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Numerical Demonstration of the Transmission of Low Frequency Fluctuation Dynamics Generated by a Semiconductor Laser with Optical Feedback. PHOTONICS 2022. [DOI: 10.3390/photonics9070483] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this paper, the transmission mechanism of the spike information embedded in the low frequency fluctuation (LFF) dynamic in a cascaded laser system is numerically demonstrated. In the cascaded laser system, the LFF waveform is first generated by a drive laser with optical feedback and is then injected into a response laser. The range of crucial system parameters that can make the response laser generate the LFF dynamic is studied, and the effect of parameter mismatch on the transmission of LFF dynamics is explored through a method of symbolic time-series analysis and the index, such as the spike rate and the cross-correlation coefficient. The results show that the mismatch of the pump current has a more significant influence on the transmission of LFF waveforms than that of the internal physical parameter of the laser, such as the linewidth enhancement factor. Moreover, increasing the injection strength can enhance the robustness of LFF transmission. As spikes of the LFF dynamic generated by lasers with optical feedback is similar to the spike of neurons, the results of this paper can help understanding the information transporting and processing inside the photonic neurons.
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2
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Tiana-Alsina J, Masoller C. Time crystal dynamics in a weakly modulated stochastic time delayed system. Sci Rep 2022; 12:4914. [PMID: 35318359 PMCID: PMC8940923 DOI: 10.1038/s41598-022-08776-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Accepted: 02/22/2022] [Indexed: 11/20/2022] Open
Abstract
Time crystal oscillations in interacting, periodically driven many-particle systems are highly regular oscillations that persist for long periods of time, are robust to perturbations, and whose frequency differs from the frequency of the driving signal. Making use of underlying similarities of spatially-extended systems and time-delayed systems (TDSs), we present an experimental demonstration of time-crystal-like behavior in a stochastic, weakly modulated TDS. We consider a semiconductor laser near threshold with delayed feedback, whose output intensity shows abrupt spikes at irregular times. When the laser current is driven with a small-amplitude periodic signal we show that the interaction of delayed feedback and modulation can generate long-range regularity in the timing of the spikes, which lock to the modulation and, despite the presence of noise, remain in phase over thousands of modulation cycles. With pulsed modulation we find harmonic and subharmonic locking, while with sinusoidal modulation, we find only subharmonic locking, which is a characteristic feature of time-crystal behavior.
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Affiliation(s)
- Jordi Tiana-Alsina
- Department de Física Aplicada, Facultat de Fisica, Universitat de Barcelona, Marti i Franques 1, 08028, Barcelona, Spain
| | - Cristina Masoller
- Departament de Fisica, Universitat Politecnica de Catalunya, Rambla Sant Nebridi 22, 08222, Terrassa, Barcelona, Spain.
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3
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Tiana-Alsina J, Masoller C. Dynamics of a semiconductor laser with feedback and modulation: experiments and model comparison. OPTICS EXPRESS 2022; 30:9441-9449. [PMID: 35299371 DOI: 10.1364/oe.451983] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Accepted: 02/04/2022] [Indexed: 06/14/2023]
Abstract
We study experimentally and numerically the dynamics of a semiconductor laser near threshold, subject to optical feedback and sinusoidal current modulation. The laser operates in the low frequency fluctuation (LFF) regime where, without modulation, the intensity shows sudden spikes at irregular times. Under particular modulation conditions the spikes lock to the modulation and their timing becomes highly regular. While the modulated LFF dynamics has received a lot of attention, an in-depth comparison with the predictions of the Lang-Kobayashi (LK) model has not yet been performed. Here we use the LK model to simulate the laser dynamics and use the Fano factor to quantify the regularity of the timing of the spikes. The Fano factor is calculated by counting the number of spikes in successive segments of the intensity time-series and keeps information about temporal order in the spike sequence that is lost when the analysis is based on the distribution of inter-spike intervals. Here we compare the spike timing regularity in experimental and in simulated spike sequences as a function of the modulation amplitude and frequency and find a good qualitative agreement. We find that in both experiments and simulation for appropriate conditions the spike timing can be highly regular, as revealed by very small values of the Fano factor.
