Abstract

A novel Four-channels reservoir computing (RC) based on polarization dynamics in mutually coupled vertical cavity surface emitting lasers (MDC-VCSELs) is proposed and demonstrated numerically. Here, the four channels are realized in two orthogonal polarization modes (x-polarization and y-polarization modes) of two VCSELs for the first time. A chaotic time series prediction task is employed to quantitatively evaluated the prediction performance of the proposed system. It is found that the Four-channels RC based on MDC-VCSELs can produce comparable prediction performance with One-channel RC, and it is possible to increase four times information processing rate by using the Four-channels RC. Besides, the effects of injection current, external injection strength, frequency detuning, coupling strength, as well as internal parameters on the prediction performance of the Four-channels RC based on MDC-VCSELs are carefully examined. Moreover, the influences of sampled period of input signal and the number of virtual nodes are also considered. The proposed Four-channels RC based on MDC-VCSELs is valuable for further enhancing the information processing rate of RC-based neuromorphic photonic systems.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Parallel information processing by a reservoir computing system based on a VCSEL subject to double optical feedback and optical injection

XiangSheng Tan, YuShuang Hou, ZhengMao Wu, and GuangQiong Xia
Opt. Express 27(18) 26070-26079 (2019)

Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection

YuShuang Hou, GuangQiong Xia, WenYan Yang, Dan Wang, Elumalai Jayaprasath, ZaiFu Jiang, ChunXia Hu, and ZhengMao Wu
Opt. Express 26(8) 10211-10219 (2018)

Performance optimization research of reservoir computing system based on an optical feedback semiconductor laser under electrical information injection

DianZuo Yue, ZhengMao Wu, YuShuang Hou, Bing Cui, YanHong Jin, Min Dai, and GuangQiong Xia
Opt. Express 27(14) 19931-19939 (2019)

