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

Vaudel O., Péraud N., Besnard P.

We report the first experimental observation of multi-pulses excitability in a 1.55 μm injection-locked bulk semi-conductor laser. Several temporal waveforms are presented showing different excitability orders. We complete these observations by drawing the excitability areas in the map "detuning-injected power" of the injected laser. We show for the first time synchronization on excitable pulses between a receiver and a transmitter, using a cascade of optically injected systems (a master, a transmitter and a receiver).

Goulding D., Hegarty S.P., Rasskazov O., Melnik S., Hartnett M., Greene G., McInerney J.G., Rachinskii D., Huyet G.

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.

Wieczorek S., Krauskopf B., Simpson T.B., Lenstra D.

This report presents a modern approach to the theoretical and experimental study of complex nonlinear behavior of a semiconductor laser with optical injection—an example of a widely applied and technologically relevant forced nonlinear oscillator. We show that the careful bifurcation analysis of a rate equation model yields (i) a deeper understanding of already studied physical phenomena, and (ii) the discovery of new dynamical effects, such as multipulse excitability. Different instabilities, cascades of bifurcations, multistability, and sudden chaotic transitions, which are often viewed as independent, are in fact logically connected into a consistent web of bifurcations via special points called organizing centers. This theoretical bifurcation analysis has predictive power, which manifests itself in good agreement with experimental measurements over a wide range of parameters and diversity of dynamics. While it is dealing with the specific system of an optically injected laser, our work constitutes the state-of-the-art in the understanding and modeling of a nonlinear physical system in general.

Martinez A., Lemaître A., Merghem K., Ferlazzo L., Dupuis C., Ramdane A., Provost J.-., Dagens B., Le Gouezigou O., Gauthier-Lafaye O.

The “material” and “device” linewidth enhancement factor α of five-quantum-dot (QD)-layer single-mode lasers emitting at 1.3μm are investigated using two methods. The Hakki–Paoli method associated with pulsed analysis of Fabry–Perot modes below threshold demonstrates a record value of 0.7 at 1295 nm. High-frequency current modulation experiments showed a value of 2.0 just above threshold at 1.3μm with a steady increase with the current. Dynamic measurements on a three-QD layer device, with a reduced ground state optical gain, showed a similar increase of α with current but at a higher rate.

O’Brien D., Hegarty S.P., Huyet G., Uskov A.V.

The sensitivity of quantum-dot semiconductor lasers to optical feedback is analyzed with a Lang–Kobayashi approach applied to a standard quantum-dot laser model. The carriers are injected into a quantum well and are captured by, or escape from, the quantum dots through either carrier–carrier or phonon–carrier interaction. Because of Pauli blocking, the capture rate into the dots depends on the carrier occupancy level in the dots. Here we show that different carrier capture dynamics lead to a strong modification of the damping of the relaxation oscillations. Regions of increased damping display reduced sensitivity to optical feedback even for a relatively large α factor.

O'Brien D., Hegarty S.P., Huyet G., McInerney J.G., Kettler T., Laemmlin M., Bimberg D., Ustinov V.M., Zhukov A.E., Mikhrin S.S., Kovsh A.R.

The behaviour of InAs/GaAs quantum dot lasers (QDL) emitting at 1.3 µm under the influence of external optical feedback has been studied. A threshold for coherence collapse of −8 dB has been measured. This very high threshold has been explained as a consequence of high relaxation oscillation damping in these lasers.

Lam W., Guzdar P.N., Roy R.

The nonlinear dynamics of a semiconductor laser with an optical feedback is studied using Hilbert phase analysis, which reveals interesting facets of the nonlinear dynamical behavior, including the formation and interaction of external cavity modes with increasing external feedback. Here we report measurements on two illustrative cases with very different dynamics; the laser is first biased just near threshold, and then far above threshold. We observe 2pi phase jumps at intervals that are multiples of the external cavity round-trip time, indicating the interaction and transfer of energy between external cavity modes.

Krauskopf B., Schneider K., Sieber J., Wieczorek S., Wolfrum M.

