All-optical reservoir computing system based on polarization dynamics

Fang Nian; Qian Ruo-Lan; Wang Shuai

doi:10.7498/aps.72.20230722

Abstract

Reservoir computing (RC) is a simplified recurrent neural network and can be implemented by using a nonlinear system with delay feedback, thus it is called delay-based RC. Various nonlinear nodes and feedback loop structures have been proposed. Most of existing researches are based on the dynamical responses in intensity of the nonlinear systems. There are also a photoelectric RC system based on wavelength dynamics and an all-optical RC based on the phase dynamics of a semiconductor laser with optical feedback, as well as so-called polarization dynamics of a vertical cavity surface emitting laser (VCSEL). However, these VCSEL-RCs actually are based on the intensity dynamics of two mutually orthogonal polarization modes, or polarization-resolved intensity dynamics. The RC based on rich dynamical responses in polarization has not yet been found. A semiconductor optical amplifier (SOA) fiber ring laser can produce rich dynamical states in polarization, and is used in optical chaotic secure communication and distributed optical fiber sensing. To further expand the application of polarization dynamics of the SOA fiber ring laser and open up a new direction for the research of optical RC neural network, an all-optical RC system based on polarization dynamics of the ring laser is proposed. The ring laser is used as the reservoir, and the SOA as the nonlinear node. After the input signal is masked according to a synchronization scheme, it is injected into the reservoir by intensity modulation for a continuous wave generated by a superluminescent light emitting diode (SLED). The dynamical response in polarization of the ring laser is detected by a polarizer and a photodetector. The influences of the SOA operation current, output power of the SLED and attenuation of a variable optical attenuator (VOA) in the fiber loop on the polarization dynamic characteristic (mainly referring to the output degree of polarization) of the laser are analyzed experimentally. The fading memory and nonlinear response of the RC system based on the polarization dynamic response and intensity dynamic response are compared experimentally. The influences of output power of the SLED and attenuation of the VOA on fading memory, consistency and separation of the RC system based on the two kinds of dynamic responses are investigated experimentally. Thus the range of the VOA attenuation is determined. The network performance of the polarization dynamics RC system is evaluated by processing a Santa Fe time series prediction task and a multi-waveform recognition task. The normalized mean square error can be as low as 0.0058 for the time series prediction task, and the identification rate can be as high as 100% for the recognition task under the appropriate system parameters and only 30 virtual nodes. The experimental results show that the polarization dynamics RC system has good prediction performance and classification capability, which are comparable to the existing RC system based on intensity dynamics of the ring laser. The system can be expected to process two tasks in parallel when the polarization dynamics and intensity dynamics are used at the same time.

Keywords:

Authors and contacts

Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai University, Shanghai 200444, China

Corresponding author: Fang Nian, nfang@shu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 62075123) and the 111 Project, China (Grant No. D20031).

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References

[1]	Jaeger H 2001 The “Echo State” Approach to Analysing and Training Recurrent Neural Networks (Bonn, Germany: National Research Center for Information Technology) Technical Report GMD Report 148
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[33]	Hübner U, Abraham N B, Weiss C O 1989 Phys. Rev. A 40 6354 Google Scholar
[34]	Fang N, Qian R L, Wang S 2023 Opt. Express 31 35377 Google Scholar

Cited By

图 1 基于SOA光纤环形激光器的偏振动力学储备池计算系统. AWG, 任意波形发生器; SLED, 超辐射发光二极管; IM, 强度调制器; FC, 光纤耦合器; PC, 偏振控制器; ISO, 隔离器; SOA, 半导体光放大器; VOA, 可调光衰减器; PD, 光电探测器

Figure 1. Polarization dynamics reservoir computing system based on a SOA fiber ring laser. AWG, arbitrary waveform generator; SLED, superluminescent light emitting diode; IM, intensity modulator; FC, fiber coupler; PC, polarization controller; ISO, isolator; SOA, semiconductor optical amplifier; VOA, variable optical attenuator; PD, photodetector

DownLoad: Full-Size Img PowerPoint

图 2 偏振动力学储备池计算系统模型

Figure 2. Schematic diagram of polarization dynamics reservoir computing system.

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图 3 系统输出功率与偏振度随SOA工作电流的变化

Figure 3. Output power and DOP of the system vs. current of SOA.