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Experimental and Numerical Study of Locking of Low-Frequency Fluctuations of a Semiconductor Laser with Optical Feedback. PHOTONICS 2022. [DOI: 10.3390/photonics9020103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
We study the output of a semiconductor laser with optical feedback operated in the low-frequency fluctuations (LFFs) regime and subject to weak sinusoidal current modulation. In the LFF regime, the laser intensity exhibits abrupt drops, after which it recovers gradually. Without modulation, the drops occur at irregular times, while, with weak modulation, they can lock to the external modulation and they can occur, depending on the parameters, every two or every three modulation cycles. Here, we characterize experimentally the locking regions and use the well-known Lang–Kobayashi model to simulate the intensity dynamics. We analyze the effects of several parameters and find that the simulations are in good qualitative agreement with the experimental observations.
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Locking Phenomena in Semiconductor Lasers near Threshold with Optical Feedback and Sinusoidal Current Modulation. APPLIED SCIENCES-BASEL 2021. [DOI: 10.3390/app11177871] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The dynamics of semiconductor lasers with optical feedback and current modulation has been extensively studied, and it is, by now, well known that the interplay of modulation and feedback can produce a rich variety of nonlinear phenomena. Near threshold, in the so-called low frequency fluctuations regime, the intensity emitted by the laser, without modulation, exhibits feedback-induced spikes, which occur at irregular times. When the laser current is sinusoidally modulated, under appropriate conditions, the spikes lock to the modulation and become periodic. In previous works, we studied experimentally the locked behavior and found sub-harmonic locking (regular spike timing such that a spike is emitted every two or three modulation cycles), but we did not find spikes with regular timing, emitted every modulation cycle. To understand why 1:1 regular locking was not observed, here, we perform simulations of the well-known Lang–Kobayashi model. We find a good qualitative agreement with the experiments: with small modulation amplitudes, we find wide parameter regions in which the spikes are sub-harmonically locked to the modulation, while 1:1 locking occurs at much higher modulation amplitudes.
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Dillane M, Lingnau B, Viktorov EA, Dubinkin I, Fedorov N, Kelleher B. Asymmetric excitable phase triggering in an optically injected semiconductor laser. OPTICS LETTERS 2021; 46:440-443. [PMID: 33449048 DOI: 10.1364/ol.410085] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2020] [Accepted: 11/24/2020] [Indexed: 06/12/2023]
Abstract
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.
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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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Ryan P, Keane A, Amann A. Border-collision bifurcations in a driven time-delay system. CHAOS (WOODBURY, N.Y.) 2020; 30:023121. [PMID: 32113218 DOI: 10.1063/1.5119982] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2019] [Accepted: 01/23/2020] [Indexed: 06/10/2023]
Abstract
We show that a simple piecewise-linear system with time delay and periodic forcing gives rise to a rich bifurcation structure of torus bifurcations and Arnold tongues, as well as multistability across a significant portion of the parameter space. The simplicity of our model enables us to study the dynamical features analytically. Specifically, these features are explained in terms of border-collision bifurcations of an associated Poincaré map. Given that time delay and periodic forcing are common ingredients in mathematical models, this analysis provides widely applicable insight.
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Affiliation(s)
- Pierce Ryan
- School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland
| | - Andrew Keane
- School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland
| | - Andreas Amann
- School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland
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Keane A, Krauskopf B, Dijkstra HA. The effect of state dependence in a delay differential equation model for the El Niño Southern Oscillation. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2019; 377:20180121. [PMID: 31329066 PMCID: PMC6661334 DOI: 10.1098/rsta.2018.0121] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 11/15/2018] [Indexed: 05/26/2023]
Abstract
Delay differential equations (DDEs) have been used successfully in the past to model climate systems at a conceptual level. An important aspect of these models is the existence of feedback loops that feature a delay time, usually associated with the time required to transport energy through the atmosphere and/or oceans across the globe. So far, such delays are generally assumed to be constant. Recent studies have demonstrated that even simple DDEs with non-constant delay times, which change depending on the state of the system, can produce surprisingly rich dynamical behaviour. Here, we present arguments for the state dependence of the delay in a DDE model for the El Niño Southern Oscillation phenomenon in the climate system. We then conduct a bifurcation analysis by means of continuation software to investigate the effect of state dependence in the delay on the observed dynamics of the system. More specifically, we show that the underlying delay-induced structure of resonance regions may change considerably in the presence of state dependence. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.
