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Tian H, Zhang L, Lyu W, Fu Z, Xu Z, Su L, Zeng Z, Li H, Zhang Z, Liu Y. Temporal dissipative soliton with controllable morphology in a time-delayed coupled optoelectronic oscillator. OPTICS LETTERS 2024; 49:6265-6268. [PMID: 39485463 DOI: 10.1364/ol.540648] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2024] [Accepted: 10/14/2024] [Indexed: 11/03/2024]
Abstract
A temporal dissipative soliton (TDS) with controllable morphology is demonstrated in a time-delayed coupled optoelectronic oscillator (OEO) driven by two optical carriers with different wavelengths. The morphology of the TDS is controlled by the power difference between the two optical carriers and the delay difference induced by the group-velocity dispersion (GVD) in the OEO loop. When the delay difference is small, the OEO operates in a single-soliton state. With the increase of the wavelength interval between the two optical carriers, the delay difference becomes significant so that various compound TDS structures are observed, where the TDS interval is equal to the delay difference. The morphology of the compound TDSs can be switched between a pulsating TDS packet and a stable compound TDS structure by further tuning the power difference between the two optical carriers. This discovery not only facilitates the investigation of novel soliton dynamics but also provides a method for generating customized pulse waveforms.
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2
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Li N, Feng Y, Huang Y, Zhou P, Mu P, Xiang S. Characterizing the aggregated encoding method utilizing bursts activated by a VCSEL-neuron with a feedback structure. OPTICS EXPRESS 2024; 32:20370-20384. [PMID: 38859150 DOI: 10.1364/oe.521746] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2024] [Accepted: 05/02/2024] [Indexed: 06/12/2024]
Abstract
The rapid advancement of photonic technologies has facilitated the development of photonic neurons that emulate neuronal functionalities akin to those observed in the human brain. Neuronal bursts frequently occur in behaviors where information is encoded and transmitted. Here, we present the demonstration of the bursting response activated by an artificial photonic neuron. This neuron utilizes a single vertical-cavity surface-emitting laser (VCSEL) and encodes multiple stimuli effectively by varying the spike count during a burst based on the polarization competition in the VCSEL. By virtue of the modulated optical injection in the VCSEL employed to trigger the spiking response, we activate bursts output in the VCSEL with a feedback structure in this scheme. The bursting response activated by the VCSEL-neuron exhibits neural signal characteristics, promising an excitation threshold and the refractory period. Significantly, this marks the inaugural implementation of a controllable integrated encoding scheme predicated on bursts within photonic neurons. There are two remarkable merits; on the one hand, the interspike interval of bursts is distinctly diminished, amounting to merely one twenty-fourth compared to that observed in optoelectronic oscillators. Moreover, the interspike period of bursts is about 70.8% shorter than the period of spikes activated by a VCSEL neuron without optical feedback. Our results may shed light on the analogy between optical and biological neurons and open the door to fast burst encoding-based optical systems with a speed several orders of magnitude faster than their biological counterparts.
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3
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Tian H, Zhang L, Zeng Z, Lyu W, Fu Z, Xu Z, Zhang Z, Zhang Y, Zhang S, Li H, Liu Y. Neuromorphic regenerative memory optoelectronic oscillator. OPTICS EXPRESS 2023; 31:27529-27542. [PMID: 37710826 DOI: 10.1364/oe.495015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2023] [Accepted: 07/28/2023] [Indexed: 09/16/2023]
Abstract
Neuromorphic spiking information processing based on neuron-like excitable effect has achieved rapid development in recent years due to its advantages such as ultra-high operation speed, programming-free implementation and low power consumption. However, the current physical platforms lack building blocks like compilers, logic gates, and more importantly, data memory. These factors become the shackles to construct a full-physical layer neural network. In this paper, a neuromorphic regenerative memory scheme is proposed based on a time-delayed broadband nonlinear optoelectronic oscillator (OEO), which enables reshaping and regenerating on-off keying encoding sequences. Through biasing the dual-drive Mach-Zehnder electro-optic modulator in the OEO cavity near its minimum transmission point, the OEO can work in excitable regime, where localized states are maintained for robust nonlinear spiking response. Both simulation and experiment are carried out to demonstrate the proposed scheme, where the simulation results and the experimental results fit in with each other. The proposed OEO-based neuromorphic regenerative memory scheme exhibits long-term response ability for short-term excitation, which shows an enormous application potential for high-speed neuromorphic information buffering, optoelectronic interconnection and computing.
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Hejda M, Malysheva E, Owen-Newns D, Ali Al-Taai QR, Zhang W, Ortega-Piwonka I, Javaloyes J, Wasige E, Dolores-Calzadilla V, Figueiredo JML, Romeira B, Hurtado A. Artificial optoelectronic spiking neuron based on a resonant tunnelling diode coupled to a vertical cavity surface emitting laser. NANOPHOTONICS 2023; 12:857-867. [PMID: 36909291 PMCID: PMC9995654 DOI: 10.1515/nanoph-2022-0362] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/21/2022] [Accepted: 10/26/2022] [Indexed: 06/18/2023]
Abstract
Excitable optoelectronic devices represent one of the key building blocks for implementation of artificial spiking neurons in neuromorphic (brain-inspired) photonic systems. This work introduces and experimentally investigates an opto-electro-optical (O/E/O) artificial neuron built with a resonant tunnelling diode (RTD) coupled to a photodetector as a receiver and a vertical cavity surface emitting laser as a transmitter. We demonstrate a well-defined excitability threshold, above which the neuron produces optical spiking responses with characteristic neural-like refractory period. We utilise its fan-in capability to perform in-device coincidence detection (logical AND) and exclusive logical OR (XOR) tasks. These results provide first experimental validation of deterministic triggering and tasks in an RTD-based spiking optoelectronic neuron with both input and output optical (I/O) terminals. Furthermore, we also investigate in simulation the prospects of the proposed system for nanophotonic implementation in a monolithic design combining a nanoscale RTD element and a nanolaser; therefore demonstrating the potential of integrated RTD-based excitable nodes for low footprint, high-speed optoelectronic spiking neurons in future neuromorphic photonic hardware.
