Skip to main content
SpringerLink
Log in

Characteristics of multi-channel reservoir computing based on mutually-coupled spin-VCSELs: a comprehensive investigation

  • Research
  • Published:
Applied Physics B Aims and scope Submit manuscript

Abstract

We studied the characteristics of a four-channel multi-task reservoir computing (RC) system based on mutually-coupled and optically pumped spin vertical-cavity surface-emitting lasers (Spin-VCSELs). By analyzing bifurcation and state diagrams, we investigated the polarization dynamics of the system. Additionally, we examined the effects of key parameters such as coupling strength, injection strength, frequency detuning, optical pumping intensity, and pump polarization ellipticity on RC performance, with one-step time-series prediction as the benchmark. Our findings indicate that an increase in coupling strength results in a reduced frequency detuning range, accompanied by a lower normalized mean squared error (NMSE). Excessive coupling strength and optical pumping intensity are detrimental to RC performance. The influence of pump polarization ellipticity is smaller and exhibits a symmetry feature. Furthermore, the parameter optimization regime for orthogonal polarized optical coupling (OPOC) is wider than that for parallel polarized optical coupling (PPOC). Under optimized parameters, both PPOC and OPOC-based RC system can achieve NMSE as low as 0.033 and 0.041 respectively. This work can provide a valuable insight on the design and mechanism analysis for parallel and multi-task processing RC systems based on the platform of Spin-VCSELs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Data availability

The data that support the findings of this study are available in this paper and on a request from the corresponding author.

References

  1. G. Hinton, D. Li, Y. Dong, G.E. Dahl, A. Mohamed, N. Jaitly, A. Senior, V. Vanhoucke, P. Nguyen, T.N. Sainath, B. Kingsbury, Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups. IEEE Signal Process. Mag. 29(6), 82–97 (2012)

    Article  ADS  Google Scholar 

  2. D. Silver, A. Huang, C.J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, D. Hassabis, Mastering the game of go with deep neural networks and tree search. Nature 529, 484–489 (2016)

    Article  ADS  Google Scholar 

  3. H. Aeger, The ‘echo state’ approach to analyzing and training recurrent neural networks-with an erratum note Technical Report GMD Report 148 German National Research Center for Information Technology (2001)

  4. M. Cai, X.M. Fan, C. Wang, L.L. Gao, X. Zhang, Research for parameters optimization of echo state network 2018 11th International Symposium on Computational Intelligence and Design (2018)

  5. W. Maass, T. Natschläger, H. Markram, Real-time computing without stable states: a new framework for neural computation based on perturbations. Neural Comput. 14(11), 2531–2560 (2002)

    Article  Google Scholar 

  6. D. Verstraeten, B. Schrauwen, M. D’Haene, D. Stroobandt, An experimental unification of reservoir computing methods. Neural Netw. 20(3), 391–403 (2007)

    Article  Google Scholar 

  7. L. Appeltant, M.C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C.R. Mirasso, I. Fischer, Information processing using a single dynamical node as complex system. Nat. Commun. 2(468), 1476 (2011)

    Google Scholar 

  8. D. Brunner, M.C. Soriano, C.R. Mirasso, I. Fischer, Parallel photonic information processing at gigabyte per second data rates using transient states. Nat. Commun. 4, 2368 (2013)

    Article  Google Scholar 

  9. Y.S. Hou, G.Q. Xia, W.Y. Yang, D. Wang, E. Jayaprasath, Z.F. Jiang, C.X. Hu, Z.M. Wu, Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection. Opt. Express 26(8), 10211–10219 (2018)

    Article  ADS  Google Scholar 

  10. Y. Kuriki, J. Nakayama, K. Takano, A. Uchida, Impact of input mask signals on delay-based photonic reservoir computing with semiconductor lasers. Opt. Express 26(5), 5777–5788 (2018)

    Article  ADS  Google Scholar 

  11. K. Hicke, M. Escalona-Morán, D. Brunner, M.C. Soriano, I. Fischer, C.R. Mirasso, Information processing using transient dynamics of semiconductor lasers subject to delayed feedback. IEEE J. Quantum Electron. 19(4), 1501610 (2013)

