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SCIENCE CHINA Information Sciences, Volume 63 , Issue 6 : 160405(2020) https://doi.org/10.1007/s11432-020-2820-y

Real-time optical spike-timing dependent plasticity in a single VCSEL with dual-polarized pulsed optical injection

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  • ReceivedJan 3, 2020
  • AcceptedFeb 27, 2020
  • PublishedMay 9, 2020

Abstract

We propose and numerically realize an optical spike-timing dependent plasticity (STDP) scheme by using a single vertical-cavity surface-emitting laser (VCSEL). In the scheme, the VCSEL is subjected to an orthogonally-polarized continuous-wave optical injection (OPCWOI) and dual-polarized pulsed optical injections (DPPOI). Based on the widely used spin-flip model, the response spiking dynamics of VCSEL is numerically studied, and then the optical STDP in a single VCSEL is explored. The roles of bias current, the strength of OPCWOI and DPPOI, and the frequency detuning on the optical STDP curve are numerically analyzed. It is found that, by simultaneously utilizing the response spiking dynamics in two orthogonal polarization modes, an optical STDP could be achieved by using a single VCSEL. Furthermore, the weight update of STDP curve can be calculated in real-time. Additionally, the STDP curves can also be controlled by adjusting some controllable parameters. The real-time optical STDP based on a single VCSEL is numerically realized for the first time, which paves the way towards fully VCSELs-based photonic neuromorphic systems with low power consumption.


Acknowledgment

This work was supported in part by National Key Research and Development Program of China (Grant No. 2018YFB2200500) and National Natural Science Foundation of China (Grant Nos. 61974177, 61674119).


References

[1] Prucnal P R, Shastri B J, Ferreira de Lima T. Recent progress in semiconductor excitable lasers for photonic spike processing. Adv Opt Photon, 2016, 8: 228-299 CrossRef ADS Google Scholar

[2] Diez-Ardanuy C, Greaves J, Munro K R. A cluster of palmitoylated cysteines are essential for aggregation of cysteine-string protein mutants that cause neuronal ceroid lipofuscinosis. Sci Rep, 2017, 7: 10 CrossRef PubMed ADS Google Scholar

[3] de Lima T F, Peng H T, Tait A N. Machine Learning With Neuromorphic Photonics. J Lightwave Technol, 2019, 37: 1515-1534 CrossRef ADS Google Scholar

[4] Feldmann J, Youngblood N, Wright C D. All-optical spiking neurosynaptic networks with self-learning capabilities. Nature, 2019, 569: 208-214 CrossRef PubMed ADS Google Scholar

[5] Xu S, Wang J, Wang R. High-accuracy optical convolution unit architecture for convolutional neural networks by cascaded acousto-optical modulator arrays. Opt Express, 2019, 27: 19778 CrossRef PubMed ADS Google Scholar

[6] Roy K, Jaiswal A, Panda P. Towards spike-based machine intelligence with neuromorphic computing. Nature, 2019, 575: 607-617 CrossRef PubMed ADS Google Scholar

[7] Xiang S, Zhang Y, Gong J. STDP-Based Unsupervised Spike Pattern Learning in a Photonic Spiking Neural Network With VCSELs and VCSOAs. IEEE J Sel Top Quantum Electron, 2019, 25: 1-9 CrossRef ADS Google Scholar

[8] Robertson J, Wade E, Kopp Y. Toward Neuromorphic Photonic Networks of Ultrafast Spiking Laser Neurons. IEEE J Sel Top Quantum Electron, 2020, 26: 1-15 CrossRef ADS Google Scholar

[9] Peng H T, Angelatos G, de Lima T F. Temporal Information Processing With an Integrated Laser Neuron. IEEE J Sel Top Quantum Electron, 2020, 26: 1-9 CrossRef ADS Google Scholar

[10] Hurtado A, Henning I D, Adams M J. Optical neuron using polarisation switching in a 1550nm-VCSEL. Opt Express, 2010, 18: 25170 CrossRef PubMed ADS Google Scholar