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Affiliation(s)
- Matěj Hejda
- SUPA Department of Physics, Institute of Photonics, University of Strathclyde, Glasgow, UK
| | - Ekaterina Malysheva
- Eindhoven Hendrik Casimir Institute, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Dafydd Owen-Newns
- SUPA Department of Physics, Institute of Photonics, University of Strathclyde, Glasgow, UK
| | | | - Weikang Zhang
- SUPA Department of Physics, Institute of Photonics, University of Strathclyde, Glasgow, UK
| | | | - Julien Javaloyes
- Dept de Física and IAC-3, Universitat de les Illes Balears, Palma de Mallorca, Spain
| | - Edward Wasige
- High Frequency Electronics Group, University of Glasgow, Glasgow, UK
| | | | - José M. L. Figueiredo
- Centra-Ciências and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal
| | - Bruno Romeira
- INL – International Iberian Nanotechnology Laboratory, Ultrafast Bio- and Nanophotonics Group, Braga, Portugal
| | - Antonio Hurtado
- SUPA Department of Physics, Institute of Photonics, University of Strathclyde, Glasgow, UK
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5
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Terrien S, Krauskopf B, Broderick NGR, Pammi VA, Braive R, Sagnes I, Beaudoin G, Pantzas K, Barbay S. Merging and disconnecting resonance tongues in a pulsing excitable microlaser with delayed optical feedback. CHAOS (WOODBURY, N.Y.) 2023; 33:023142. [PMID: 36859235 DOI: 10.1063/5.0124693] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Accepted: 01/26/2023] [Indexed: 06/18/2023]
Abstract
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).
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Affiliation(s)
- Soizic Terrien
- Laboratoire d'Acoustique de l'Université du Mans (LAUM), UMR 6613, Institut d'Acoustique - Graduate School (IA-GS), CNRS, Le Mans Université, Le Mans, France
| | - Bernd Krauskopf
- Department of Mathematics and Dodd-Walls Centre for Photonic and Quantum Technologies, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - Neil G R Broderick
- Department of Physics and Dodd-Walls Centre for Photonic and Quantum Technologies, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - Venkata A Pammi
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France
| | - Rémy Braive
- Université Paris-Saclay, Université Paris Cité, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France and Institut Universitaire de France, Paris, France
| | - Isabelle Sagnes
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France
| | - Grégoire Beaudoin
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France
| | - Konstantinos Pantzas
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France
| | - Sylvain Barbay
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France
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6
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Laing CR, Krauskopf B. Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0292] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
We consider a single theta neuron with delayed self-feedback in the form of a Dirac delta function in time. Because the dynamics of a theta neuron on its own can be solved explicitly—it is either excitable or shows self-pulsations—we are able to derive algebraic expressions for the existence and stability of the periodic solutions that arise in the presence of feedback. These periodic solutions are characterized by one or more equally spaced pulses per delay interval, and there is an increasing amount of multistability with increasing delay time. We present a complete description of where these self-sustained oscillations can be found in parameter space; in particular, we derive explicit expressions for the loci of their saddle-node bifurcations. We conclude that the theta neuron with delayed self-feedback emerges as a prototypical model: it provides an analytical basis for understanding pulsating dynamics observed in other excitable systems subject to delayed self-coupling.
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Affiliation(s)
- Carlo R. Laing
- School of Natural and Computational Sciences Massey University, Private Bag 102-904, North Shore Mail Centre, Auckland 0745, New Zealand
| | - Bernd Krauskopf
- Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
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7
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Pfenning A, Krüger S, Jabeen F, Worschech L, Hartmann F, Höfling S. Single-Photon Counting with Semiconductor Resonant Tunneling Devices. NANOMATERIALS (BASEL, SWITZERLAND) 2022; 12:2358. [PMID: 35889583 PMCID: PMC9318172 DOI: 10.3390/nano12142358] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/28/2022] [Revised: 06/27/2022] [Accepted: 06/28/2022] [Indexed: 11/17/2022]
Abstract
Optical quantum information science and technologies require the capability to generate, control, and detect single or multiple quanta of light. The need to detect individual photons has motivated the development of a variety of novel and refined single-photon detectors (SPDs) with enhanced detector performance. Superconducting nanowire single-photon detectors (SNSPDs) and single-photon avalanche diodes (SPADs) are the top-performer in this field, but alternative promising and innovative devices are emerging. In this review article, we discuss the current state-of-the-art of one such alternative device capable of single-photon counting: the resonant tunneling diode (RTD) single-photon detector. Due to their peculiar photodetection mechanism and current-voltage characteristic with a region of negative differential conductance, RTD single-photon detectors provide, theoretically, several advantages over conventional SPDs, such as an inherently deadtime-free photon-number resolution at elevated temperatures, while offering low dark counts, a low timing jitter, and multiple photon detection modes. This review article brings together our previous studies and current experimental results. We focus on the current limitations of RTD-SPDs and provide detailed design and parameter variations to be potentially employed in next-generation RTD-SPD to improve the figure of merits of these alternative single-photon counting devices. The single-photon detection capability of RTDs without quantum dots is shown.
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Affiliation(s)
- Andreas Pfenning
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
- Technische Physik, Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Würzburg-Dresden Cluster of Excellence ct.qmat, University of Würzburg, 97074 Würzburg, Germany; (S.K.); (F.J.); (L.W.); (F.H.); (S.H.)
| | - Sebastian Krüger
- Technische Physik, Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Würzburg-Dresden Cluster of Excellence ct.qmat, University of Würzburg, 97074 Würzburg, Germany; (S.K.); (F.J.); (L.W.); (F.H.); (S.H.)
| | - Fauzia Jabeen
- Technische Physik, Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Würzburg-Dresden Cluster of Excellence ct.qmat, University of Würzburg, 97074 Würzburg, Germany; (S.K.); (F.J.); (L.W.); (F.H.); (S.H.)
| | - Lukas Worschech
- Technische Physik, Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Würzburg-Dresden Cluster of Excellence ct.qmat, University of Würzburg, 97074 Würzburg, Germany; (S.K.); (F.J.); (L.W.); (F.H.); (S.H.)
| | - Fabian Hartmann
- Technische Physik, Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Würzburg-Dresden Cluster of Excellence ct.qmat, University of Würzburg, 97074 Würzburg, Germany; (S.K.); (F.J.); (L.W.); (F.H.); (S.H.)
| | - Sven Höfling
- Technische Physik, Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Würzburg-Dresden Cluster of Excellence ct.qmat, University of Würzburg, 97074 Würzburg, Germany; (S.K.); (F.J.); (L.W.); (F.H.); (S.H.)