    Article  Google Scholar 

  12. R.M. Nguimdo, G. Verschaffelt, J. Danckaert, G. Van der Sande, Fast photonic information processing using semiconductor lasers with delayed optical feedback: Role of phase dynamics. Opt. Express 22(7), 8672–8686 (2014)

    Article  ADS  Google Scholar 

  13. J. Nakayama, K. Kanno, A. Uchida, Laser dynamical reservoir computing with consistency: An approach of a chaos mask signal. Opt. Express 24(8), 8679–8692 (2016)

    Article  ADS  Google Scholar 

  14. R.M. Nguimdo, G. Verschaffelt, J. Danckaert, G. Van der Sande, Reducing the phase sensitivity of laser-based optical reservoir computing systems. Opt. Express 24(2), 1238–1252 (2016)

    Article  ADS  Google Scholar 

  15. J. Bueno, D. Brunner, M.C. Soriano, I. Fischer, Conditions for reservoir computing performance using semiconductor lasers with delayed optical feedback. Opt. Express 25(3), 2401–2412 (2017)

    Article  ADS  Google Scholar 

  16. Y.S. Hou, G.Q. Xia, E. Jayaprasath, D.Z. Yue, W.Y. Yang, Z.M. Wu, Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers. Opt. Commun. 433(15), 215–220 (2019)

    Article  ADS  Google Scholar 

  17. Y.S. Hou, G.Q. Xia, E. Jayaprasath, D.Z. Yue, Z.M. Wu, Parallel information processing using a reservoir computing system based on mutually coupled semiconductor lasers. Appl. Phys. B 126(3), 40 (2020)

    Article  ADS  Google Scholar 

  18. Q. Cai, Y. Guo, P. Li, A. Bogris, K.A. Shore, Y.M. Zhong, Y.C. Wang, Modulation format identification in fiber communications using single dynamical node-based photonic reservoir computing. Photon. Res. 9(1), B1–B8 (2021)

    Article  Google Scholar 

  19. W.Y. Liang, S.R. Xu, L. Jiang, X.H. Jia, J.B. Lin, Y.L. Yang, L.M. Liu, Design of parallel reservoir computing by mutually-coupled semiconductor lasers with optoelectronic feedback. Opt. Commun. 495(3), 127120 (2021)

    Article  Google Scholar 

  20. W.Y. Liang, L. Jiang, W.J. Song, X.H. Jia, Q.X. Deng, L.M. Liu, X. Zhang, Q.Y. Wang, Enhanced optoelectronic reservoir computation using semiconductor laser with double delay feedbacks. Appl. Opt. 62(3), 620–626 (2023)

    Article  ADS  Google Scholar 

  21. Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, Optoelectronic reservoir computing. Sci. Rep. 287(2), 1–6 (2012)

    Google Scholar 

  22. M.C. Soriano, S. Ortín, D. Brunner, L. Larger, C.R. Mirasso, I. Fischer, L. Pesquera, Optoelectronic reservoir computing: Tackling noise-induced performance degradation. Opt. Express 21(1), 12–20 (2013)

    Article  ADS  Google Scholar 

  23. F. Duport, A. Smerieri, A. Akrout, M. Haelterman, S. Massar, Fully analogue photonic reservoir computer. Sci. Rep. 6, 22381 (2016)

    Article  ADS  Google Scholar 

  24. Y.P. Chen, L.L. Yi, J.X. Ke, Z. Yang, Y.P. Yang, L.Y. Huang, Q. Zhuge, W.S. Hu, Reservoir computing system with double optoelectronic feedback loops. Opt. Express 27(20), 27431–27440 (2019)

    Article  ADS  Google Scholar 

  25. K. Saito, K. Kanno, A. Uchida, Parallelization in reservoir computing based on a mutually coupled electro-optic delay system. Frontiers in Optics/Laser Science (2019)

  26. M. Tezuka, K. Kanno, M. Bunsen, Reservoir computing with a slowly modulated mask signal for preprocessing using a mutually coupled optoelectronic system. Jpn. J. Appl. Phys. 55(08RE06), 1–8 (2016)

    Google Scholar 

  27. Q.C. Zhao, H.X. Yin, H.G. Zhu, Simultaneous recognition of two channels of optical packet headers utilizing reservoir computing subject to mutual-coupling optoelectronic feedback. Optik 157, 951–956 (2018)