References

  • View by:
  • |
  • |
  • |

  1. H. Jaeger and H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304(5667), 78–80 (2004).
    [Crossref] [PubMed]
  2. H. Jaeger, W. Maass, and J. Principe, “Special issue on echo state networks and liquid state machines,” Neural Netw. 20(3), 287–289 (2007).
    [Crossref] [PubMed]
  3. D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. Van Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95(6), 521–528 (2005).
    [Crossref]
  4. D. Verstraeten, B. Schrauwen, and D. Stroobandt, “Reservoir-based techniques for speech recognition,” in Proceedings of IJCNN06, International Joint Conference on Neural Networks, ed. (Academic), 1050–1053 (2006).
  5. L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
    [Crossref] [PubMed]
  6. Q. Vinckier, F. Duport, A. Smerieri, K. Vandoorne, P. Bienstman, M. Haelterman, and S. Massar, “High-performance photonic reservoir computer based on a coherently driven passive cavity,” Optica 2(5), 438–446 (2015).
    [Crossref]
  7. M. Lukoševičius, H. Jaeger, and B. Schrauwen, “Reservoir computing trends,” Künstl. Intell 26(4), 365–371 (2012).
  8. M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3(3), 127–149 (2009).
    [Crossref]
  9. C. Du, F. Cai, M. A. Zidan, W. Ma, S. H. Lee, and W. D. Lu, “Reservoir computing using dynamic memristors for temporal information processing,” Nat. Commun. 8(1), 2204 (2017).
    [Crossref] [PubMed]
  10. J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, “Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach,” Phys. Rev. Lett. 120(2), 024102 (2018).
    [Crossref] [PubMed]
  11. D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Netw. 20(3), 391–403 (2007).
    [Crossref] [PubMed]
  12. K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
    [Crossref] [PubMed]
  13. B. Schneider, J. Dambre, and P. Bienstman, “Using digital masks to enhance the bandwidth tolerance and improve the performance of on-chip reservoir computing systems,” IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2748–2753 (2016).
    [Crossref] [PubMed]
  14. Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
    [Crossref] [PubMed]
  15. M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, and L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21(1), 12–20 (2013).
    [Crossref] [PubMed]
  16. A. Dejonckheere, F. Duport, A. Smerieri, L. Fang, J. L. Oudar, M. Haelterman, and S. Massar, “All-optical reservoir computer based on saturation of absorption,” Opt. Express 22(9), 10868–10881 (2014).
    [Crossref] [PubMed]
  17. D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
    [Crossref] [PubMed]
  18. R. M. Nguimdo, E. Lacot, O. Jacquin, O. Hugon, G. Van der Sande, and H. Guillet de Chatellus, “Prediction performance of reservoir computing systems based on a diode-pumped erbium-doped microchip laser subject to optical feedback,” Opt. Lett. 42(3), 375–378 (2017).
    [Crossref] [PubMed]
  19. J. Nakayama, K. Kanno, and A. Uchida, “Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal,” Opt. Express 24(8), 8679–8692 (2016).
    [Crossref] [PubMed]
  20. J. Bueno, D. Brunner, M. C. Soriano, and I. Fischer, “Conditions for reservoir computing performance using semiconductor lasers with delayed optical feedback,” Opt. Express 25(3), 2401–2412 (2017).
    [Crossref] [PubMed]
  21. R. M. Nguimdo, E. Lacot, O. Jacquin, O. Hugon, G. Van der Sande, and H. Guillet de Chatellus, “Prediction performance of reservoir computing systems based on a diode-pumped erbium-doped microchip laser subject to optical feedback,” Opt. Lett. 42(3), 375–378 (2017).
    [Crossref] [PubMed]
  22. Y. Hou, G. Xia, W. Yang, D. Wang, E. Jayaprasath, Z. Jiang, C. Hu, and Z. 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).
    [Crossref] [PubMed]
  23. J. Vatin, D. Rontani, and M. Sciamanna, “Enhanced performance of a reservoir computer using polarization dynamics in VCSELs,” Opt. Lett. 43(18), 4497–4500 (2018).
    [Crossref] [PubMed]
  24. R. M. Nguimdo and T. Erneux, “Enhanced performances of a photonic reservoir computer based on a single delayed quantum cascade laser,” Opt. Lett. 44(1), 49–52 (2019).
    [Crossref] [PubMed]
  25. Y. S. Hou, G. Q. Xia, E. Jayaprasath, D. Z. Yue, W. Y. Yang, and Z. M. Wu, “Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers,” Opt. Commun. 433(15), 215–220 (2019).
    [Crossref]
  26. S. Ortín and L. Pesquera, “Reservoir computing with an ensemble of time-delay reservoirs,” Cognit. Comput. 9(3), 327–336 (2017).
    [Crossref]
  27. L. Keuninckx, J. Danckaert, and G. Van der Sande, “Real-time audio processing with a cascade of discrete-time delay line-based reservoir computers,” Cognit. Comput. 9(3), 315–326 (2017).
    [Crossref]
  28. F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. 24(12), 4502–4513 (2006).
    [Crossref]
  29. R. Michalzik, VCSELs: Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers (Springer-Verlag, 2013).
  30. S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and 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).
    [Crossref]
  31. H. Zhang, S. Xiang, Y. Zhang, and 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).
    [Crossref] [PubMed]
  32. N. Jiang, W. Pan, B. Luo, S. Y. Xiang, and L. Yang, “Bidirectional dual-channel communication based on polarization-division-multiplexed chaos synchronization in mutually coupled VCSELs,” IEEE Photonics Technol. Lett. 24(13), 1094–1096 (2012).
    [Crossref]
  33. T. Deng, J. Robertson, and 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).
    [Crossref]
  34. N. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A (Coll. Park) 96(1), 013840 (2017).
    [Crossref]
  35. T. Deng, J. Robertson, Z. Wu, G. Xia, X. Lin, X. Tang, Z. Wang, and A. Hurtado, “Stable propagation of inhibited spiking dynamics in vertical-cavity surface-emitting lasers for neuromorphic photonic networks,” IEEE Access 6, 67951–67958 (2018).
    [Crossref]
  36. J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
    [Crossref]
  37. C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59(4), 3021–3031 (1999).
    [Crossref]
  38. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and 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).
    [Crossref] [PubMed]
  39. A. S. Weigend and N. A. Gershenfeld, “Time series prediction: Forecasting the future and understanding the past,” http://www-psych.stanford.edu/~andreas/Time-Series/SantaFe.html (1993).
  40. K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
    [Crossref]
  41. A. Hurtado, D. Labukhin, I. D. Henning, and 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).
    [Crossref]

2019 (2)

R. M. Nguimdo and T. Erneux, “Enhanced performances of a photonic reservoir computer based on a single delayed quantum cascade laser,” Opt. Lett. 44(1), 49–52 (2019).
[Crossref] [PubMed]

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

2018 (4)

Y. Hou, G. Xia, W. Yang, D. Wang, E. Jayaprasath, Z. Jiang, C. Hu, and Z. 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).
[Crossref] [PubMed]