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8
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Seidel TG, Javaloyes J, Gurevich SV. Influence of time-delayed feedback on the dynamics of temporal localized structures in passively mode-locked semiconductor lasers. CHAOS (WOODBURY, N.Y.) 2022; 32:033102. [PMID: 35364839 DOI: 10.1063/5.0075449] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Accepted: 02/07/2022] [Indexed: 06/14/2023]
Abstract
In this paper, we analyze the effect of optical feedback on the dynamics of a passively mode-locked ring laser operating in the regime of temporal localized structures. This laser system is modeled by a set of delay differential equations, which include delay terms associated with the laser cavity and the feedback loop. Using a combination of direct numerical simulations and path-continuation techniques, we show that the feedback loop creates echoes of the main pulse whose position and size strongly depend on the feedback parameters. We demonstrate that in the long-cavity regime, these echoes can successively replace the main pulses, which defines their lifetime. This pulse instability mechanism originates from a global bifurcation of the saddle-node infinite-period type. In addition, we show that, under the influence of noise, the stable pulses exhibit forms of a behavior characteristic of excitable systems. Furthermore, for the harmonic solutions consisting of multiple equispaced pulses per round-trip, we show that if the location of the pulses coincides with the echo of another, the range of stability of these solutions is increased. Finally, it is shown that around these resonances, branches of different solutions are connected by period-doubling bifurcations.
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Affiliation(s)
- Thomas G Seidel
- Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
| | - Julien Javaloyes
- Departament de Física and IAC-3, Universitat de les Illes Balears, C/ Valldemossa km 7.5, 07122 Mallorca, Spain
| | - Svetlana V Gurevich
- Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
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9
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Prants WT, Bonatto C. Triple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillator. Phys Rev E 2021; 103:032201. [PMID: 33862802 DOI: 10.1103/physreve.103.032201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2020] [Accepted: 02/08/2021] [Indexed: 11/07/2022]
Abstract
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.
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Affiliation(s)
- Willian T Prants
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
| | - Cristian Bonatto
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
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10
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Wedgwood KCA, Słowiński P, Manson J, Tsaneva-Atanasova K, Krauskopf B. Robust spike timing in an excitable cell with delayed feedback. J R Soc Interface 2021; 18:20210029. [PMID: 33849329 DOI: 10.1098/rsif.2021.0029] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The initiation and regeneration of pulsatile activity is a ubiquitous feature observed in excitable systems with delayed feedback. Here, we demonstrate this phenomenon in a real biological cell. We establish a critical role of the delay resulting from the finite propagation speed of electrical impulses in the emergence of persistent multiple-spike patterns. We predict the coexistence of a number of such patterns in a mathematical model and use a biological cell subject to dynamic clamp to confirm our predictions in a living mammalian system. Given the general nature of our mathematical model and experimental system, we believe that our results capture key hallmarks of physiological excitability that are fundamental to information processing.
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Affiliation(s)
- Kyle C A Wedgwood
- Living Systems Institute and Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Stocker Road, Exeter EX4 4QD, UK
| | - Piotr Słowiński
- Living Systems Institute and Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Stocker Road, Exeter EX4 4QD, UK
| | - James Manson
- Living Systems Institute and Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Stocker Road, Exeter EX4 4QD, UK
| | - Krasimira Tsaneva-Atanasova
- Living Systems Institute and Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Stocker Road, Exeter EX4 4QD, UK.,Institute for Advanced Study, Technical University of Munich, Lichtenbergstrasse 2 a, 85748 Garching, Germany.,Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria
| | - Bernd Krauskopf
- Department of Mathematics, University of Auckland, Auckland 1010, New Zealand.,Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin 9054, New Zealand
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11
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D’Huys O, Veltz R, Dolcemascolo A, Marino F, Barland S. Canard resonance: on noise-induced ordering of trajectories in heterogeneous networks of slow-fast systems. JPHYS PHOTONICS 2021. [DOI: 10.1088/2515-7647/abcbe3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
We analyse the dynamics of a network of semiconductor lasers coupled via their mean intensity through a non-linear optoelectronic feedback loop. We establish experimentally the excitable character of a single node, which stems from the slow-fast nature of the system, adequately described by a set of rate equations with three well separated time scales. Beyond the excitable regime, the system undergoes relaxation oscillations where the nodes display canard dynamics. We show numerically that, without noise, the coupled system follows an intricate canard trajectory, with the nodes switching on one by one. While incorporating noise leads to a better correspondence between numerical simulations and experimental data, it also has an unexpected ordering effect on the canard orbit, causing the nodes to switch on closer together in time. We find that the dispersion of the trajectories of the network nodes in phase space is minimized for a non-zero noise strength, and call this phenomenon canard resonance.
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12
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Terrien S, Pammi VA, Krauskopf B, Broderick NGR, Barbay S. Pulse-timing symmetry breaking in an excitable optical system with delay. Phys Rev E 2021; 103:012210. [PMID: 33601571 DOI: 10.1103/physreve.103.012210] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 11/10/2020] [Indexed: 06/12/2023]
Abstract
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.