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Affiliation(s)
- Andrew Keane
- Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - Bernd Krauskopf
- Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - Henk A. Dijkstra
- Department of Physics, Center for Complex Systems Studies, Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Utrecht, The Netherlands
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Tiana-Alsina J, Quintero-Quiroz C, Torrent MC, Masoller C. Quantifying the degree of locking in weakly forced stochastic systems. Phys Rev E 2019; 99:022207. [PMID: 30934356 DOI: 10.1103/physreve.99.022207] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2018] [Indexed: 11/07/2022]
Abstract
Controlling an stochastic nonlinear system with a small amplitude signal is a fundamental problem with many practical applications. Quantifying locking is challenging, and current methods, such as spectral or correlation analysis, do not provide a precise measure of the degree of locking. Here we study locking in an experimental system, consisting of a semiconductor laser with optical feedback operated in the regime where it randomly emits abrupt spikes. To quantify the locking of the optical spikes to small electric perturbations, we use two measures, the success rate (SR) and the false positive rate (FPR). The SR counts the spikes that are emitted shortly after each perturbation, while the FPR counts the additional extra spikes. We show that the receiver operating characteristic (ROC) curve (SR versus FPR plot) uncovers parameter regions where the electric perturbations fully control the laser spikes, such that the laser emits, shortly after each perturbation, one and only one spike. To demonstrate the general applicability of the ROC analysis we also study a stochastic bistable system under square-wave forcing and show that the ROC curve allows identifying the parameters that produce best locking.
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Affiliation(s)
- Jordi Tiana-Alsina
- Departament de Física, Universitat Politècnica de Catalunya, Rambla St. Nebridi 2, 08222 Terrassa, Barcelona, Spain
| | - Carlos Quintero-Quiroz
- Departament de Física, Universitat Politècnica de Catalunya, Rambla St. Nebridi 2, 08222 Terrassa, Barcelona, Spain
| | - M C Torrent
- Departament de Física, Universitat Politècnica de Catalunya, Rambla St. Nebridi 2, 08222 Terrassa, Barcelona, Spain
| | - Cristina Masoller
- Departament de Física, Universitat Politècnica de Catalunya, Rambla St. Nebridi 2, 08222 Terrassa, Barcelona, Spain
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11
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Chaotic optical power dropouts driven by low frequency bias forcing in a mid-infrared quantum cascade laser. Sci Rep 2019; 9:4451. [PMID: 30872670 PMCID: PMC6418083 DOI: 10.1038/s41598-019-40861-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2018] [Accepted: 02/23/2019] [Indexed: 11/27/2022] Open
Abstract
Mid-infrared quantum cascade lasers operating under external optical feedback and external periodic bias forcing are shown to exhibit a deterministic chaotic pattern composed of frequencies which are linked to the one of the forcing. Results also show that both the amplitude and the frequency of the forcing play a key role in the number of retrieved spikes per modulation period. These findings are of paramount importance for chaotic operation of quantum cascade lasers in applications such as optical countermeasure systems and secure atmospheric transmission lines, as well as for simulating neuronal systems and the communication between neurons due to sudden bursts.
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12
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Tiana-Alsina J, Quintero-Quiroz C, Panozzo M, Torrent MC, Masoller C. Experimental study of modulation waveforms for entraining the spikes emitted by a semiconductor laser with optical feedback. OPTICS EXPRESS 2018; 26:9298-9309. [PMID: 29715883 DOI: 10.1364/oe.26.009298] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2018] [Accepted: 03/26/2018] [Indexed: 06/08/2023]
Abstract
The entrainment phenomenon, by which an oscillator adjusts its natural rhythm to an external periodic signal, has been observed in many natural systems. Recently, attention has focused on which are the optimal conditions for achieving entrainment. Here we use a semiconductor laser with optical feedback, operating in the low-frequency fluctuations (LFFs) regime, as a testbed for a controlled entrainment experiment. In the LFF regime the laser intensity displays abrupt spikes, which can be entrained to a weak periodic signal that directly modulates the laser pump current. We compare the performance of three modulation waveforms for producing 1:1 locking (one spike is emitted in each modulation cycle), as well as higher order locking regimes. We characterize the parameter regions where high-quality locking occurs, and those where the laser emits spikes which are not entrained to the external signal. The role of the modulation amplitude and frequency, and the role of the dc value of the laser pump current (that controls the natural spike frequency) in the entrainment quality are discussed.