Many laser systems show self-pulsations with a large amplitude that are born suddenly in a homoclinic bifurcation. Just before the onset of these self-pulsations the laser is excitable where the excitability threshold is formed by the stable manifold of a saddle point. We show that there exists a special configuration, a codimension-two bifurcation called a non-central saddle-node homoclinic orbit, that acts as an organising centre of excitability in lasers. It is the key to understanding excitability in laser systems as diverse as lasers with saturable absorbers, lasers with optical injection and lasers with optical feedback.

Kuntz M., Ledentsov N.N., Bimberg D., Kovsh A.R., Ustinov V.M., Zhukov A.E., Shernyakov Y.M.

We report the spectrotemporal measurements on 1.3 μm quantum-dot lasers with picosecond time resolution. The relaxation oscillations of the various mode groups monitored separately are identical and thus allow us to examine the spectrally integrated transient of the laser pulse for its characteristics. A modulation bandwidth of 2.3 GHz at room temperature is determined, demonstrating the potential of high-speed operation of these devices at wavelengths relevant for optical data transmission. The differential gain at room temperature was measured to be g′=1×10−15 cm2, the gain compression factor is ε=1×10−15 cm3.

Wieczorek S., Krauskopf B., Lenstra D.

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.

Wünsche H.J., Brox O., Radziunas M., Henneberger F.

We report on the preparation of optical excitability in a distributed feedback semiconductor laser. The device integrates a single-mode laser and a 250 microm long passive section with cleaved facet. The phase of the light fed back from the passive section is tunable by current. The theoretical analysis shows an ultimate hop between external cavity modes within every phase cycle that is associated with a two-mode homoclinic bifurcation close to which the system becomes excitable. This excitability is clearly demonstrated in the experimental response to optical injection comparing well with simulation calculations.

Wieczorek S., Krauskopf B., Lenstra D.

We present a theoretical study of unnested period-doubling islands in three-dimensional rate equations modeling a semiconductor laser subject to external optical injection. In this phenomenon successive curves of period doublings are not arranged in nicely nested islands, but intersect each other. This overall structure is globally organized by several codimension-2 bifurcations. As a consequence, the chaotic region existing inside an unnested island of period doublings can be entered not only via a period-doubling cascade but also via the breakup of a torus, and even via the sudden appearance of a chaotic attractor. In order to fully understand these different chaotic transitions we reveal underlying global bifurcations and we show how they are connected to codimension-2 bifurcation points. Unnested islands of period doublings appear to be generic and hence must be expected in a large class of dynamical systems.

Coullet P., Daboussy D., Tredicce J.R.

We show that an optical system, a laser with an injected signal, behaves as an excitable medium. This property gives rise to propagating pulses if the active medium is spatially extended. We study the properties of those waves and we demonstrate that they may annihilate or cross each other depending on the control parameter values.

Giudici M., Green C., Giacomelli G., Nespolo U., Tredicce J.R.

We experimentally investigate the dynamical behavior of a semiconductor laser with optical feedback. We show that noise plays an important role close to the instability threshold, while determinism controls the so-called coherence collapse regime. We identify the bifurcation which is at the origin of the low frequency fluctuations. It is the result of a collision between a stable fixed point and a saddle point (Andronov's bifurcation). We provide experimental proof that the laser with optical feedback behaves as an excitable medium.

Plaza F., Velarde M.G., Arecchi F.T., Boccaletti S., Ciofini M., Meucci R.

Excitability and relaxation oscillations are shown to appear in the vicinity of subcritical or transcritical bifurcations with a different scenario from those previously introduced in biology, chemistry and liquid-crystal physics. Experimental observation of such a scenario has been done in a laser with intracavity saturable absorber.

Schegolev Andrey E., Bastrakova Marina V., Sergeev Michael A., Maksimovskaya Anastasia A., Klenov Nikolay V., Soloviev Igor

The extensive development of the field of spiking neural networks has led to many areas of research that have a direct impact on people’s lives. As the most bio-similar of all neural networks, spiking neural networks not only allow for the solution of recognition and clustering problems (including dynamics), but they also contribute to the growing understanding of the human nervous system. Our analysis has shown that hardware implementation is of great importance, since the specifics of the physical processes in the network cells affect their ability to simulate the neural activity of living neural tissue, the efficiency of certain stages of information processing, storage and transmission. This survey reviews existing hardware neuromorphic implementations of bio-inspired spiking networks in the ”semiconductor”, ”superconductor”, and ”optical” domains. Special attention is given to the potentials for effective ”hybrids” of different approaches.