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Affiliation(s)
- Soizic Terrien
- The Dodd-Walls Centre for Photonic and Quantum Technologies, The University of Auckland, New Zealand
| | - Venkata A Pammi
- Université Paris-Saclay, Centre National de la Recherche Scientifique, Centre de Nanosciences et de Nanotechnologies, Palaiseau, France
| | - Bernd Krauskopf
- The Dodd-Walls Centre for Photonic and Quantum Technologies, The University of Auckland, New Zealand
| | - Neil G R Broderick
- The Dodd-Walls Centre for Photonic and Quantum Technologies, The University of Auckland, New Zealand
| | - Sylvain Barbay
- Université Paris-Saclay, Centre National de la Recherche Scientifique, Centre de Nanosciences et de Nanotechnologies, Palaiseau, France
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13
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Marino F, Giacomelli G. Spatiotemporal representation of long-delayed systems: An alternative approach. Phys Rev E 2020; 102:052217. [PMID: 33327079 DOI: 10.1103/physreve.102.052217] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Accepted: 11/03/2020] [Indexed: 11/07/2022]
Abstract
Dynamical systems with long-delay feedback can exhibit complicated temporal phenomena, which once reorganized in a two-dimensional space are reminiscent of spatiotemporal behavior. In this framework, a normal forms description has been developed to reproduce the dynamics, and the opportunity to treat the corresponding variables as true space and time has since been established. However, recently, an alternative approach has been proposed [F. Marino and G. Giacomelli, Phys. Rev. E 98, 060201(R) (2018)2470-004510.1103/PhysRevE.98.060201] with a different interpretation of the variables involved, which better takes into account their physical character and allows for an easier determination of the normal forms. In this paper, we extend such idea and apply it to a number of paradigmatic examples, paving the way to a rethinking of the concept of spatiotemporal representation of long-delayed systems.
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Affiliation(s)
- Francesco Marino
- CNR - Istituto Nazionale di Ottica, largo E. Fermi 6, I-50125 Firenze, Italy
| | - Giovanni Giacomelli
- CNR - Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
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14
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Garbin B, Javaloyes J, Tissoni G, Barland S. Hopping and emergent dynamics of optical localized states in a trapping potential. CHAOS (WOODBURY, N.Y.) 2020; 30:093126. [PMID: 33003904 DOI: 10.1063/5.0006130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2020] [Accepted: 08/30/2020] [Indexed: 06/11/2023]
Abstract
The position and motion of localized states of light in propagative geometries can be controlled via an adequate parameter modulation. Here, we show theoretically and experimentally that this process can be accurately described as the phase locking of oscillators to an external forcing and that non-reciprocal interactions between light bits can drastically modify this picture. Interactions lead to the convective motion of defects and to an unlocking as a collective emerging phenomenon.
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Affiliation(s)
- B Garbin
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France
| | - J Javaloyes
- Departament de Física and IAC-3, Universitat de les Illes Balears, C/ Valldemossa km 7.5, 07122 Mallorca, Spain
| | - G Tissoni
- Institut de Physique de Nice, Université Côte d'Azur, CNRS, F-06560 Valbonne, France
| | - S Barland
- Institut de Physique de Nice, Université Côte d'Azur, CNRS, F-06560 Valbonne, France
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15
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Munsberg L, Javaloyes J, Gurevich SV. Topological localized states in the time delayed Adler model: Bifurcation analysis and interaction law. CHAOS (WOODBURY, N.Y.) 2020; 30:063137. [PMID: 32611116 DOI: 10.1063/5.0002015] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Accepted: 05/28/2020] [Indexed: 06/11/2023]
Abstract
The time-delayed Adler equation is the simplest model for an injected semiconductor laser with coherent injection and optical feedback. It is, however, able to reproduce the existence of topological localized structures (LSs) and their rich interactions. In this paper, we perform the first extended bifurcation analysis of this model and we explore the mechanisms by which LSs emerge. We also derive the effective equations governing the motion of distant LSs and we stress how the lack of parity in time-delayed systems leads to exotic, non-reciprocal, interactions between topological localized states.
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Affiliation(s)
- L Munsberg
- Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, D-48149 Münster, Germany
| | - J Javaloyes
- Departament de Fìsica & IAC-3, Universitat de les Illes Balears, C/ Valldemossa km 7.5, 07122 Mallorca, Spain
| | - S V Gurevich
- Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, D-48149 Münster, Germany
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16
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Dolcemascolo A, Miazek A, Veltz R, Marino F, Barland S. Effective low-dimensional dynamics of a mean-field coupled network of slow-fast spiking lasers. Phys Rev E 2020; 101:052208. [PMID: 32575292 DOI: 10.1103/physreve.101.052208] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2019] [Accepted: 04/05/2020] [Indexed: 06/11/2023]
Abstract
Low-dimensional dynamics of large networks is the focus of many theoretical works, but controlled laboratory experiments are comparatively very few. Here, we discuss experimental observations on a mean-field coupled network of hundreds of semiconductor lasers, which collectively display effectively low-dimensional mixed mode oscillations and chaotic spiking typical of slow-fast systems. We demonstrate that such a reduced dimensionality originates from the slow-fast nature of the system and of the existence of a critical manifold of the network where most of the dynamics takes place. Experimental measurement of the bifurcation parameter for different network sizes corroborates the theory.
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Affiliation(s)
- A Dolcemascolo
- Université Côte d'Azur, CNRS, INPHYNI, 1361 Route des Lucioles, 06560 Valbonne, France
| | - A Miazek
- Université Côte d'Azur, CNRS, INPHYNI, 1361 Route des Lucioles, 06560 Valbonne, France
| | - R Veltz
- Inria Sophia Antipolis, MathNeuro Team, 2004 Route des Lucioles - BP93, 06902 Sophia Antipolis, France
| | - F Marino
- CNR-Istituto Nazionale di Ottica and INFN, Sez. di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy
| | - S Barland
- Université Côte d'Azur, CNRS, INPHYNI, 1361 Route des Lucioles, 06560 Valbonne, France
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17
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Robertson J, Hejda M, Bueno J, Hurtado A. Ultrafast optical integration and pattern classification for neuromorphic photonics based on spiking VCSEL neurons. Sci Rep 2020; 10:6098. [PMID: 32269249 PMCID: PMC7142074 DOI: 10.1038/s41598-020-62945-5] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2020] [Accepted: 03/19/2020] [Indexed: 11/24/2022] Open
Abstract
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.
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Affiliation(s)
- Joshua Robertson
- Institute of Photonics, University of Strathclyde, 99 George St, Glasgow, G11RD, United Kingdom
| | - Matěj Hejda
- Institute of Photonics, University of Strathclyde, 99 George St, Glasgow, G11RD, United Kingdom
| | - Julián Bueno
- Institute of Photonics, University of Strathclyde, 99 George St, Glasgow, G11RD, United Kingdom
| | - Antonio Hurtado
- Institute of Photonics, University of Strathclyde, 99 George St, Glasgow, G11RD, United Kingdom.
