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SCIENCE CHINA Information Sciences, Volume 63 , Issue 6 : 160407(2020) https://doi.org/10.1007/s11432-020-2862-7

Enhanced memory capacity of a neuromorphic reservoir computing system based on a VCSEL with double optical feedbacks

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  • ReceivedJan 12, 2020
  • AcceptedApr 1, 2020
  • PublishedMay 12, 2020

Abstract

In this paper, a neuromorphic reservoir computing (RC) system with enhanced memory capacity (MC) based on a vertical-cavity surface-emitting laser (VCSEL) subject to double optical feedbacks (DOF) is proposed and investigated numerically. The aim of this study is to explore the MC of the proposed system. For the purpose of comparison, the MC of the VCSEL-based RC system with single optical feedback (SOF) is also taken into account. It is found that, compared with the VCSEL-based RC system subject to SOF, enhanced MC can be obtained for the VCSEL-based RC system with DOF. Besides, the effects of feedback strength, injected strength, frequency detuning as well as injection current on the MC of the VCSEL-based RC system with DOF are considered. Moreover, the influence of feedback delays is also carefully examined. Thus, such proposed VCSEL-based RC system with DOF provides a prospect for the further development of the neuromorphic photonic system based on RC.


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).


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  • Figure 1

    (Color online) Schematic diagram of the VCSEL-based RC system with DOF. MZM: Mach-Zehnder modulator; PC1 (PC2): polarization controller; VOA1 (VOA2): variable optical attenuator; DL1 (DL2): fiber delay line; CIR: optical circulator; FC1 (FC2): fiber coupler; SL: semiconductor laser; $u(k)$: input data.

  • Figure 2

    (Color online) The polarization-resolved intensities as a function of the injection current $\mu$ for XP and YP modes of the VCSEL, for (a) $k_{d1x}=k_{d2x}=k_{d1y}=k_{d2y}=0$, (b) $k_{d1x}=k_{d2x}=k_{d1y}=k_{d2y}=10~{\rm~ns}^{-1}$, with $k_{\rm~inj}=0$, $\tau_1=1$ ns, $\tau_2=3.1$ ns, $\Delta~f=0$ GHz.

  • Figure 3

    (Color online) (a) The $j$-delay memory capacity ${\rm~mc}_j$ with $k_{ds}=20~{\rm~ns}^{-1}$ for both systems; (b) memory capacity MC as a function of the feedback strength $k_{ds}$ when $j$ is set to be $30$, with $k_{\rm~inj}=20~{\rm~ns}^{-1}$, $\tau_1=1$ ns, $\tau_2=3.1$ ns, $\mu=1.2$, $\Delta~f=0$ GHz for the VCSEL-based RC with DOF and SOF.

  • Figure 4

    (Color online) (a1) and (a2) Comparison between the target values (blue) and predicted values (orange) for $j=3$ (top) and for $j=20$ (bottom). (b1) and (b2) Scatter plots of the target values verses predicted values. (c1) and (c2) the MC values for training (brown) and validation data sets (yellow).

  • Figure 5

    (Color online) Two dimensional map of the values of MC in the parameter space of $k_{d1x}$ and $k_{d2x}$, for protectłinebreak (a) $k_{\rm~inj}=20~{\rm~ns}^{-1}$, (b) $k_{\rm~inj}=30~{\rm~ns}^{-1}$, with $\tau_1=1$ ns, $\tau_2=3.1$ ns, $\mu=1.2$, $\Delta~f=0$ GHz for the VCSEL-based RC with DOF.

  • Figure 6

    (Color online) Two dimensional map of the values of MC in the parameter space of $k_{\rm~inj}$ and $k_{d1x}$, for protectłinebreak (a) $k_{d1x}=k_{d2x}$, (b) $k_{d1x}=10$ ns$^{-1}$, with $\tau_1=1$ ns, $\tau_2=3.1$ ns, $\mu=1.2$, $\Delta~f=0$ GHz for the VCSEL-based RC with DOF.

