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半导体激光器储备池计算系统的工作点选取方法

花飞 方捻 王陆唐

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半导体激光器储备池计算系统的工作点选取方法

花飞, 方捻, 王陆唐

Method of selecting operating point of reservoir computing system based on semiconductor lasers

Hua Fei, Fang Nian, Wang Lu-Tang
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  • 半导体激光器储备池计算系统的性能受很多因素的影响, 如虚节点间隔、激光器的偏置电流和反馈强度等. 对于光注入信号方式, 注入强度和频率失谐的大小也会影响系统的性能, 使得工作点更难确定. 为此, 本文以10阶非线性自回归移动平均任务为基础, 提出一种选取半导体激光器储备池计算系统的最佳反馈强度与注入强度的方法. 该方法通过寻找在某一反馈强度和连续光注入条件下, 对应于储备池的注入锁定状态的最小注入强度来确定注入锁定状态的边缘; 沿此边缘, 通过测试系统性能选取最佳反馈强度以及与之配套的注入强度. 综合前人对其他参数的研究, 进一步提出完整工作点参数的选取方法. 在所选取的工作点参数下, 仅用50个虚节点即获得低至0.3431的归一化均方根误差, 说明所提出的工作点选取方法是可行的. 通过混沌时间序列预测和手写数字识别任务, 验证了该方法对回归和分类问题的通用性.
    Reservoir computing (RC) is an improved recurrent neural network with the simplified training process, therefore has broad application prospects. The RC can be implemented in hardware based on a nonlinear physical node and a delay feedback loop. Among the optical implementation schemes, the RC system based on semiconductor lasers can process information at high speed due to the inherently short time scales. However, the performance of the RC system, especially using the optical injection way of input signals, is affected by many factors, such as the virtual node interval, bias current, frequency detuning, feedback strength, injection strength, etc. The first three parameters can be reasonably set according to the existing studies. The feedback strength and injection strength are mostly determined through multiple attempts, and there is no method to follow, which brings great uncertainty to the RC. Although some researchers suggest that the optimal feedback strength is at the edge of consistency, the conclusion is only reached at some specific injection strengths, and nobody knows whether it is still valid when the injection strength and feedback strength change at the same time. Therefore, in this paper we investigate numerically the relationships between the optimal feedback strength and the consistency region under different injection strengths, based on the nonlinear auto regressive moving average of the 10th order (NARMA10) task. It is found that the optimal feedback strength is independent of the edge of consistency when the injection strength is large. Further research shows that the best performance of the RC system occurs at the edge of the injection locking states of the reservoir under the injection of continuous waveform light, different injection strengths and feedback strengths. Therefore this paper presents a method to select the optimal feedback strength and injection strength by using the edge of injection locking states of the reservoir under the injection of continuous waveform light. The method determines the edge of the injection locking states by searching the minimum injection strength for the injection locking states of the reservoir under one feedback strength and the injection of continuous waveform light. Then, along this edge, the optimal feedback strength and the matching injection strength are found by testing the system performance. Based on existing studies of other parameters, a method to select all parameters at the operating point is proposed. For the NARMA10 task, the normalized root mean square error at the operating point selected is as low as 0.3431 only by using 50 virtual nodes, showing that the proposed method of selecting operating point is feasible. From three properties of reservoirs, the reasons for the best performance of the system under these parameters are explained. The universality of this method for regression and classification task is tested by chaotic time series prediction task and handwritten digit recognition task. The results show that the two tasks can achieve good performance under the operating point selected by this proposed method, which verifies the universality of the method.
      通信作者: 方捻, nfang@shu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 61377082, 61108004)和上海市浦江人才计划(批准号: 14 PJD017)资助的课题
      Corresponding author: Fang Nian, nfang@shu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61377082, 61108004) and Shanghai Pujiang Program, China (Grant No. 14 PJD017)
    [1]

    Lin F Y, Liu J M 2003 Opt. Commun. 221 173Google Scholar

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    Hwang S K, Liu J M 2000 Opt. Commun. 183 195Google Scholar

    [3]

    Delfyett P J, Gee S, Choi M T, Izadpanah H, Yilmaz T 2006 J. Lightwave Technol. 24 2701Google Scholar

    [4]

    Juan Y S, Lin F Y 2009 Opt. Lett. 34 1636Google Scholar

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    Annovazzi-Lodi V, Donati S, Scire A 1996 IEEE J. Quantum. Elect. 32 953Google Scholar

    [6]

    Jiang N, Zhao A, Xue C, Tang J, Qiu K 2019 Opt. Lett. 44 1536Google Scholar

    [7]