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18
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Song ZW, Xiang SY, Ren ZX, Wang SH, Wen AJ, Hao Y. Photonic spiking neural network based on excitable VCSELs-SA for sound azimuth detection. OPTICS EXPRESS 2020; 28:1561-1573. [PMID: 32121864 DOI: 10.1364/oe.381229] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2019] [Accepted: 12/30/2019] [Indexed: 06/10/2023]
Abstract
We propose a photonic spiking neural network (SNN) based on excitable vertical-cavity surface-emitting lasers with an embedded saturable absorber (VCSELs-SA) for emulating the sound azimuth detection function of the brain for the first time. Here, the spike encoding and response properties based on the excitability of VCSELs-SA are employed, and the difference between spike timings of two postsynaptic neurons serves as an indication of sound azimuth. Furthermore, the weight matrix contributing to the successful sound azimuth detection is carefully identified, and the effect of the time interval between two presynaptic spikes is considered. It is found that the weight range that can achieve sound azimuth detection decreases gradually with the increase of the time interval between the sound arriving at the left and right ears. Besides, the effective detection range of the time interval between two presynaptic spikes is also identified, which is similar to that of the biological auditory system, but with a much higher resolution which is at the nanosecond time scale. We further discuss the effect of device variations on the photonic sound azimuth detection. Hence, this photonic SNN is biologically plausible, which has comparable low energy consumption and higher resolution compared with the biological system. This work is valuable for brain-inspired information processing and a promising foundation for more complex spiking information processing implemented by photonic neuromorphic computing systems.
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19
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Zhu J, Liu Y, Yu X, Zhou R, Jin JM, Goddard LL. Sensing Sub-10 nm Wide Perturbations in Background Nanopatterns Using Optical Pseudoelectrodynamics Microscopy (OPEM). NANO LETTERS 2019; 19:5347-5355. [PMID: 31283882 DOI: 10.1021/acs.nanolett.9b01806] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Using light as a probe to investigate perturbations with deep subwavelength dimensions in large-scale wafers is challenging because of the diffraction limit and the weak Rayleigh scattering. In this Letter, we report on a nondestructive noninterference far-field imaging method, which is built upon electrodynamic principles (mechanical work and force) of the light-matter interaction, rather than the intrinsic properties of light. We demonstrate sensing of nanoscale perturbations with sub-10 nm features in semiconductor nanopatterns. This framework is implemented using a visible-light bright-field microscope with a broadband source and a through-focus scanning apparatus. This work creates a new paradigm for exploring light-matter interactions at the nanoscale using microscopy that can potentially be extended to many other problems, for example, bioimaging, material analysis, and nanometrology.
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Affiliation(s)
- Jinlong Zhu
- Photonic Systems Laboratory, Department of Electrical and Computer Engineering , University of Illinois at Urbana-Champaign , Urbana , Illinois 61801 , United States
| | - Yanan Liu
- Center for Computational Electromagnetics, Department of Electrical and Computer Engineering , University of Illinois at Urbana-Champaign , Urbana , Illinois 61801-2991 , United States
| | - Xin Yu
- Photonic Systems Laboratory, Department of Electrical and Computer Engineering , University of Illinois at Urbana-Champaign , Urbana , Illinois 61801 , United States
| | - Renjie Zhou
- Photonic Systems Laboratory, Department of Electrical and Computer Engineering , University of Illinois at Urbana-Champaign , Urbana , Illinois 61801 , United States
- Department of Biomedical Engineering , The Chinese University of Hong Kong , Shatin, New Territories , Hong Kong , China
| | - Jian-Ming Jin
- Center for Computational Electromagnetics, Department of Electrical and Computer Engineering , University of Illinois at Urbana-Champaign , Urbana , Illinois 61801-2991 , United States
| | - Lynford L Goddard
- Photonic Systems Laboratory, Department of Electrical and Computer Engineering , University of Illinois at Urbana-Champaign , Urbana , Illinois 61801 , United States
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20
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Penkovsky B, Porte X, Jacquot M, Larger L, Brunner D. Coupled Nonlinear Delay Systems as Deep Convolutional Neural Networks. PHYSICAL REVIEW LETTERS 2019; 123:054101. [PMID: 31491321 DOI: 10.1103/physrevlett.123.054101] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2019] [Revised: 06/20/2019] [Indexed: 06/10/2023]
Abstract
Neural networks are transforming the field of computer algorithms, yet their emulation on current computing substrates is highly inefficient. Reservoir computing was successfully implemented on a large variety of substrates and gave new insight in overcoming this implementation bottleneck. Despite its success, the approach lags behind the state of the art in deep learning. We therefore extend time-delay reservoirs to deep networks and demonstrate that these conceptually correspond to deep convolutional neural networks. Convolution is intrinsically realized on a substrate level by generic drive-response properties of dynamical systems. The resulting novelty is avoiding vector matrix products between layers, which cause low efficiency in today's substrates. Compared to singleton time-delay reservoirs, our deep network achieves accuracy improvements by at least an order of magnitude in Mackey-Glass and Lorenz time series prediction.
