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

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.

Refractory times for excitable dual-state quantum dot laser neurons

Excitable photonic systems show promise for ultrafast analog computation, several orders of magnitude faster than biological neurons. Optically injected quantum dot lasers display several excitable mechanisms with dual-state quantum lasers recently emerging as true all-or-none excitable artificial neurons. For use in applications, deterministic triggering is necessary and this has previously been demonstrated in the literature. In this work we analyze the crucially important refractory time for this dual-state system, which defines the minimum time between distinct pulses in any train.

Inhibitory and excitatory integration with a quantum dot laser neuron

Neuromorphic computing has garnered a lot of attention in recent years. Excitable photonic systems in particular demonstrate great potential for ultrafast, controllable spike processing. Optically injected quantum dot lasers display several distinct excitable regimes. We demonstrate here that optically injected dual-state quantum dot lasers can display the classic leaky integrate-and-fire mechanism where the integration of several sub-threshold perturbations can yield an effective supra-threshold perturbation. Intriguingly, a contrasting integrate-and-inhibit mechanism is demonstrated in this work where the integration of two supra-threshold perturbations yields an effective sub-threshold perturbation similar to the pre-pulse inhibition mechanism of biological neurons. This is the first such mechanism in neuromorphic photonics to the best of our knowledge.

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.

Nonlinear dynamics of a quantum cascade laser with optical injection

This work presents the nonlinear dynamics of a quantum cascade laser subject to optical injection. Within the stable locking regime, the optical power shows a hysteresis behavior as a function of the detuning frequency. Outside the stable locking regime, the laser mostly produces periodic oscillations. However, the laser pumped at a high pump current also generates spiking pulsations with uniform amplitude, which occur in the vicinity of the negative locking boundary.

Mapping the Stability and Dynamics of Optically Injected Dual State Quantum Dot Lasers

Optical injection is a key nonlinear laser configuration both for applications and fundamental studies. An important figure for understanding the optically injected laser system is the two parameter stability mapping of the dynamics found by examining the output of the injected laser under different combinations of the injection strength and detuning. We experimentally and theoretically generate this map for an optically injected quantum dot laser, biased to emit from the first excited state and optically injected near the ground state. Regions of different dynamical behaviours including phase-locking, excitability, and bursting regimes are identified. At the negatively detuned locking boundary, ground state dropouts and excited state pulses are observed near a hysteresis cycle for low injection strengths. Higher injection strengths reveal μs duration square wave trains where the intensities of the ground state and excited state operate in antiphase. A narrow region of extremely slow oscillations with periods of several tens of milliseconds is observed at the positively detuned boundary. Two competing optothermal couplings are introduced and are shown to reproduce the experimental results extremely well. In fact, the dynamics of the system are dominated by these optothermal effects and their interplay is central to reproducing detailed features of the stability map.

Optical information processing using dual state quantum dot lasers: complexity through simplicity

We review results on the optical injection of dual state InAs quantum dot-based semiconductor lasers. The two states in question are the so-called ground state and first excited state of the laser. This ability to lase from two different energy states is unique amongst semiconductor lasers and in combination with the high, intrinsic relaxation oscillation damping of the material and the novel, inherent cascade like carrier relaxation process, endows optically injected dual state quantum dot lasers with many unique dynamical properties. Particular attention is paid to fast state switching, antiphase excitability, novel information processing techniques and optothermally induced neuronal phenomena. We compare and contrast some of the physical properties of the system with other optically injected two state devices such as vertical cavity surface emitting lasers and ring lasers. Finally, we offer an outlook on the use of quantum dot material in photonic integrated circuits.

Adaptive sigmoid-like and PReLU activation functions for all-optical perceptron

We present an approach for the generation of an adaptive sigmoid-like and PReLU nonlinear activation function of an all-optical perceptron, exploiting the bistability of an injection-locked Fabry-Perot semiconductor laser. The profile of the activation function can be tailored by adjusting the injection-locked side-mode order, frequency detuning of the input optical signal, Henry factor, or bias current. The universal fitting function for both families of the activation functions is presented.

Triple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillator

We report the discovery of a codimension-two phenomenon in the phase diagram of a second-order self-sustained nonlinear oscillator subject to a constant external periodic forcing, around which three regimes associated with the synchronization phenomenon exist, namely phase-locking, frequency-locking without phase-locking, and frequency-unlocking states. The triple point of synchronization arises when a saddle-node homoclinic cycle collides with the zero-amplitude state of the forced oscillator. A line on the phase diagram where limit-cycle solutions contain a phase singularity departs from the triple point, giving rise to a codimension-one transition between the regimes of frequency unlocking and frequency locking without phase locking. At the parameter values where the critical transition occurs, the forced oscillator exhibits a separatrix with a π phase jump, i.e., a particular trajectory in phase space that separates two distinct behaviors of the phase dynamics. Close to the triple point, noise induces excitable pulses where the two variants of type-I excitability, i.e., pulses with and without 2π phase slips, appear stochastically. The impacts of weak noise and some other dynamical aspects associated with the transition induced by the singular phenomenon are also discussed.

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.

Exploiting a monolithic passively Q-switched Nd:YAG laser to mimic a single neuron cell under periodic stimulation

A monolithic passively Q-switched Nd:YAG laser under periodic pulse pumping is originally exploited to emulate the response of a single neuron cell stimulated by periodic pulse inputs. Experimental results reveal that the output characteristics of the monolithic passively Q-switched laser can analogously manifest not only the firing patterns but also the frequency-locked plateaus of the single neuron cell. Moreover, the sine circle map is innovatively used to generate the output pulse sequences that can exactly correspond to experimental firing patterns. The present exploration indicates that a monolithic passively Q-switched solid-state laser is highly feasible to be developed as a compact artificial neuron cell.