DownLoad: Full-Size Img PowerPoint

图 4 系统输出偏振度随宽带激光器输出功率及VOA衰减量的变化

Figure 4. Output DOP of the system vs. output power of SLED and attenuation of VOA.

DownLoad: Full-Size Img PowerPoint

图 5 系统的渐衰记忆和非线性响应　(a) 偏振动力学响应; (b) 强度动力学响应

Figure 5. Fading memory and nonlinear response of the system: (a) Polarization dynamic response; (b) intensity dynamic response.

DownLoad: Full-Size Img PowerPoint

图 6 系统的渐衰记忆随VOA衰减量的变化　(a) 偏振动力学响应; (b) 强度动力学响应

Figure 6. Fading memory of the system vs. attenuation of VOA: (a) Polarization dynamic response; (b) intensity dynamic response.

DownLoad: Full-Size Img PowerPoint

图 7 系统的一致性和分离性随宽带激光器输出功率和VOA衰减量的变化　(a) 一致性的互相关值; (b) 分离性的互相关值

Figure 7. Consistency and separation of the system vs. output power of SLED and attenuation of VOA: (a) Cross correlation of the consistency; (b) cross correlation of the separation.

DownLoad: Full-Size Img PowerPoint

图 8 Santa Fe时间序列预测任务的信号波形　(a) 掩码后的输入信号和偏振动力学响应; (b) 预测结果

Figure 8. Signal waveforms of Santa Fe time series prediction task: (a) Masked input signal and polarization dynamic response; (b) prediction results.

DownLoad: Full-Size Img PowerPoint

图 9 预测性能随宽带激光器输出功率的变化　(a) 偏振动力学RC测试结果; (b) 强度动力学RC测试结果

Figure 9. Prediction performance vs. output power of SLED: (a) Polarization dynamics RC testing results; (b) intensity dynamics RC testing results.

DownLoad: Full-Size Img PowerPoint

图 10 预测性能随缩放因子(a)和虚节点数(b)的变化

Figure 10. Prediction performance vs. scaling factor (a) and number of virtual nodes (b).

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图 11 多波形识别任务的信号波形　(a) 原始信号; (b) 掩码后的输入信号; (c) 目标输出信号的局部放大; (d) 目标输出信号; (e) 实际输出信号

Figure 11. Signal waveforms of multi-waveform recognition task: (a) Original signal; (b) masked input signal; (c) locally amplified target output signal; (d) target output signal; (e) actual output signal.

DownLoad: Full-Size Img PowerPoint

图 12 识别性能随宽带激光器输出功率的变化　(a) 偏振动力学RC实验结果; (b) 强度动力学RC实验结果

Figure 12. Recognition performance vs. output power of SLED: (a) Polarization dynamics RC experiment results; (b) intensity dynamics RC experiment results.

DownLoad: Full-Size Img PowerPoint

图 13 分类能力随缩放因子(a)和虚节点数(b)的变化

Figure 13. Classification capability vs. scaling factor (a) and number of virtual nodes (b).