    Article  ADS  Google Scholar 

  28. S.Y. Xiang, W. Pan, B. Luo, L.S. Yan, X.H. Zou, N. Jiang, L. Yang, H.N. Zhu, Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable- polarization optical feedback. J. Lightw. Technol. 29(14), 2173–2179 (2011)

    Article  ADS  Google Scholar 

  29. W.L. Zhang, W. Pan, B. Luo, X.F. Li, X.H. Zuo, M.Y. Wang, Theoretical study on polarization dynamics of VCSELs with negative optoelectronic feedback. Appl. Opt. 46(29), 7262–7266 (2007)

    Article  ADS  Google Scholar 

  30. I. Gatare, M. Sciamanna, A. Locquet, K. Panajotov, Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers. Opt. Lett. 32(12), 1629–1631 (2007)

    Article  ADS  Google Scholar 

  31. N. Jiang, W. Pan, B. Luo, S.Y. Xiang, L. Yang, Bidirectional dual-channel communication based on polarization-division-multiplexed chaos synchronization in mutually coupled VCSELs. IEEE Photon. Technol. Lett. 24(13), 1094–1096 (2012)

    Article  ADS  Google Scholar 

  32. S.Y. Xiang, W. Pan, B. Luo, L.S. Yan, X.H. Zou, N.Q. Li, Influence of variable-polarization optical feedback on polarization switching properties of mutually coupled VCSELs. IEEE J. Sel. Top. Quantum Electron. 19(4), 1700108 (2013)

    Article  ADS  Google Scholar 

  33. J.F. Liao, J.Q. Sun, Polarization dynamics and chaotic synchronization in unidirectionally coupled VCSELs subjected to optoelectronic feedback. Opt. Commun. 295(15), 188–196 (2013)

    Article  ADS  Google Scholar 

  34. H. Zhang, S.Y. Xiang, Y.H. Zhang, X.X. Guo, Complexity-enhanced polarization- resolved chaos in a ring network of mutually coupled vertical-cavity surface-emitting lasers with multiple delays. Appl. Opt. 56(24), 6728–6734 (2017)

    Article  ADS  Google Scholar 

  35. T. Deng, J. Robertson, A. Hurtado, Controlled propagation of spiking dynamics in vertical-cavity surface-emitting lasers: Towards neuromorphic photonic networks. IEEE J. Sel. Top. Quantum Electron. 23(6), 1800408 (2017)

    Article  Google Scholar 

  36. N.Q. Li, H. Susanto, B.R. Cemlyn, I.D. Henning, M.J. Adams, Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers. Phys. Rev. A 96(1), 013840 (2017)

    Article  ADS  Google Scholar 

  37. T. Deng, J. Robertson, Z.M. Wu, G.Q. Xia, X.D. Lin, X. Tang, Z.J. Wang, A. Hurtado, Stable propagation of inhibited spiking dynamics in vertical-cavity surface-emitting lasers for neuromorphic photonic networks. IEEE Access 6, 67951–67958 (2018)

    Article  Google Scholar 

  38. J. Vatin, D. Rontani, M. Sciamanna, Enhanced performance of a reservoir computer using polarization dynamics in VCSELs. Opt. Lett. 43(18), 4450–4497 (2018)

    Article  Google Scholar 

  39. Y.G. Yang, P. Zhou, P.H. Mu, N.Q. Li, Time-delayed reservoir computing based on an optically pumped spin VCSEL for high-speed processing. Nonlinear Dyn. 107, 2619–2632 (2022)

    Article  Google Scholar 

  40. L. Larger, M.C. Soriano, D. Brunner, L. Appeltant, J.M. Gutierrez, L. Pesquera, C.R. Mirasso, I. Fischer, Photonic information processing beyond turing: An optoelectronic implementation of reservoir computing. Opt. Express 20(3), 241–249 (2012)

    Article  Google Scholar 

  41. J. Vatin, D. Rontani, M. Sciamanna, Experimental realization of dual task processing with a photonic reservoir computer. APL Photonics 5(8), 086105 (2020)

    Article  ADS  Google Scholar 

  42. W.Y. Liang, L. Jiang, W.J. Song, X.H. Jia, Q.X. Deng, L.M. Liu, X. Zhang, Q.Y. Wang, Characteristic study on parallel reservoir computation based on VCSEL dynamics with optoelectronic feedback. IEEE J. Quantum Electron. 58(5), 2400608 (2022)