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.

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.

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.

Interactions and collisions of topological solitons in a semiconductor laser with optical injection and feedback

We present experimental and numerical results about dynamical interactions of topological solitons in a semiconductor laser with coherent injection and feedback. We show different kind of interactions such as repulsion, annihilation, or formation of soliton bound states, depending on laser parameters. Collisions between single structures and bound states conserve momentum and charge.

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.

Refractory period of an excitable semiconductor laser with optical injection

Injection-locked semiconductor lasers can be brought to a neuronlike excitable regime when parameters are set close to the unlocking transition. Here we study experimentally the response of this system to repeated optical perturbations and observe the existence of a refractory period during which perturbations are not able to elicit an excitable response. The results are analyzed via simulations of a set of dynamical equations which reproduced adequately the experimental results.

Single-sideband photonic microwave generation with an optically injected quantum-dot semiconductor laser

We studied single-sideband (SSB) photonic microwave generation with a high sideband rejection ratio (SRR) based on the period-one dynamical states of an optically injected quantum-dot (QD) semiconductor laser and demonstrated that the SSB signals have SRRs of approximately 15 dB higher than those generated with a conventional quantum-well semiconductor laser under conditions of optimal microwave power. The enhancement of SRR in the QD laser, which is important in mitigating the power penalty effect in applications such as radio-over-fiber optical communications, could be primarily attributed to a lower carrier decay rate in the dots, smaller linewidth enhancement factor, and reduced photon decay rate.

Optically injected InAs/GaAs quantum dot laser for tunable photonic microwave generation

We present an experimental investigation on the period-one dynamics of an optically injected InAs/GaAs quantum dot laser as a photonic microwave source. It is shown that the microwave frequency of the quantum dot laser's period-one oscillation is continuously tunable through the adjustment of the frequency detuning. The microwave power is enhanced by increasing the injection strength providing that the operation is away from the Hopf bifurcation, whereas the second-harmonic distortion of the electrical signal is well reduced by increasing the detuning frequency. Both strong optical injection and high detuning frequency are favorable for obtaining a single sideband optical signal. In addition, particular period-one oscillation points of low sensitivity to the frequency detuning are found close to the Hopf bifurcation line.

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.

Amplitude-phase coupling and chirp in quantum-dot lasers: influence of charge carrier scattering dynamics

We investigate the dependence of the amplitude-phase coupling in quantum-dot (QD) lasers on the charge-carrier scattering timescales. The carrier scattering processes influence the relaxation oscillation parameters, as well as the frequency chirp, which are both important parameters when determining the modulation performance of the laser device and its reaction to optical perturbations. We find that the FM/AM response exhibits a strong dependence on the modulation frequency, which leads to a modified optical response of QD lasers when compared to conventional laser devices. Furthermore, the frequency response curve changes with the scattering time scales, which can allow for an optimization of the laser stability towards optical perturbations.

Incoherent optical triggering of excitable pulses in an injection-locked semiconductor laser

We experimentally study the response of an injection-locked quantum dot semiconductor laser in the excitable regime to perturbations from an external, incoherent laser. We show that excitable pulses may be triggered both for perturbation wavelengths close to that of the quantum dot device and wavelengths detuned even by a few tens of nanometers.

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.

Failure of the α factor in describing dynamical instabilities and chaos in quantum-dot lasers

We show that the long-established concept of a linewidth-enhancement factor α to describe carrier-induced refractive index changes in semiconductor lasers breaks down in quantum-dot (QD) lasers when describing complex dynamic scenarios, found, for example, under high-excitation or optical injection. By comparing laser simulations using a constant α factor with results from a more complex nonequilibrium model that separately treats gain and refractive index dynamics, we examine the conditions under which an approximation of the amplitude-phase coupling by an α factor becomes invalid. The investigations show that while a quasiequilibrium approach for conventional quantum well lasers is valid over a reasonable parameter range, allowing one to introduce an α factor as a constant parameter, the concept is in general not applicable to predict QD laser dynamics due to the different time scales of the involved scattering processes.

Stability of the nonlinear dynamics of an optically injected VCSEL

Automated protocols have been developed to characterize time series data in terms of stability. These techniques are applied to the output power time series of an optically injected vertical cavity surface emitting laser (VCSEL) subject to varying injection strength and optical frequency detuning between master and slave lasers. Dynamic maps, generated from high resolution, computer controlled experiments, identify regions of dynamic instability in the parameter space.

Bounded phase phenomena in the optically injected laser

Two routes to phase-locking in the optically injected laser system are investigated both involving limit cycles where the phase of the slave laser is unlocked but is nevertheless bounded. We use an experimental phase-resolving technique to unambiguously demonstrate the phenomenon via explicit phasors for the slave laser electric field. Theoretical considerations show that for locking mechanisms involving Hopf bifurcations, such limit cycles of bounded phase are generic. For weakly damped devices, such as quantum well lasers, this can involve an excited resonance at the relaxation oscillation frequency. For highly damped devices there is no such excitation but the bounded phase behavior must persist. Phasor portraits for other regimes are also obtained including a chaotic regime.

Transition from unidirectional to delayed bidirectional coupling in optically coupled semiconductor lasers

We investigate the transition from unidirectional to delayed bidirectional coupling of semiconductor lasers. By tuning the coupling strength in one direction we show how the locking region evolves as a function of the detuning and coupling strength. We consider two representative values of the relaxation oscillation damping: one where the relaxation oscillations are very underdamped and one where they are very overdamped. Qualitatively different dynamical scenarios are shown to emerge for each case. Several features of the delayed bidirectional system can be seen as remaining from the unidirectional system while others clearly arise due to the delayed coupling and are similar to effects seen in delayed feedback configurations.

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.