Zhang Y., Xiang S., Yu C., Gao S., Han Y., Guo X., Zhang Y., Shi Y., Hao Y.

AbstractPhotonic neuromorphic computing is a competitive paradigm to overcome the bottleneck of von Neumann architectures. Incoherent and coherent synaptic networks are two popular schemes realizing photonic weighting functions. Previous works have proved the distributed feedback (DFB) laser with an intracavity saturable absorber (DFB‐SA) can behavior like a spiking neuron. However, the compatibility with the incoherent synaptic architecture has not yet been demonstrated. Here the neuron‐like dynamics of a DFB‐SA laser subject to single‐wavelength and multiple‐wavelengths incoherent optical injections are experimentally demonstrated. The results show that, for the DFB‐SA laser subject to single‐wavelength incoherent injection, the neuron‐like dynamics including threshold, temporal integration, and refractory period are achieved. Besides, the range of injection wavelength that leads to a successful neuron‐like response is identified. For the DFB‐SA laser with four‐wavelength incoherent optical injection, the neuron‐like dynamics can also be achieved. In addition, the effect of wavelength interval is also considered. The logic XOR operation and Iris recognition tasks are successfully implemented. Furthermore, the feasibility of a cascaded system for the DFB‐SA lasers with four‐wavelengths incoherent optical injection is demonstrated. This work provides a feasible scheme for the system integration of photonic spiking neurons and incoherent synaptic networks.

Zhang X., Mu P., Liu G., Wang Y., Li X.

Significant progress has been made in the research of all-optical neural networks in recent years. In this paper, we theoretically explore the properties of a neural system composed of semiconductor ring lasers (SRLs). Our study demonstrates that external optical signals generated by a tunable laser (TL) are injected into the first semiconductor ring laser photonic neuron (SRL1). Subsequently, the responses of SRL1 in the clockwise (CW) and counterclockwise (CCW) directions are unidirectionally injected into the CW and CCW directions of the second semiconductor ring laser photonic neuron (SRL2), respectively, which then exhibits similar spiking inhibition behaviors. Numerical simulations reveal that the spiking inhibition behavior of the SRL response can be precisely controlled by adjusting the perturbation time and intensity of the external injection signal, and this behavior is highly repeatable. Most importantly, we successfully achieve the stable transmission of these responses between the two SRL photonic neurons. These inhibition behaviors are analogous to those of biological neurons, but with a response speed reaching the sub-nanosecond level. Additionally, we indicate that SRL photonic neurons undergo a refractory-period-like phenomenon when subjected to two consecutive perturbations. These findings highlight the immense potential for the design and implementation of future all-optical neural networks, providing critical theoretical foundations and support for them.

Zhang Y., Xiang S., Song Z., Guo X., Zhang Y., Shi Y., Hao Y.

Mu P., Wang K., Liu G., Wang Y., Liu X., Guo G., Hu G.

In this paper, a method of generating controllable spikes utilizing symmetric semiconductor ring lasers (SRLs) is investigated, and various optical behaviors of biological neurons are successfully emulated on a faster timescale. We demonstrate the synchronized spike phenomena in two directions, generated in both the clockwise (CW) and counterclockwise (CCW) modes of the tunable laser (TL)-injected SRL. The size of the peaks and the interval between them can be manipulated by adjusting the output complex amplitude of the TL and bias current. At the same time, we also analyzed the CW mode of the TL-injected SRL and successfully replicated the four distinct discharge patterns of biological neurons. These findings offer promising prospects for future neuromorphic research.

Zhao Y., Ma B., Zhang J., Zou W.

Dillane M., Viktorov E., Kelleher B.

Kelleher B., Dillane M., Viktorov E.A.

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.

Köster F., Lingnau B., Krimlowski A., Hövel P., Lüdge K.