    Zhao A, Jiang N, Liu S, Xue C, Tang J, Qiu K 2019 Opt. Express 27 12336Google Scholar

    [8]

    Wang D M, Wang L S, Guo Y Y, Wang Y C, Wang A B 2019 Opt. Express 27 3065Google Scholar

    [9]

    Wang Y, Xiang S, Wang B, Cao X, Wen A, Hao Y 2019 Opt. Express 27 8446Google Scholar

    [10]

    Brunner D, Soriano M C, Mirasso C R, Fischer I 2013 Nat. Commun. 4 1364Google Scholar

    [11]

    Appeltant L, Soriano M C, Van D S G, Danckaert J, Massar S, Dambre J, Schrauwen B, Mirasso C R, Fischer I 2011 Nat. Commun. 2 468Google Scholar

    [12]

    Larger L, Soriano M C, Brunner D, Appeltant L, Gutierrez J M, Pesquera L, Mirasso C R, Fischer I 2012 Opt. Express 20 3241Google Scholar

    [13]

    Duport F, Schneider B, Smerieri A, Haelterman M, Massar S 2012 Opt. Express 20 22783Google Scholar

    [14]

    Dejonckheere A, Duport F, Smerieri A, Fang L, Oudar J L, Haelterman M, Massar S 2014 Opt. Express 22 10868Google Scholar

    [15]

    Hicke K, Escalona-Morán M A, Brunner D, Soriano M C, Fischer I, Mirasso C R 2013 IEEE J Sel. Top. Quant. 19 1501610Google Scholar

    [16]

    Nguimdo R M, Verschaffelt G, Danckaert J, Danckaert J, Sande G V D 2014 Opt. Express 22 8672Google Scholar

    [17]

    Oliver N, Jüngling T, Fischer I 2015 Phys. Rev. Lett. 114 123902Google Scholar

    [18]

    Nakayama J, Kanno K, Uchida A 2016 Opt. Express 24 8679Google Scholar

    [19]

    Qin J, Zhao Q, Xu D, Yin H, Chang Y, Huang D 2016 Mod. Phys. Lett. B 30 1650199

    [20]

    Fischer I, Bueno J, Brunner D, Soriano M C, Mirasso C R 2016 Proceedings of the 42 nd European Conference on Optical Communication Dusseldorf, Germany, September 18−22, 2016 p336

    [21]

    Bueno J, Brunner D, Soriano M C 2017 Opt. Express 25 2401Google Scholar

    [22]

    Hou Y S, Xia G Q, Yang W Y, Wang D, Jayaprasath E, Jiang Z F, Hu C X, Wu M Z 2018 Opt. Express 26 10211Google Scholar

    [23]

    Argyris A, Bueno J, Fischer I 2018 Sci. Rep. 8 8487Google Scholar

    [24]

    Lang R, Kobayashi K 1980 IEEE J. Quantum. Elect. 16 347Google Scholar

    [25]

    Deng L 2012 IEEE Signal. Proc. Mag. 29 141

  • 图 1  半导体激光器储备池计算系统示意图

    Fig. 1.  Schematic diagram of semiconductor laser reservoir computing system.

    图 2  在注入强度为8 ns–1和不同反馈强度下, (a)储备池一致性的互相关值, (b) NARMA10任务的NRMSE

    Fig. 2.  (a) Cross correlation of the reservoir consistency; (b) NRMSE of NARMA10 task under the injection strength of 8 ns–1 and different feedback strengths.

    图 3  在注入强度为23 ns–1和不同反馈强度下, (a)储备池一致性的互相关值, (b) NARMA10任务的NRMSE

    Fig. 3.  (a) Cross correlation of the reservoir consistency; (b) NRMSE of NARMA10 task under the injection strength of 23 ns–1 and different feedback strengths.

    图 4  不同反馈强度和注入强度下半导体激光器RC系统对NARMA10任务的测试性能

    Fig. 4.  Test performances of the RC system based on semiconductor lasers for NARMA10 task under different feedback strengths and injection strengths.

    图 5  连续光注入、不同反馈强度和注入强度下的储备池的非线性状态

    Fig. 5.  Nonlinear states of the reservoir under the injection of continuous waveform light, different feedback strengths and injection strengths.

    图 6  RC性能 (a)较好, (b)一般两种情况对应的连续光注入下储备池的输出功率

    Fig. 6.  Output powers of the reservoir with the injection of continuous waveform light under (a) better RC performance, (b) general RC performance.

    图 7  从三种不同的初始化状态选取最佳反馈强度和注入强度的过程

    Fig. 7.  The process of selecting the optimal feedback strength and injection strength from three different initialization states.