[11] Coomans W, Gelens L, Beri S. Solitary and coupled semiconductor ring lasers as optical spiking neurons. Phys Rev E, 2011, 84: 036209 CrossRef PubMed ADS arXiv Google Scholar

[12] Barbay S, Kuszelewicz R, Yacomotti A M. Excitability in a semiconductor laser with saturable absorber. Opt Lett, 2011, 36: 4476-4478 CrossRef PubMed ADS Google Scholar

[13] Hurtado A, Schires K, Henning I D. Investigation of vertical cavity surface emitting laser dynamics for neuromorphic photonic systems. Appl Phys Lett, 2012, 100: 103703 CrossRef ADS Google Scholar

[14] Romeira B, Javaloyes J, Ironside C N. Excitability and optical pulse generation in semiconductor lasers driven by resonant tunneling diode photo-detectors. Opt Express, 2013, 21: 20931 CrossRef PubMed ADS Google Scholar

[15] Nahmias M A, Shastri B J, Tait A N. A Leaky Integrate-and-Fire Laser Neuron for Ultrafast Cognitive Computing. IEEE J Sel Top Quantum Electron, 2013, 19: 1-12 CrossRef ADS Google Scholar

[16] Alexander K, Van Vaerenbergh T, Fiers M. Excitability in optically injected microdisk lasers with phase controlled excitatory and inhibitory response. Opt Express, 2013, 21: 26182-26191 CrossRef PubMed ADS Google Scholar

[17] Selmi F, Braive R, Beaudoin G. Relative Refractory Period in an Excitable Semiconductor Laser. Phys Rev Lett, 2014, 112: 183902 CrossRef PubMed ADS Google Scholar

[18] Hurtado A, Javaloyes J. Controllable spiking patterns in long-wavelength vertical cavity surface emitting lasers for neuromorphic photonics systems. Appl Phys Lett, 2015, 107: 241103 CrossRef ADS arXiv Google Scholar

[19] Mesaritakis C, Kapsalis A, Bogris A. Artificial Neuron Based on Integrated Semiconductor Quantum Dot Mode-Locked Lasers. Sci Rep, 2016, 6: 39317 CrossRef PubMed ADS Google Scholar

[20] Garbin B, Dolcemascolo A, Prati F. Refractory period of an excitable semiconductor laser with optical injection. Phys Rev E, 2017, 95: 012214 CrossRef ADS arXiv Google Scholar

[21] Robertson J, Deng T, Javaloyes J. Controlled inhibition of spiking dynamics in VCSELs for neuromorphic photonics: theory and experiments. Opt Lett, 2017, 42: 1560-1563 CrossRef PubMed ADS Google Scholar

[22] Xiang S Y, Zhang H, Guo X X. Cascadable Neuron-Like Spiking Dynamics in Coupled VCSELs Subject to Orthogonally Polarized Optical Pulse Injection. IEEE J Sel Top Quantum Electron, 2017, 23: 1-7 CrossRef ADS Google Scholar

[23] Deng T, Robertson J, Hurtado A. Controlled Propagation of Spiking Dynamics in Vertical-Cavity Surface-Emitting Lasers: Towards Neuromorphic Photonic Networks. IEEE J Sel Top Quantum Electron, 2017, 23: 1-8 CrossRef ADS Google Scholar

[24] Ma P Y, Shastri B J, de Lima T F. All-optical digital-to-spike conversion using a graphene excitable laser. Opt Express, 2017, 25: 33504-33513 CrossRef ADS Google Scholar

[25] Ma P Y, Shastri B J, Ferreira de Lima T. Simultaneous excitatory and inhibitory dynamics in an excitable laser. Opt Lett, 2018, 43: 3802-3805 CrossRef PubMed ADS Google Scholar

