled excitable systems

We study the stochastic dynamics of an ensemble of N globally coupled excitable elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is disturbed by independent Gaussian noise. In simulations of the Langevin dynamics we characterize the collective behavior of the ensemble in terms of its mean field and show that with the increase of noise the mean field displays a transition from a steady equilibrium to global oscillations and then, for sufficiently large noise, back to another equilibrium. In the course of this transition diverse regimes of collective dynamics ranging from periodic subthreshold oscillations to large-amplitude oscillations and chaos are observed. In order to understand the details and mechanisms of these noise-induced dynamics we consider the thermodynamic limit N-->infinity of the ensemble, and derive the cumulant expansion describing temporal evolution of the mean field fluctuations. In Gaussian approximation this allows us to perform the bifurcation analysis; its results are in good qualitative agreement with dynamical scenarios observed in the stochastic simulations of large ensembles.

Excitability mediated by localized structures in a dissipative nonlinear optical cavity

We find and characterize an excitability regime mediated by localized structures in a dissipative nonlinear optical cavity. The scenario is that stable localized structures exhibit a Hopf bifurcation to self-pulsating behavior, that is followed by the destruction of the oscillation in a saddle-loop bifurcation. Beyond this point there is a regime of excitable localized structures under the application of suitable perturbations. Excitability emerges from the spatial dependence since the system does not exhibit any excitable behavior locally. We show that the whole scenario is organized by a Takens-Bogdanov codimension-2 bifurcation point.

Limits on the excitable behavior of a semiconductor laser with optical feedback

Recently, it was proposed that semiconductor lasers with optical feedback present a complex behavior that can be described as noise driven excitable. In this work we investigate in which region of parameter space this description is adequate. We conclude that the region of the parameter space in which the system displays noise driven excitable behavior is a subset of the region in which presents low frequency fluctuations.

Analysis of the dynamics of a blue-violet Inx Ga1-x N laser with a saturable absorber

We report the results of numerical investigations of the dynamical behavior of a blue-violet InGaN laser with a specially incorporated saturable absorber. We have identified the nature of the bifurcation that occurs in the device dynamics and also the conditions that are necessary for self-pulsating and excitable operations. We also demonstrate the influence of the relevant device parameters on the laser dynamics and show how the properties of the saturable absorber and its position in the device have a considerable influence on the laser behavior. Finally theoretical investigations of the excitable behavior and a confirmation of the excitability properties of an InGaN laser are presented and discussed.

Self-organization in semiconductor lasers with ultrashort optical feedback

The dynamical behavior of a single-mode laser subject to optical feedback is investigated in the limit, when the delay time is much shorter than the period of the relaxation oscillations. Use of an integrated distributed feedback device allows us to control the feedback phase. We observe two kinds of Hopf bifurcations associated with regular self-pulsations of different frequencies.

Nonlinear dynamics of semiconductor lasers with active optical feedback

An in-depth theoretical as well as experimental analysis of the nonlinear dynamics in semiconductor lasers with active optical feedback is presented. Use of a monolithically integrated multisection device of submillimeter total length provides access to the short-cavity regime. By introducing an amplifier section as a special feature, phase and strength of the feedback can be separately tuned. In this way, the number of modes involved in the laser action can be adjusted. We predict and observe specific dynamical scenarios. Bifurcations mediate various transitions in the device output, from single-mode steadystate to self-pulsation and between different kinds of self-pulsations, reaching eventually chaotic behavior in the multimode limit.

Spontaneously excited pulses in an optically driven semiconductor laser

In optically injected semiconductor lasers, intrinsic quantum noise alone, namely, the spontaneous emission and the shot noise, are capable of exciting intensity multipulses from a steady state operation. Noisy lasers exhibit self-pulsations in the locking region of the corresponding deterministic system. The interpulse time statistics are studied in parameter regions near k-homoclinic (Shilnikov) bifurcations where the corresponding deterministic model exhibits single-, double-, and triple-pulse excitability. These statistics differ significantly among each other, and they could be used to characterize regions of different multipulse excitability in a real laser device.

Experimental evidence of van der Pol-Fitzhugh-Nagumo dynamics in semiconductor optical amplifiers

Thermo-optical pulsing in semiconductor amplifiers is experimentally shown to correspond to a very common excitable scenario (the van der Pol-Fitzhugh-Nagumo system). Self-sustained oscillations appear in the sequence predicted by this simple dynamical model as we change either the injection level or the bias current. Periodic modulation of these parameters leads to the characteristic phase-locking structure. Furthermore, coherence resonance is observed when external noise is added to the system.

Direct observation of homoclinic orbits in human heart rate variability

Homoclinic trajectories of the interbeat intervals between contractions of ventricles of the human heart are identified. The interbeat intervals are extracted from 24-h Holter ECG recordings. Three such recordings are discussed in detail. Mappings of the measured consecutive interbeat intervals are constructed. In the second and in some cases in the fourth iterate of the map of interbeat intervals homoclinic trajectories associated with a hyperbolic saddle are found. The homoclinic trajectories are often persistent for many interbeat intervals, sometimes spanning many thousands of heartbeats. Several features typical for homoclinic trajectories found in other systems were identified, including a signature of the gluing bifurcation. The homoclinic trajectories are present both in recordings of heart rate variability obtained from patients with an increased number of arrhythmias and in cases in which the sinus rhythm is dominant. The results presented are a strong indication of the importance of deterministic nonlinear instabilities in human heart rate variability.

Multipulse excitability in a semiconductor laser with optical injection

An optically injected semiconductor laser can produce excitable multipulses. Homoclinic bifurcation curves confine experimentally accessible regions in parameter space where the laser emits a certain number of pulses after being triggered from its steady state by a single perturbation. This phenomenon is organized by a generic codimension-two homoclinic bifurcation and should also be observable in other systems.