  • Figure 7

    (Color online) Two dimensional map of the values of MC in the parameter space of $k_{\rm~inj}$ and $\Delta~f$, with $\tau_1=1$ ns, $\tau_2=3.1$ ns, $\mu=1.2$, for (a) $k_{d1x}=5~{\rm~ns}^{-1}$ and $k_{d2x}=15~{\rm~ns}^{-1}$, (b) $k_{d1x}=10~{\rm~ns}^{-1}$ and $k_{d2x}=10~{\rm~ns}^{-1}$, (c) $k_{d1x}=12~{\rm~ns}^{-1}$ and $k_{d2x}=8~{\rm~ns}^{-1}$ for the VCSEL-based RC with DOF.

  • Figure 8

    (Color online) The MC values as a function of $\mu$ for $k_{\rm~inj}=20~{\rm~ns}^{-1}$, $k_{\rm~inj}=30~{\rm~ns}^{-1}$ and $k_{\rm~inj}=40~{\rm~ns}^{-1}$, with $k_{d1x}=k_{d2x}=10~{\rm~ns}^{-1}$, with $\tau_1=1$ ns, $\tau_2=3.1$ ns, $\Delta~f=0$ GHz for the VCSEL-based RC with DOF.

  • Figure 9

    (Color online) The MC values as a function of $\tau_2$ for (a) $k_{\rm~inj}=30~{\rm~ns}^{-1}$ and (b) $k_{\rm~inj}=40~{\rm~ns}^{-1}$, point “a" ($\tau_2$= 5 ns), point “b" ($\tau_2$ = 6.5 ns), point “c" ($\tau_2$ = 8 ns), and point “d" ($\tau_2$ = 9 ns), with $k_{d1x}=5~{\rm~ns}^{-1}$ and $k_{d2x}=15~{\rm~ns}^{-1}$, $k_{d1x}=10~{\rm~ns}^{-1}$ and $k_{d2x}=10~{\rm~ns}^{-1}$, $k_{d1x}=12~{\rm~ns}^{-1}$ and $k_{d2x}=8~{\rm~ns}^{-1}$, $\tau_1=1$ ns, $\Delta~f=0$ GHz for the VCSEL-based RC with DOF.

  • Figure 10

    (Color online) The MC values as a function of $k_{d1x}$ for (a1) $\tau_2=2.8~{\rm~ns}^{-1}$ and (a2) $\tau_2=3~{\rm~ns}^{-1}$, protectłinebreak (b1) $\tau_2=3.8~{\rm~ns}^{-1}$ and (b2) $\tau_2=4~{\rm~ns}^{-1}$, (c1) $\tau_2=4.4~{\rm~ns}^{-1}$ and (c2) $\tau_2=4.5~{\rm~ns}^{-1}$, with (a1)–(c1) $k_{\rm~inj}=30~{\rm~ns}^{-1}$, and (a2)–(c2) $k_{\rm~inj}=40~{\rm~ns}^{-1}$, with $k_{d1x}=k_{d2x}$, $\tau_1=1$ ns, $\Delta~f=0$ GHz for the VCSEL-based RC with DOF.

  • Figure 11

    (Color online) The MC values as a function of $\tau_2$ for (a) $\tau_1=2~{\rm~ns}^{-1}$, point “a” ($\tau_2=3\tau_1=6$ ns), point “b” ($\tau_2=4\tau_1=8$ ns), point “c” ($\tau_2=6.5\tau_1=13$ ns), and point “d” ($\tau_2=8\tau_1=16$ ns); (b) $\tau_1=3~{\rm~ns}^{-1}$, point “a” ($\tau_2=3\tau_1=9$ ns), point “b” ($\tau_2=5\tau_1=15$ ns), point “c” ($\tau_2=6.5\tau_1=19.5$ ns), and point “d” ($\tau_2=9\tau_1=27$ ns); protectłinebreak (c) $\tau_1=4~{\rm~ns}^{-1}$, point “a” ($\tau_2=3\tau_1=12$ ns), point “b” ($\tau_2=4\tau_1=16$ ns), point “c” ($\tau_2=7\tau_1=28$ ns), and point “d” ($\tau_2=8.5\tau_1=34$ ns) with $k_{\rm~inj}=30~{\rm~ns}^{-1}$, $k_{d1x}=k_{d2x}=10~{\rm~ns}^{-1}$, $\Delta~f=0$ GHz for the VCSEL-based RC with DOF.

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