[26] Robertson J, Ackemann T, Lester L F. Externally-Triggered Activation and Inhibition of Optical Pulsating Regimes in Quantum-Dot Mode-locked Lasers. Sci Rep, 2018, 8: 12515 CrossRef PubMed ADS Google Scholar

[27] Xiang S, Zhang Y, Guo X. Photonic Generation of Neuron-Like Dynamics Using VCSELs Subject to Double Polarized Optical Injection. J Lightwave Technol, 2018, 36: 4227-4234 CrossRef ADS Google Scholar

[28] Zhang Y, Xiang S, Guo X. Polarization-resolved and polarization- multiplexed spike encoding properties in photonic neuron based on VCSEL-SA. Sci Rep, 2018, 8: 16095 CrossRef PubMed ADS Google Scholar

[29] Deng T, Robertson J, Wu Z M. Stable Propagation of Inhibited Spiking Dynamics in Vertical-Cavity Surface-Emitting Lasers for Neuromorphic Photonic Networks. IEEE Access, 2018, 6: 67951-67958 CrossRef Google Scholar

[30] Zhang Y, Xiang S, Guo X. All-optical inhibitory dynamics in photonic neuron based on polarization mode competition in a VCSEL with an embedded saturable absorber. Opt Lett, 2019, 44: 1548-1551 CrossRef PubMed ADS Google Scholar

[31] Tait A N, Ferreira de Lima T, Nahmias M A. Silicon Photonic Modulator Neuron. Phys Rev Appl, 2019, 11: 064043 CrossRef ADS arXiv Google Scholar

[32] Pammi V A, Alfaro-Bittner K, Clerc M G. Photonic Computing With Single and Coupled Spiking Micropillar Lasers. IEEE J Sel Top Quantum Electron, 2020, 26: 1-7 CrossRef ADS Google Scholar

[33] Iga K. Forty years of vertical-cavity surface-emitting laser: Invention and innovation. Jpn J Appl Phys, 2018, 57: 08PA01 CrossRef ADS Google Scholar

[34] Jiang B, Wu Z M, Deng T. Polarization Switching Characteristics of 1550-nm Vertical-Cavity Surface-Emitting Lasers Subject to Double Polarization Pulsed Injection. IEEE J Quantum Electron, 2016, 52: 1-7 CrossRef ADS Google Scholar

[35] Bi G, Poo M. Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type. J Neurosci, 1998, 18: 10464-10472 CrossRef Google Scholar

[36] Bi G, Poo M. Synaptic Modification by Correlated Activity: Hebb's Postulate Revisited. Annu Rev Neurosci, 2001, 24: 139-166 CrossRef Google Scholar

[37] Fok M P, Tian Y, Rosenbluth D. Pulse lead/lag timing detection for adaptive feedback and control based on optical spike-timing-dependent plasticity. Opt Lett, 2013, 38: 419-421 CrossRef PubMed ADS Google Scholar

[38] Toole R, Fok M P. Photonic implementation of a neuronal algorithm applicable towards angle of arrival detection and localization. Opt Express, 2015, 23: 16133-16141 CrossRef PubMed ADS Google Scholar

[39] Ren Q, Zhang Y, Wang R. Optical spike-timing-dependent plasticity with weight-dependent learning window and reward modulation. Opt Express, 2015, 23: 25247-25258 CrossRef PubMed ADS Google Scholar

[40] Toole R, Tait A N, Ferreira de Lima T. Photonic Implementation of Spike-Timing-Dependent Plasticity and Learning Algorithms of Biological Neural Systems. J Lightwave Technol, 2016, 34: 470-476 CrossRef ADS Google Scholar

[41] Li Q, Wang Z, Le Y S, et al. Optical implementation of neural learning algorithms based on cross-gain modulation in a semiconductor optical amplifier. Proc SPIE, 2016, 10019 DOI: 10.1117/12.2245976. Google Scholar

[42] Xiang S, Gong J, Zhang Y. Numerical Implementation of Wavelength-Dependent Photonic Spike Timing Dependent Plasticity Based on VCSOA. IEEE J Quantum Electron, 2018, 54: 1-7 CrossRef ADS Google Scholar