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13
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Quintero-Quiroz C, Tiana-Alsina J, Romà J, Torrent MC, Masoller C. Quantitative identification of dynamical transitions in a semiconductor laser with optical feedback. Sci Rep 2016; 6:37510. [PMID: 27857229 PMCID: PMC5114591 DOI: 10.1038/srep37510] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2016] [Accepted: 10/25/2016] [Indexed: 11/27/2022] Open
Abstract
Identifying transitions to complex dynamical regimes is a fundamental open problem with many practical applications. Semi- conductor lasers with optical feedback are excellent testbeds for studying such transitions, as they can generate a rich variety of output signals. Here we apply three analysis tools to quantify various aspects of the dynamical transitions that occur as the laser pump current increases. These tools allow to quantitatively detect the onset of two different regimes, low-frequency fluctuations and coherence collapse, and can be used for identifying the operating conditions that result in specific dynamical properties of the laser output. These tools can also be valuable for analyzing regime transitions in other complex systems.
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Affiliation(s)
- C. Quintero-Quiroz
- Universitat Politècnica de Catalunya, Departament de Física, Colom 11, 08222 Terrassa, Barcelona, Spain
| | - J. Tiana-Alsina
- Universitat Politècnica de Catalunya, Departament de Física, Colom 11, 08222 Terrassa, Barcelona, Spain
| | - J. Romà
- Universitat Politècnica de Catalunya, Departament de Física, Colom 11, 08222 Terrassa, Barcelona, Spain
| | - M. C. Torrent
- Universitat Politècnica de Catalunya, Departament de Física, Colom 11, 08222 Terrassa, Barcelona, Spain
| | - C. Masoller
- Universitat Politècnica de Catalunya, Departament de Física, Colom 11, 08222 Terrassa, Barcelona, Spain
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Shastri BJ, Nahmias MA, Tait AN, Rodriguez AW, Wu B, Prucnal PR. Spike processing with a graphene excitable laser. Sci Rep 2016; 6:19126. [PMID: 26753897 PMCID: PMC4709573 DOI: 10.1038/srep19126] [Citation(s) in RCA: 103] [Impact Index Per Article: 12.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Accepted: 12/07/2015] [Indexed: 12/22/2022] Open
Abstract
Novel materials and devices in photonics have the potential to revolutionize optical information processing, beyond conventional binary-logic approaches. Laser systems offer a rich repertoire of useful dynamical behaviors, including the excitable dynamics also found in the time-resolved "spiking" of neurons. Spiking reconciles the expressiveness and efficiency of analog processing with the robustness and scalability of digital processing. We demonstrate a unified platform for spike processing with a graphene-coupled laser system. We show that this platform can simultaneously exhibit logic-level restoration, cascadability and input-output isolation--fundamental challenges in optical information processing. We also implement low-level spike-processing tasks that are critical for higher level processing: temporal pattern detection and stable recurrent memory. We study these properties in the context of a fiber laser system and also propose and simulate an analogous integrated device. The addition of graphene leads to a number of advantages which stem from its unique properties, including high absorption and fast carrier relaxation. These could lead to significant speed and efficiency improvements in unconventional laser processing devices, and ongoing research on graphene microfabrication promises compatibility with integrated laser platforms.
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Affiliation(s)
- Bhavin J Shastri
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Mitchell A Nahmias
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Alexander N Tait
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Alejandro W Rodriguez
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Ben Wu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Paul R Prucnal
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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Nahmias MA, Tait AN, Shastri BJ, de Lima TF, Prucnal PR. Excitable laser processing network node in hybrid silicon: analysis and simulation. OPTICS EXPRESS 2015; 23:26800-26813. [PMID: 26480191 DOI: 10.1364/oe.23.026800] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The combination of ultrafast laser dynamics and dense on-chip multiwavelength networking could potentially address new domains of real-time signal processing that require both speed and complexity. We present a physically realistic optoelectronic simulation model of a circuit for dynamical laser neural networks and verify its behavior. We describe the physics, dynamics, and parasitics of one network node, which includes a bank of filters, a photodetector, and excitable laser. This unconventional circuit exhibits both cascadability and fan-in, critical properties for the large-scale networking of information processors based on laser excitability. In addition, it can be instantiated on a photonic integrated circuit platform and requires no off-chip optical I/O. Our proposed processing system could find use in emerging applications, including cognitive radio and low-latency control.
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