The dynamical properties of an optical neuron formed by a quantum dot semiconductor laser model subjected to optical injection and optical feedback are analyzed. The parameter space spanned by the injection strength and frequency detuning of the optical injection is systematically scanned and modulations of the bifurcation boundaries that induce complex scenarios are found, which enable new opportunities to introduce the optical setup as an optical neuron. The counterintuitive behavior of coherence resonance for different setups of a single-driven optical neuron under optical feedback is also found. Following the results, the microscopically motivated quantum dot laser rate equation model is reduced to the normal form of a saddle-node infinite period (SNIPER) bifurcation for low injection strengths and a network of four such SNIPER systems in a globally coupled setup is studied. A new phenomenon is observed, which is called collective coherence resonance. This novel dynamical behavior is connected to the coexistence of a network-wide SNIPER bifurcation and a change in stability for the synchronized manifold, analyzed via the master stability function.

Prants W.T., Bonatto C.

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 $\ensuremath{\pi}$ 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 $2\ensuremath{\pi}$ 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.

Dillane M., Lingnau B., Viktorov E.A., Dubinkin I., Fedorov N., Kelleher B.

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.

Tiana-Alsina J., Garbin B., Barland S., Masoller C.

We use statistical tools to characterize the response of an excitable system to periodic perturbations. The system is an optically injected semiconductor laser under pulsed perturbations of the phase of the injected field. We characterize the laser response by counting the number of pulses emitted by the laser, within a time interval, $\Delta$T , that starts when a perturbation is applied. The success rate, SR($\Delta$T), is then defined as the number of pulses emitted in the interval $\Delta$T , relative to the number of perturbations. The analysis of the variation of SR with $\Delta$T allows to separate a constant lag of technical origin and a frequency-dependent lag of physical and dynamical origin. Once the lag is accounted for, the success rate clearly captures locked and unlocked regimes and the transitions between them. We anticipate that the success rate will be a practical tool for analyzing the output of periodically forced systems, particularly when very regular oscillations need to be generated via small periodic perturbations.

Lingnau B., Perrott A.H., Dernaika M., Caro L., Peters F.H., Kelleher B.

We investigate the dynamics of asymmetrically coupled semiconductor lasers on photonic integrated circuits in experiment and theory. The experimental observations are explained using a rate-equation model for coupled lasers incorporating a saturable coupling waveguide. We perform a bifurcation analysis of the coupled laser dynamics, focusing on the effects of the coupling phase and the dynamical difference between passive and saturable coupling waveguides. For a passive waveguide, we find a bifurcation scenario closely resembling the well-known optical injection setup, which is largely insensitive to the coupling phase. When the coupling waveguide is saturable, the dynamics become increasingly complex and unpredictable, with a strong phase-dependence. Our results show the possibility of a simple layout for reproducible laser dynamics on a chip.

Zhang Z., Wu Z., Lu D., Xia G., Deng T.

We propose a photonic neural system composed of three cascaded vertical-cavity surface-emitting lasers with an embedded saturable absorbers (VCSEL-SAs) and numerically investigate the encoding, propagation and storage characteristics of the spiking patterns in this system. The results show that, with suitable perturbation strength, the first VCSEL-SA (VCSEL-SA1) can convert the stimulus into spike response. Increasing both the perturbation strength and the bias current of active region is beneficial to improve the conversion rate. Moreover, the spiking patterns generated by VCSEL-SA1 can be stably propagated into another two VCSEL-SAs (VCSEL-SA2 and VCSEL-SA3) with a certain delay through adjusting the coupling weight. Additionally, after introducing a feedback into VCSEL-SA1, the fired spiking patterns can be successfully stored in this proposed system. The obtained results can offer great potential for future, brain-inspired ultrafast neuromorphic computing system.

Dillane M., Robertson J., Peters M., Hurtado A., Kelleher B.

Optically injected quantum dot lasers display many unique nonlinear phenomena and are in particular, excellent testbeds for different forms of excitability. We analyse the recent discovery of Type II excitability in such devices. An optothermal instability leads to the phenomenon and while an underlying Hopf bifurcation is ultimately responsible for the observation, intriguingly there are two potential routes: One via a subcritical bifurcation and an associated bistable region and the other via a supercritical bifurcation and an associated canard explosion.