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Affiliation(s)
- Bogdan Penkovsky
- FEMTO-ST/Optics Dept., UMR CNRS 6174, Université Bourgogne Franche-Comté, 15B avenue des Montboucons, 25030 Besançon Cedex, France
| | - Xavier Porte
- FEMTO-ST/Optics Dept., UMR CNRS 6174, Université Bourgogne Franche-Comté, 15B avenue des Montboucons, 25030 Besançon Cedex, France
| | - Maxime Jacquot
- FEMTO-ST/Optics Dept., UMR CNRS 6174, Université Bourgogne Franche-Comté, 15B avenue des Montboucons, 25030 Besançon Cedex, France
| | - Laurent Larger
- FEMTO-ST/Optics Dept., UMR CNRS 6174, Université Bourgogne Franche-Comté, 15B avenue des Montboucons, 25030 Besançon Cedex, France
| | - Daniel Brunner
- FEMTO-ST/Optics Dept., UMR CNRS 6174, Université Bourgogne Franche-Comté, 15B avenue des Montboucons, 25030 Besançon Cedex, France
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21
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Yanchuk S, Ruschel S, Sieber J, Wolfrum M. Temporal Dissipative Solitons in Time-Delay Feedback Systems. PHYSICAL REVIEW LETTERS 2019; 123:053901. [PMID: 31491298 DOI: 10.1103/physrevlett.123.053901] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2019] [Revised: 06/12/2019] [Indexed: 06/10/2023]
Abstract
Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, autosolitons, and spot or pulse solutions, these states play an important role in data transmission using optical pulses, neural signal propagation, and other processes. While this phenomenon was thoroughly studied in spatially extended systems, temporally localized states are gaining attention only recently, driven primarily by applications from fiber or semiconductor lasers. Here we present a theory for temporal dissipative solitons (TDS) in systems with time-delayed feedback. In particular, we derive a system with an advanced argument, which determines the profile of the TDS. We also provide a complete classification of the spectrum of TDS into interface and pseudocontinuous spectrum. We illustrate our theory with two examples: a generic delayed phase oscillator, which is a reduced model for an injected laser with feedback, and the FitzHugh-Nagumo neuron with delayed feedback. Finally, we discuss possible destabilization mechanisms of TDS and show an example where the TDS delocalizes and its pseudocontinuous spectrum develops a modulational instability.
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Affiliation(s)
- Serhiy Yanchuk
- Institute of Mathematics, Technical University of Berlin, Strasse des 17 Juni 136, 10623 Berlin, Germany
| | - Stefan Ruschel
- Institute of Mathematics, Technical University of Berlin, Strasse des 17 Juni 136, 10623 Berlin, Germany
| | - Jan Sieber
- Harrison Building, North Park Road, CEMPS University of Exeter, Exeter EX44QF, United Kingdom
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22
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Marino F, Giacomelli G. Excitable Wave Patterns in Temporal Systems with Two Long Delays and their Observation in a Semiconductor Laser Experiment. PHYSICAL REVIEW LETTERS 2019; 122:174102. [PMID: 31107096 DOI: 10.1103/physrevlett.122.174102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2018] [Indexed: 06/09/2023]
Abstract
Excitable waves arise in many spatially extended systems of either a biological, chemical, or physical nature due to the interplay between local reaction and diffusion processes. Here we demonstrate that similar phenomena are encoded in the time dynamics of an excitable system with two, hierarchically long delays. The transition from 1D localized structures to curved wave segments is experimentally observed in an excitable semiconductor laser with two feedback loops and reproduced by numerical simulations of a prototypical model. While closely related to those found in 2D excitable media, wave patterns in delayed systems exhibit unobserved features originating from causality related constraints. An appropriate dynamical representation of the data uncovers these phenomena and permits us to interpret them as the result of an effective 2D advection-reaction-diffusion process.
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Affiliation(s)
- Francesco Marino
- CNR-Istituto Nazionale di Ottica, largo E. Fermi 6, I-50125 Firenze, Italy
| | - Giovanni Giacomelli
- CNR-Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
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23
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Tait AN, Jayatilleka H, De Lima TF, Ma PY, Nahmias MA, Shastri BJ, Shekhar S, Chrostowski L, Prucnal PR. Feedback control for microring weight banks. OPTICS EXPRESS 2018; 26:26422-26443. [PMID: 30469730 DOI: 10.1364/oe.26.026422] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2018] [Accepted: 07/22/2018] [Indexed: 06/09/2023]
Abstract
Microring weight banks present novel opportunities for reconfigurable, high-performance analog signal processing in photonics. Controlling microring filter response is a challenge due to fabrication variations and thermal sensitivity. Prior work showed continuous weight control of multiple wavelength-division multiplexed signals in a bank of microrings based on calibration and feedforward control. Other prior work has shown resonance locking based on feedback control by monitoring photoabsorption-induced changes in resistance across in-ring photoconductive heaters. In this work, we demonstrate continuous, multi-channel control of a microring weight bank with an effective 5.1 bits of accuracy on 2Gbps signals. Unlike resonance locking, the approach relies on an estimate of filter transmission versus photo-induced resistance changes. We introduce an estimate still capable of providing 4.2 bits of accuracy without any direct transmission measurements. Furthermore, we present a detailed characterization of this response for different values of carrier wavelength offset and power. Feedback weight control renders tractable the weight control problem in reconfigurable analog photonic networks.
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24
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Semenov VV, Maistrenko YL. Dissipative solitons for bistable delayed-feedback systems. CHAOS (WOODBURY, N.Y.) 2018; 28:101103. [PMID: 30384630 DOI: 10.1063/1.5062268] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2018] [Accepted: 10/06/2018] [Indexed: 06/08/2023]
Abstract
We study how nonlinear delayed-feedback in the Ikeda model can induce solitary impulses, i.e., dissipative solitons. The states are clearly identified in a virtual space-time representation of the equations with delay, and we find that conditions for their appearance are bistability of a nonlinear function and negative character of the delayed feedback. Both dark and bright solitons are identified in numerical simulations and physical electronic experiment, showing an excellent qualitative correspondence and proving thereby the robustness of the phenomenon. Along with single spiking solitons, a variety of compound soliton-based structures is obtained in a wide parameter region on the route from the regular dynamics (two quiescent states) to developed spatiotemporal chaos. The number of coexisting soliton-based states is fast growing with delay, which can open new perspectives in the context of information storage.