    Google Scholar 

  43. N.C. Gerhardt, M.R. Hofmann, Spin-controlled vertical-cavity surface-emitting lasers. Adv. Opt. Technol. 2012(1), 1–15 (2012)

    Article  Google Scholar 

  44. M. Holub, J. Shin, D. Saha, Electrical spin injection and threshold reduction in a semiconductor laser. Phys. Rev. Lett. 98(14), 146603 (2007)

    Article  ADS  Google Scholar 

  45. J. Rudolph, D. Hagele, Laser threshold reduction in a spintronic device. Appl. Phys. Lett.Phys. Lett. 82(25), 4516–4518 (2003)

    Article  ADS  Google Scholar 

  46. S. Hövel, N.C. Gerhardt, C. Brenner, M.R. Hofmann, F.Y. Lo, D. Reuter, A.D. Wieck, E. Schuster, W. Keune, Spin-controlled LEDs and VCSELs. Physica Status Solidi (A) 204(2), 500–507 (2007)

    Article  ADS  Google Scholar 

  47. S.S. Alharthi, A. Hurtado, V.M. Korpijarvi, M. Guina, I.D. Henning, M.J. Adams, Circular polarization switching and bistability in an optically injected 1300nm spin-vertical cavity surface emitting laser. Appl. Phys. Lett. 106(2), 021117 (2015)

    Article  ADS  Google Scholar 

  48. N.Q. Li, H. Susanto, B.R. Cemlyn, I.D. Henning, M.J. Adams, Secure communication systems based on chaos in optically-pumped spin-VCSELs. Opt. Lett. 42(17), 3494–3497 (2017)

    Article  ADS  Google Scholar 

  49. P. Xu, G.Q. Xia, Z.M. Wu, X.D. Lin, X. Tang, L. Fan, T. Deng, Circular polarization switching and polarization bistability of optically pumped 1300 nm spin vertical-cavity surface-emitting lasers. Chin. J. Lasers 45(4), 0401002 (2018)

    Article  Google Scholar 

  50. S. Alharthi, I. Henning, M. Adams, Control of emitted light polarization in a 1310 nm dilute nitride spin-vertical cavity surface emitting laser subject to circularly polarized optical injection. Appl. Phys. Lett. 105(18), 181106 (2014)

    Article  ADS  Google Scholar 

  51. B.R. Cemlyn, I.D. Henning, M.J. Adams, E. Harbord, R. Oulton, V.M. Korpijärvi, M. Guina, Polarization responses of a solitary and optically injected vertical cavity spin laser. IEEE J. Quantum Electron. 55(6), 1–9 (2019)

    Article  Google Scholar 

  52. M.S. Torre, H. Susanto, N.Q. Li, K. Schires, M.F. Salvide, I.D. Henning, M.J. Adams, A. Hurtado, High frequency continuous birefringence oscillations in spin-polarized vertical- cavity surface-emitting lasers. Opt. Lett. 42(8), 1628–1631 (2017)

    Article  ADS  Google Scholar 

  53. N. Yokota, K. Nisaka, H. Yasaka, K. Ikeda, Spin polarization modulation for high-speed vertical-cavity surface-emitting lasers. Appl. Phys. Lett.Phys. Lett. 113(17), 171102 (2018)

    Article  ADS  Google Scholar 

  54. M. Lindemann, G.F. Xu, T. Pusch, R. Michalzik, M.R. Hofmann, I. Žutić, N.C. Gerhardt, Ultrafast spin-lasers. Nature 568, 212–215 (2019)

    Article  ADS  Google Scholar 

  55. M. Lindemann, G.F. Xu, T. Pusch, R. Michalzik, M.R. Hofmann, I. Žutić, N.C. Gerhardt, Ultrafast spin-lasers for optical data communication. 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (2019)

  56. T.T. Song, Y.Y. Xie, Y.C. Ye, B.C. Liu, J.X. Chai, X. Jiang, Y.L. Zheng, Numerical analysis of nonlinear dynamics based on spin-VCSELs with optical feedback. Photonics 8(1), 10 (2021)

    Article  Google Scholar 

  57. K. Harkhoe, G. Verschaffelt, G. Van der Sande, High-speed neuromorphic computing using spin-controlled VCSELs. Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (2021)