[43] Martin-Regalado J, Prati F, San Miguel M. Polarization properties of vertical-cavity surface-emitting lasers. IEEE J Quantum Electron, 1997, 33: 765-783 CrossRef ADS Google Scholar

[44] Perez P, Valle A, Pesquera L. All-Optical Inverter Based on Polarization Switching in VCSELs Subject to Single and Dual Optical Injection. IEEE J Sel Top Quantum Electron, 2013, 19: 1700408-1700408 CrossRef ADS Google Scholar

[45] Shui Ying Xiang , Wei Pan , Bin Luo . Influence of Variable-Polarization Optical Feedback on Polarization Switching Properties of Mutually Coupled VCSELs. IEEE J Sel Top Quantum Electron, 2013, 19: 1700108-1700108 CrossRef ADS Google Scholar

[46] Salvide M F, Torre M S, Henning I D. Dynamics of Normal and Reverse Polarization Switching in 1550-nm VCSELs Under Single and Double Optical Injection. IEEE J Sel Top Quantum Electron, 2015, 21: 643-651 CrossRef ADS Google Scholar

[47] Jiang N, Xue C, Liu D. Secure key distribution based on chaos synchronization of VCSELs subject to symmetric random-polarization optical injection. Opt Lett, 2017, 42: 1055-1058 CrossRef PubMed ADS Google Scholar

[48] Li N, Susanto H, Cemlyn B R. Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers. Phys Rev A, 2017, 96: 013840 CrossRef ADS Google Scholar

[49] Jiang N, Wang Y, Zhao A. Simultaneous bandwidth-enhanced and time delay signature-suppressed chaos generation in semiconductor laser subject to feedback from parallel coupling ring resonators. Opt Express, 2020, 28: 1999 CrossRef PubMed ADS Google Scholar

[50] Xiang S, Ren Z, Zhang Y. All-optical neuromorphic XOR operation with inhibitory dynamics of a single photonic spiking neuron based on a VCSEL-SA.. Opt Lett, 2020, 45: 1104-1107 CrossRef PubMed Google Scholar

  • Figure 1

    (Color online) A schematic illustration of real-time optical STDP based on a single VCSEL with DPPOI and OPCWOI. $E_{\rm~cwx}$ represents OPCWOI; $E_{{\rm~inj}x}$ and $E_{{\rm~inj}y}$ denote the stimuli pulses; VOA is variable optical attenuator; OC means optical coupler; VODL represents variable optical delay line; PBC (PBS) denotes polarization beam combiner (splitter).

  • Figure 2

    (Color online) Stimuli pulses ((a), (f)) and the responses ((b)–(e), (g)–(j)) of VCSEL under different conditions, (b) $E_{\rm~cwx}=0$, $k_{{\rm~inj}x}=k_{{\rm~inj}y}=0$, (c) $E_{\rm~cwx}=0$, $k_{{\rm~inj}x}=0,~k_{{\rm~inj}y}=100~\rm{ns}^{-1}$, (d) $E_{\rm~cwx}=0.65$, $k_{{\rm~inj}x}=k_{{\rm~inj}y}=0$, (e) $E_{\rm~cwx}=0.65$, $k_{{\rm~inj}x}=0,~k_{{\rm~inj}y}=100~\rm{ns}^{-1}$, (g) $E_{\rm~cwx}=0$, $k_{{\rm~inj}x}=~k_{{\rm~inj}y}=100~\rm{ns}^{-1}$, (h) $E_{\rm~cwx}=0.65$, $k_{{\rm~inj}x}=k_{{\rm~inj}y}=100~\rm{ns}^{-1}$, protectłinebreak (i) $E_{\rm~cwx}=0.5$, $k_{{\rm~inj}x}=k_{{\rm~inj}y}=100~\rm{ns}^{-1}$, (j) $E_{\rm~cwx}=0.8$, $k_{{\rm~inj}x}=k_{{\rm~inj}y}=100~\rm{ns}^{-1}$.