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Affiliation(s)
- Vladimir V Semenov
- Department of Physics, Saratov State University, Astrakhanskaya str. 83, 410012 Saratov, Russia
| | - Yuri L Maistrenko
- Institute of Mathematics and Centre for Medical and Biotechnical Research, NAS of Ukraine, Tereshchenkivska St. 3, 01030 Kyiv, Ukraine
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25
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Brunner D, Penkovsky B, Levchenko R, Schöll E, Larger L, Maistrenko Y. Two-dimensional spatiotemporal complexity in dual-delayed nonlinear feedback systems: Chimeras and dissipative solitons. CHAOS (WOODBURY, N.Y.) 2018; 28:103106. [PMID: 30384622 DOI: 10.1063/1.5043391] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2018] [Accepted: 09/13/2018] [Indexed: 06/08/2023]
Abstract
We demonstrate for a photonic nonlinear system that two highly asymmetric feedback delays can induce a variety of emergent patterns which are highly robust during the system's global evolution. Explicitly, two-dimensional chimeras and dissipative solitons become visible upon a space-time transformation. Switching between chimeras and dissipative solitons requires only adjusting two system parameters, demonstrating self-organization exclusively based on the system's dynamical properties. Experiments were performed using a tunable semiconductor laser's transmission through a Fabry-Pérot resonator resulting in an Airy function as nonlinearity. Resulting dynamics were bandpass filtered and propagated along two feedback paths whose time delays differ by two orders of magnitude. An excellent agreement between experimental results and the theoretical model given by modified Ikeda equations was achieved.
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Affiliation(s)
- D Brunner
- FEMTO-ST Institute/Optics Department, CNRS & University Bourgogne Franche-Comté, 15B avenue des Montboucons, 25030 Besançon Cedex, France
| | - B Penkovsky
- FEMTO-ST Institute/Optics Department, CNRS & University Bourgogne Franche-Comté, 15B avenue des Montboucons, 25030 Besançon Cedex, France
| | - R Levchenko
- Taras Shevchenko National University of Kyiv, Volodymyrska St. 60, 01030 Kyiv, Ukraine
| | - E Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - L Larger
- FEMTO-ST Institute/Optics Department, CNRS & University Bourgogne Franche-Comté, 15B avenue des Montboucons, 25030 Besançon Cedex, France
| | - Y Maistrenko
- FEMTO-ST Institute/Optics Department, CNRS & University Bourgogne Franche-Comté, 15B avenue des Montboucons, 25030 Besançon Cedex, France
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26
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Ma PY, Shastri BJ, Ferreira de Lima T, Huang C, Tait AN, Nahmias MA, Peng HT, Prucnal PR. Simultaneous excitatory and inhibitory dynamics in an excitable laser. OPTICS LETTERS 2018; 43:3802-3805. [PMID: 30067683 DOI: 10.1364/ol.43.003802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2018] [Accepted: 07/11/2018] [Indexed: 06/08/2023]
Abstract
Neocortical systems encode information in electrochemical spike timings, not just mean firing rates. Learning and memory in networks of spiking neurons is achieved by the precise timing of action potentials that induces synaptic strengthening (with excitation) or weakening (with inhibition). Inhibition should be incorporated into brain-inspired spike processing in the optical domain to enhance its information-processing capability. We demonstrate the simultaneous excitatory and inhibitory dynamics in an excitable (i.e., a pulsed) laser neuron, both numerically and experimentally. We investigate the bias strength effect, inhibitory strength effect, and excitatory and inhibitory input timing effect, based on the simulation platform of an integrated graphene excitable laser. We further corroborate these analyses with proof-of-principle experiments utilizing a fiber-based graphene excitable laser, where we introduce inhibition by directly modulating the gain of the laser. This technology may potentially open novel spike-processing functionality for future neuromorphic photonic systems.
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27
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Terrien S, Krauskopf B, Broderick NGR, Braive R, Beaudoin G, Sagnes I, Barbay S. Pulse train interaction and control in a microcavity laser with delayed optical feedback. OPTICS LETTERS 2018; 43:3013-3016. [PMID: 29957769 DOI: 10.1364/ol.43.003013] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2018] [Accepted: 05/15/2018] [Indexed: 06/08/2023]
Abstract
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.
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28
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Erneux T, Barbay S. Two distinct excitable responses for a laser with a saturable absorber. Phys Rev E 2018; 97:062214. [PMID: 30011474 DOI: 10.1103/physreve.97.062214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Indexed: 06/08/2023]
Abstract
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.
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Affiliation(s)
- Thomas Erneux
- Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Campus Plaine, CP 231, 1050 Bruxelles, Belgium
| | - Sylvain Barbay
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Université Paris-Saclay, site de Marcoussis, 91460 Marcoussis, France
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29
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Sub-threshold signal encoding in coupled FitzHugh-Nagumo neurons. Sci Rep 2018; 8:8276. [PMID: 29844354 PMCID: PMC5974132 DOI: 10.1038/s41598-018-26618-8] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Accepted: 05/15/2018] [Indexed: 11/09/2022] Open
Abstract
Despite intensive research, the mechanisms underlying the neural code remain poorly understood. Recent work has focused on the response of a single neuron to a weak, sub-threshold periodic signal. By simulating the stochastic FitzHugh-Nagumo (FHN) model and then using a symbolic method to analyze the firing activity, preferred and infrequent spike patterns (defined by the relative timing of the spikes) were detected, whose probabilities encode information about the signal. As not individual neurons but neuronal populations are responsible for sensory coding and information transfer, a relevant question is how a second neuron, which does not perceive the signal, affects the detection and the encoding of the signal, done by the first neuron. Through simulations of two stochastic FHN neurons we show that the encoding of a sub-threshold signal in symbolic spike patterns is a plausible mechanism. The neuron that perceives the signal fires a spike train that, despite having an almost random temporal structure, has preferred and infrequent patterns which carry information about the signal. Our findings could be relevant for sensory systems composed by two noisy neurons, when only one detects a weak external input.
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30
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Garbin B, Javaloyes J, Barland S, Tissoni G. Interactions and collisions of topological solitons in a semiconductor laser with optical injection and feedback. CHAOS (WOODBURY, N.Y.) 2017; 27:114308. [PMID: 29195338 DOI: 10.1063/1.5006751] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
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.