  58. D.Z. Zhong, K.K. Zhao, Z. Xu, Y.L. Hu, W.A. Deng, P. Hou, J.B. Zhang, J.M. Zhang, Deep optical reservoir computing and chaotic synchronization predictions based on the cascade coupled optically pumped spin-VCSELs. Opt. Express 30(20), 36209–36233 (2022)

    Article  ADS  Google Scholar 

  59. X.S. Tan, Y.S. Hou, Z.M. Wu, G.Q. Xia, Parallel information processing by a reservoir computing system based on a VCSEL subject to double optical feedback and optical injection. Opt. Express 27(18), 26070–26079 (2019)

    Article  ADS  Google Scholar 

  60. X.X. Guo, S.Y. Xiang, Y.H. Zhang, L. Lin, A.J. Wen, Y. Hao, Four-channels reservoir computing based on polarization dynamics in mutually coupled VCSELs system. Opt. Express 27(16), 23293–23306 (2019)

    Article  ADS  Google Scholar 

  61. F. Duport, B. Schneider, A. Smerieri, M. Haelterman, S. Massar, All-optical reservoir computing. Opt. Express 20(20), 22783–22795 (2012)

    Article  ADS  Google Scholar 

  62. X.X. Guo, S.Y. Xiang, Y.H. Zhang, L. Lin, A.J. Wen, Y. Hao, Polarization multiplexing reservoir computing based on a VCSEL with polarized optical feedback. IEEE J. Sel. Top. Quantum Electron. 26(1), 1700109 (2019)

    Google Scholar 

  63. A. Hurtado, D. Labukhin, I.D. Henning, M.J. Adams, Injection locking bandwidth in 1550-nm VCSELs subject to parallel and orthogonal optical injection. IEEE J. Sel. Top. Quantum Electron. 15(3), 585–593 (2009)

    Article  ADS  Google Scholar 

  64. K.H. Sun, X. Liu, C.X. Zhu, The 0–1 test algorithm for chaos and its applications. Chin. Phys. B 11(9), 110510 (2010)

    Article  Google Scholar 

  65. B. Krese, E. Govekar, Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos. Nonlinear Dyn. 67(3), 2101–2109 (2011)

    Article  Google Scholar 

  66. P. Pérez, A. Valle, L. Pesquera, Polarization-resolved characterization of long-wavelength vertical-cavity surface-emitting laser parameters. J. Opt. Soc. Am. B 31(11), 2574–2580 (2014)

    Article  ADS  Google Scholar 

  67. B. Cemlyn, M. Adams, E. Harbord, N.Q. Li, I. Henning, R. Oulton, V.M. Korpijärvi, M. Guina, Near-threshold high spin amplification in a 1300 nm GaInNAs spin laser. Semicond. Sci. Tech. 33(9), 094005 (2018)

    Article  ADS  Google Scholar 

Download references

Funding

Natural Science Foundation of Sichuan, China, 24NSFSC2164, National Natural Science Foundation of China (NSFC), 61205079.

Author information

Author notes

  1. Li Jiang and Sha-Sha Deng have contributed equally to this work.

Authors and Affiliations

  1. School of Physics and Electronic Engineering, Sichuan Normal University, Chengdu, 610101, China

    Li Jiang, Sha-Sha Deng, Wei-Jie Song, Mei-Ling Zou, Xin-Hong Jia, Yu-Quan Tang, Ming-Yu Bao & Jiang-Tao Lv

Authors
  1. Li Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sha-Sha Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei-Jie Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mei-Ling Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xin-Hong Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yu-Quan Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Ming-Yu Bao
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Jiang-Tao Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Li Jiang and Sha-Sha Deng conducted the modeling and simulation and wrote the manuscript. Xin-Hong Jia fully supervised the research and revised the manuscript. All authors conducted investigation and reviewed the manuscript.

Corresponding author

Correspondence to Xin-Hong Jia.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, L., Deng, SS., Song, WJ. et al. Characteristics of multi-channel reservoir computing based on mutually-coupled spin-VCSELs: a comprehensive investigation. Appl. Phys. B 130, 75 (2024). https://doi.org/10.1007/s00340-024-08217-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00340-024-08217-w

Search

Navigation