DownLoad: Full-Size Img PowerPoint

[1]	Jaeger H 2001 The “Echo State” Approach to Analysing and Training Recurrent Neural Networks (Bonn, Germany: National Research Center for Information Technology) Technical Report GMD Report 148
[2]	Maass W, Natschläger T, Markram H 2002 Neural Comput. 14 2531 Google Scholar
[3]	Verstraeten D, Schrauwen B, D'Haene M, Stroobandt D 2007 Neural Networks 20 391 Google Scholar
[4]	Soriano M C, Brunner D, Escalona-Morán M, Mirasso C R, Fischer I 2015 Front Comput. Neurosci. 9 68 Google Scholar
[5]	Duport F, Schneider B, Smerieri A, Haelterman M, Massar S 2012 Opt. Express 20 22783 Google Scholar
[6]	Brunner D, Soriano M C, Mirasso C R, Fischer I 2013 Nat. Commun. 4 1364 Google Scholar
[7]	Dmitriev P S, Kovalev A V, Locquet A, Rontani D, Viktorov E A 2020 Opt. Lett. 45 6150 Google Scholar
[8]	Dejonckheere A, Duport F, Smerieri A, Fang L, Oudar J L, Haelterman M, Massar S 2014 Opt. Express 22 10868 Google Scholar
[9]	Zhang H, Feng X, Li B X, Wang Y, Cui K Y, Liu F, Dou W B, Huang Y D 2014 Opt. Express 22 31356 Google Scholar
[10]	Vinckier Q, Duport F, Smerieri A, Vandoorne K, Bienstman P, Haelterman M, Massar S 2015 Optica 2 438 Google Scholar
[11]	Nguimdo R M, Verschaffelt G, Danckaert J, Vander Sander G 2015 IEEE Trans. Neural Networks Learn. Syst. 26 3301 Google Scholar
[12]	Zhao T, Xie W L, Guo Y Q, Xu J W, Guo Y Y, Wang L S 2022 Electronics 11 1578 Google Scholar
[13]	李磊, 方捻, 王陆唐, 黄肇明 2018 电子学报 46 298 Google Scholar Li L, Fang N, Wang L T, Huang Z M 2018 Acta Electron. Sin. 46 298 Google Scholar
[14]	Hou Y S, Xia G Q, Yang W Y, Wang D, Jayaprasath E, Jiang Z F, Hu C X, Wu Z M 2018 Opt. Express 26 10211 Google Scholar
[15]	Chen Y P, Yi L L, Ke J X, Yang Z, Yang Y P, Huang L Y, Zhuge Q B, Hu W S 2019 Opt. Express 27 27431 Google Scholar
[16]	Martinenghi R, Rybalko S, Jacquot M, Chembo Y K, Larger L 2012 Phys. Rev. Lett. 108 244101 Google Scholar
[17]	Nguimdo R M, Verschaffelt G, Danckaert J, Vander Sander G 2014 Opt. Express 22 8672 Google Scholar
[18]	Vatin J, Rontani D, Sciamanna M 2018 Opt. Lett. 43 4497 Google Scholar
[19]	Vatin J, Rontani D, Sciamanna M 2019 Opt. Express 27 18579 Google Scholar
[20]	Guo X X, Xiang S Y, Zhang Y H, Lin L, Wen A J, Hao Y 2020 Sci. China Inf. Sci. 63 160407 Google Scholar
[21]	Zhong D Z, Zhao K K, Xu Z, Hu Y L, Deng W A, Hou P, Zhang J B, Zhang J M 2022 Opt. Express 30 36209 Google Scholar
[22]	Jiang L, Liang W Y, Song W J, Jia X H, Yang Y L, Liu L M, Deng Q X, Mou X Y, Zhang X 2022 IEEE J. Quantum Electron. 58 2400608 Google Scholar
[23]	Huang Y, Zhou P, Yang Y G, Cai D Y, Li N Q 2023 IEEE J. Sel. Top. Quantum Electron. 29 1700109 Google Scholar
[24]	Wang L T, Huang Z M 2004 Proc. SPIE 5281 619 Google Scholar
[25]	Wang L T, Wu W J, Fang N, Huang Z M 2005 Proc. SPIE 6021 60210S Google Scholar
[26]	方捻, 郭小丹, 王春华, 王陆唐, 黄肇明 2008 光学学报 28 128 Google Scholar Fang N, Guo X D, Wang C H, Wang L T, Huang Z M 2008 Acta Opt. Sin. 28 128 Google Scholar
[27]	赵莉, 方捻, 王颖, 黄肇明 2009 光子学报 38 2449 Zhao L, Fang N, Wang Y, Huang Z M 2009 Acta Photon. Sin. 38 2449
[28]	方捻, 单超, 王陆唐, 黄肇明 2010 光电子∙激光 21 335 Google Scholar Fang N, Shan C, Wang L T, Huang Z M 2010 J. Optoelectron.∙Laser 21 335 Google Scholar
[29]	Nakayama J, Kanno K, Uchida A 2016 Opt. Express 24 8679 Google Scholar
[30]	Vandoorne K, Dierckx W, Schrauwen B, Verstraeten D, Baets R, Bienstman P, Van Campenhout J 2008 Opt. Express 16 11182 Google Scholar
[31]	Tanaka G, Yamane T, Héroux J B, Nakane R, Kanazawa N, Numata H, Dakano H, Hirose A 2019 Neural Networks 115 100 Google Scholar
[32]	Bueno J, Brunner D, Soriano M C, Fischer I 2017 Opt. Express 25 2401 Google Scholar
[33]	Hübner U, Abraham N B, Weiss C O 1989 Phys. Rev. A 40 6354 Google Scholar
[34]	Fang N, Qian R L, Wang S 2023 Opt. Express 31 35377 Google Scholar

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