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Affiliation(s)
- B Garbin
- The Dodd-Walls Centre for Photonic and Quantum Technologies, and Physics Department, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - J Javaloyes
- Departament de Física, Universitat de les Illes Balears, Cra. De Valldemossa, km 7.5, E-07122 Palma, Spain
| | - S Barland
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, 1361 Route des Lucioles, 06560 Valbonne, France
| | - G Tissoni
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, 1361 Route des Lucioles, 06560 Valbonne, France
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31
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Romeira B, Figueiredo JML, Javaloyes J. Delay dynamics of neuromorphic optoelectronic nanoscale resonators: Perspectives and applications. CHAOS (WOODBURY, N.Y.) 2017; 27:114323. [PMID: 29195310 DOI: 10.1063/1.5008888] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
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.
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Affiliation(s)
- Bruno Romeira
- Centro de Electrónica, Optoelectrónica e Telecomunicações (CEOT), Departmento de Física, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal
| | - José M L Figueiredo
- Centro de Electrónica, Optoelectrónica e Telecomunicações (CEOT), Departmento de Física, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal
| | - Julien Javaloyes
- Departament de Física, Universitat de les Illes Balears, C/Valldemossa km 7.5, 07122 Palma de Mallorca, Spain
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Marino F, Giacomelli G. Pseudo-spatial coherence resonance in an excitable laser with long delayed feedback. CHAOS (WOODBURY, N.Y.) 2017; 27:114302. [PMID: 29195300 DOI: 10.1063/1.5006744] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The effect of noise in an excitable semiconductor laser with feedback is studied in the framework of the spatio-temporal representation of long delayed systems. Propagation, noise-induced creation, and destruction of excitable pulses in the pseudo time are observed. The addition of a variable quantity of noise leads to the occurrence of a phenomenon that we term "pseudo-spatial coherence resonance." A phenomenological model well describes the system and allows for a comparison with the experimental observations. A simple Monte Carlo approach is also introduced and permits to explain the features observed in terms of the key dynamical ingredients of the physical system.
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Affiliation(s)
- Francesco Marino
- CNR - Istituto Nazionale di Ottica, largo E. Fermi 6, I-50125 Firenze, Italy
| | - Giovanni Giacomelli
- CNR - Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
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Abstract
Neurons communicate by brief bursts of spikes separated by silent phases and information may be encoded into the burst duration or through the structure of the interspike intervals. Inspired by the importance of bursting activities in neuronal computation, we have investigated the bursting oscillations of an optically injected quantum dot laser. We find experimentally that the laser periodically switches between two distinct operating states with distinct optical frequencies exhibiting either fast oscillatory or nearly steady state evolutions (two-color bursting oscillations). The conditions for their emergence and their control are analyzed by systematic simulations of the laser rate equations. By projecting the bursting solution onto the bifurcation diagram of a fast subsystem, we show how a specific hysteresis phenomenon explains the transitions between active and silent phases. Since size-controlled bursts can contain more information content than single spikes our results open the way to new forms of neuron inspired optical communication.
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Neuromorphic photonic networks using silicon photonic weight banks. Sci Rep 2017; 7:7430. [PMID: 28784997 PMCID: PMC5547135 DOI: 10.1038/s41598-017-07754-z] [Citation(s) in RCA: 120] [Impact Index Per Article: 17.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2017] [Accepted: 06/29/2017] [Indexed: 12/03/2022] Open
Abstract
Photonic systems for high-performance information processing have attracted renewed interest. Neuromorphic silicon photonics has the potential to integrate processing functions that vastly exceed the capabilities of electronics. We report first observations of a recurrent silicon photonic neural network, in which connections are configured by microring weight banks. A mathematical isomorphism between the silicon photonic circuit and a continuous neural network model is demonstrated through dynamical bifurcation analysis. Exploiting this isomorphism, a simulated 24-node silicon photonic neural network is programmed using “neural compiler” to solve a differential system emulation task. A 294-fold acceleration against a conventional benchmark is predicted. We also propose and derive power consumption analysis for modulator-class neurons that, as opposed to laser-class neurons, are compatible with silicon photonic platforms. At increased scale, Neuromorphic silicon photonics could access new regimes of ultrafast information processing for radio, control, and scientific computing.
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Javaloyes J, Marconi M, Giudici M. Nonlocality Induces Chains of Nested Dissipative Solitons. PHYSICAL REVIEW LETTERS 2017; 119:033904. [PMID: 28777628 DOI: 10.1103/physrevlett.119.033904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2016] [Indexed: 06/07/2023]
Abstract
Dissipative solitons often behave as quasiparticles, and they may form molecules characterized by well-defined bond distances. We show that pointwise nonlocality may lead to a new kind of molecule where bonds are not rigid. The elements of this molecule can shift mutually one with respect to the others while remaining linked together, in a manner similar to interlaced rings in a chain. We report experimental observations of these chains of nested dissipative solitons in a time-delayed laser system.
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Affiliation(s)
- J Javaloyes
- Departament de Física, Universitat de les Illes Baleares, C/Valldemossa km 7.5, 07122 Mallorca, Spain
| | - M Marconi
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, F-06560 Valbonne, France
| | - M Giudici
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, F-06560 Valbonne, France
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Marino F, Giacomelli G, Barland S. Splitting in the pinning-depinning transition of fronts in long-delayed bistable systems. Phys Rev E 2017; 95:052204. [PMID: 28618609 DOI: 10.1103/physreve.95.052204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2017] [Indexed: 06/07/2023]
Abstract
We investigate the formation of localized domains through front pinning in a periodically forced, bistable semiconductor laser with long-delayed optoelectronic feedback. At difference with 1D spatially extended systems, the transition from the pinning to the propagation regime occurs via two separated bifurcations, each corresponding to the unpinning of one of the fronts surrounding the localized domain. The bifurcation splitting is systematically explored, unveiling the crucial role played by the forcing frequency. The experimental results are reproduced and interpreted by means of a prototypical model of our system.
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Affiliation(s)
- Francesco Marino
- CNR-Istituto Nazionale di Ottica, largo E. Fermi 6, I-50125 Firenze, Italy
| | - Giovanni Giacomelli
- CNR-Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
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Robertson J, Deng T, Javaloyes J, Hurtado A. Controlled inhibition of spiking dynamics in VCSELs for neuromorphic photonics: theory and experiments. OPTICS LETTERS 2017; 42:1560-1563. [PMID: 28409798 DOI: 10.1364/ol.42.001560] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
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.
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