  • Figure 3

    (Color online) $I_{xm}$ and $I_{ym}$ as functions of $E_{\rm~cwx}$ for different cases of $\Delta~f_{{\rm~inj}yx}$. (a) $\Delta~f_{{\rm~inj}yx}=-5~\rm{GHz}$, (b) $\Delta~f_{{\rm~inj}yx}=0~\rm{GHz}$, (c) $\Delta~f_{{\rm~inj}yx}=5~\rm{GHz}$, (d) $\Delta~f_{{\rm~inj}yx}=10~\rm{GHz}$.

  • Figure 4

    (Color online) Two-dimensional maps of $I_{xm}$ (left column), $I_{ym}$ (middle column), $I_{xm}-I_{ym}$ (right column) for different combinations of $E_{\rm~cwx}$ and $\mu$. (a)–(c) $\Delta~f_{{\rm~inj}yx}=0~\rm{GHz}$, $\Delta~f_{x}=-5~\rm{GHz}$, (d)–(f) $\Delta~f_{{\rm~inj}yx}=5~\rm{GHz}$, $\Delta~f_{x}=-5~\rm{GHz}$.

  • Figure 5

    (Color online) Two-dimensional maps of $I_{xm}-I_{ym}$ for different combinations of $k_{{\rm~inj}x}$ and $E_{\rm~cwx}$. (a)–(c) $\Delta~f_{x}$ $=-5~\rm{GHz}$, (d)–(f) $\Delta~f_{{\rm~inj}yx}=0~\rm{GHz}$, (a) $\Delta~f_{{\rm~inj}yx}=0~\rm{GHz}$, (b) $\Delta~f_{{\rm~inj}yx}=5~\rm{GHz}$, (c) $\Delta~f_{{\rm~inj}yx}=10~\rm{GHz}$, (d) $\Delta~f_{x}=0~\rm{GHz}$, (e) $\Delta~f_{x}=5~\rm{GHz}$, (f) $\Delta~f_{x}=10~\rm{GHz}$.

  • Figure 6

    (Color online) (a) $I_{x}$, (b) $I_{y}$ for some representative $\Delta~t$, (c) $I_{xm}$ and $I_{ym}$ as functions of $\Delta~t$, (d) the calculated STDP curve, with $E_{\rm~cwx}=0.65$.

  • Figure 7

    (Color online) The calculated $\Delta\omega$ for (a) different $\mu$ with $k_{{\rm~inj}x}=k_{{\rm~inj}y}=100~\rm{ns}^{-1}$, (b) for different $k_{{\rm~inj}x}$ with $\mu=1.5$, with $\Delta~f_{{\rm~inj}yx}=0~\rm{GHz}$, $\Delta~f_{x}=-5~\rm{GHz}$.

  • Figure 8

    (Color online) The calculated $\Delta\omega$ for (a) different $\Delta~f_{x}$ with $\Delta~f_{{\rm~inj}yx}=0~\rm{GHz}$ and (b) different $\Delta~f_{{\rm~inj}yx}$ with $\Delta~f_{x}=-5~\rm{GHz}$.

  • Figure 9

    (Color online) The calculated $\Delta\omega$ for different $E_{\rm~cwx}$, with $\Delta~f_{{\rm~inj}yx}=5~\rm{GHz}$, $\Delta~f_{x}=-5~\rm{GHz}$.

  • Figure 10

    (Color online) (a) Stimuli pulses and responded spikes outputs for (b) $E_{\rm~cwx}=0.3$, (c) $E_{\rm~cwx}=0.45$, and protectłinebreak (d) $E_{\rm~cwx}=0.6$, with $\Delta~f_{{\rm~inj}yx}=5~\rm{GHz}$, $\Delta~f_{x}=-5~\rm{GHz}$.

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