    表 1  部分仿真参数

    Table 1.  Partial simulation parameters.

    SymbolsParametersValues
    αLinewidth enhancement factor3.0
    GGain coefficient8.4 × 10–13 m3s–1
    N0Carrier density at transparency1.4 × 1024 m–3
    εGain saturation coefficient2.0 × 10–23
    τpPhoton lifetime1.927 ps
    τsCarrier lifetime2.04 ns
    JthThreshold current of the response laser9.892 × 1032 m–3s–1
    ωFree-running angular frequency of the response laser1.23 × 1015 rad/s
    IdOutput optical intensity of the drive laser5. 65 × 1020 W/m2
    下载: 导出CSV
  • [1]

    Lin F Y, Liu J M 2003 Opt. Commun. 221 173Google Scholar

    [2]

    Hwang S K, Liu J M 2000 Opt. Commun. 183 195Google Scholar

    [3]

    Delfyett P J, Gee S, Choi M T, Izadpanah H, Yilmaz T 2006 J. Lightwave Technol. 24 2701Google Scholar

    [4]

    Juan Y S, Lin F Y 2009 Opt. Lett. 34 1636Google Scholar

    [5]

    Annovazzi-Lodi V, Donati S, Scire A 1996 IEEE J. Quantum. Elect. 32 953Google Scholar

    [6]

    Jiang N, Zhao A, Xue C, Tang J, Qiu K 2019 Opt. Lett. 44 1536Google Scholar

    [7]

    Zhao A, Jiang N, Liu S, Xue C, Tang J, Qiu K 2019 Opt. Express 27 12336Google Scholar

    [8]

    Wang D M, Wang L S, Guo Y Y, Wang Y C, Wang A B 2019 Opt. Express 27 3065Google Scholar

    [9]

    Wang Y, Xiang S, Wang B, Cao X, Wen A, Hao Y 2019 Opt. Express 27 8446Google Scholar

    [10]

    Brunner D, Soriano M C, Mirasso C R, Fischer I 2013 Nat. Commun. 4 1364Google Scholar

    [11]

    Appeltant L, Soriano M C, Van D S G, Danckaert J, Massar S, Dambre J, Schrauwen B, Mirasso C R, Fischer I 2011 Nat. Commun. 2 468Google Scholar

    [12]

    Larger L, Soriano M C, Brunner D, Appeltant L, Gutierrez J M, Pesquera L, Mirasso C R, Fischer I 2012 Opt. Express 20 3241Google Scholar

    [13]

    Duport F, Schneider B, Smerieri A, Haelterman M, Massar S 2012 Opt. Express 20 22783Google Scholar

    [14]

    Dejonckheere A, Duport F, Smerieri A, Fang L, Oudar J L, Haelterman M, Massar S 2014 Opt. Express 22 10868Google Scholar

    [15]

    Hicke K, Escalona-Morán M A, Brunner D, Soriano M C, Fischer I, Mirasso C R 2013 IEEE J Sel. Top. Quant. 19 1501610Google Scholar

    [16]

    Nguimdo R M, Verschaffelt G, Danckaert J, Danckaert J, Sande G V D 2014 Opt. Express 22 8672Google Scholar

    [17]

    Oliver N, Jüngling T, Fischer I 2015 Phys. Rev. Lett. 114 123902Google Scholar

    [18]

    Nakayama J, Kanno K, Uchida A 2016 Opt. Express 24 8679Google Scholar

    [19]

    Qin J, Zhao Q, Xu D, Yin H, Chang Y, Huang D 2016 Mod. Phys. Lett. B 30 1650199

    [20]

    Fischer I, Bueno J, Brunner D, Soriano M C, Mirasso C R 2016 Proceedings of the 42 nd European Conference on Optical Communication Dusseldorf, Germany, September 18−22, 2016 p336

    [21]

    Bueno J, Brunner D, Soriano M C 2017 Opt. Express 25 2401Google Scholar

    [22]

    Hou Y S, Xia G Q, Yang W Y, Wang D, Jayaprasath E, Jiang Z F, Hu C X, Wu M Z 2018 Opt. Express 26 10211Google Scholar

    [23]

    Argyris A, Bueno J, Fischer I 2018 Sci. Rep. 8 8487Google Scholar

    [24]

    Lang R, Kobayashi K 1980 IEEE J. Quantum. Elect. 16 347Google Scholar

    [25]

    Deng L 2012 IEEE Signal. Proc. Mag. 29 141

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出版历程
  • 收稿日期:  2019-07-08
  • 修回日期:  2019-09-02
  • 上网日期:  2019-11-01
  • 刊出日期:  2019-11-20

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