J. Vatin, D. Rontani, and M. Sciamanna, “Enhanced performance of a reservoir computer using polarization dynamics in VCSELs,” Opt. Lett. 43(18), 4497–4500 (2018).
[Crossref] [PubMed]

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

J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, “Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach,” Phys. Rev. Lett. 120(2), 024102 (2018).
[Crossref] [PubMed]

2017 (9)

C. Du, F. Cai, M. A. Zidan, W. Ma, S. H. Lee, and W. D. Lu, “Reservoir computing using dynamic memristors for temporal information processing,” Nat. Commun. 8(1), 2204 (2017).
[Crossref] [PubMed]

R. M. Nguimdo, E. Lacot, O. Jacquin, O. Hugon, G. Van der Sande, and H. Guillet de Chatellus, “Prediction performance of reservoir computing systems based on a diode-pumped erbium-doped microchip laser subject to optical feedback,” Opt. Lett. 42(3), 375–378 (2017).
[Crossref] [PubMed]

T. Deng, J. Robertson, and 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).
[Crossref]

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

H. Zhang, S. Xiang, Y. Zhang, and 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).
[Crossref] [PubMed]

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

R. M. Nguimdo, E. Lacot, O. Jacquin, O. Hugon, G. Van der Sande, and H. Guillet de Chatellus, “Prediction performance of reservoir computing systems based on a diode-pumped erbium-doped microchip laser subject to optical feedback,” Opt. Lett. 42(3), 375–378 (2017).
[Crossref] [PubMed]

S. Ortín and L. Pesquera, “Reservoir computing with an ensemble of time-delay reservoirs,” Cognit. Comput. 9(3), 327–336 (2017).
[Crossref]

L. Keuninckx, J. Danckaert, and G. Van der Sande, “Real-time audio processing with a cascade of discrete-time delay line-based reservoir computers,” Cognit. Comput. 9(3), 315–326 (2017).
[Crossref]

2016 (2)

J. Nakayama, K. Kanno, and A. Uchida, “Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal,” Opt. Express 24(8), 8679–8692 (2016).
[Crossref] [PubMed]

B. Schneider, J. Dambre, and P. Bienstman, “Using digital masks to enhance the bandwidth tolerance and improve the performance of on-chip reservoir computing systems,” IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2748–2753 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (3)

2013 (4)

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref] [PubMed]

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, and L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21(1), 12–20 (2013).
[Crossref] [PubMed]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and 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).
[Crossref]

2012 (3)

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

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref] [PubMed]

M. Lukoševičius, H. Jaeger, and B. Schrauwen, “Reservoir computing trends,” Künstl. Intell 26(4), 365–371 (2012).

2011 (1)

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref] [PubMed]

2009 (2)

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3(3), 127–149 (2009).
[Crossref]

A. Hurtado, D. Labukhin, I. D. Henning, and 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).
[Crossref]

2007 (2)

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Netw. 20(3), 391–403 (2007).
[Crossref] [PubMed]

H. Jaeger, W. Maass, and J. Principe, “Special issue on echo state networks and liquid state machines,” Neural Netw. 20(3), 287–289 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (1)

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. Van Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95(6), 521–528 (2005).
[Crossref]

2004 (1)

H. Jaeger and H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304(5667), 78–80 (2004).
[Crossref] [PubMed]

1999 (1)

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59(4), 3021–3031 (1999).
[Crossref]

1997 (1)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

Abraham, N. B.

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59(4), 3021–3031 (1999).
[Crossref]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

Adams, M. J.

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

A. Hurtado, D. Labukhin, I. D. Henning, and 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).
[Crossref]

Appeltant, L.

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref] [PubMed]

Bienstman, P.

B. Schneider, J. Dambre, and P. Bienstman, “Using digital masks to enhance the bandwidth tolerance and improve the performance of on-chip reservoir computing systems,” IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2748–2753 (2016).
[Crossref] [PubMed]

Q. Vinckier, F. Duport, A. Smerieri, K. Vandoorne, P. Bienstman, M. Haelterman, and S. Massar, “High-performance photonic reservoir computer based on a coherently driven passive cavity,” Optica 2(5), 438–446 (2015).
[Crossref]

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
[Crossref] [PubMed]

Brunner, D.

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

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, and L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21(1), 12–20 (2013).
[Crossref] [PubMed]

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref] [PubMed]

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

Bueno, J.

Cai, F.

C. Du, F. Cai, M. A. Zidan, W. Ma, S. H. Lee, and W. D. Lu, “Reservoir computing using dynamic memristors for temporal information processing,” Nat. Commun. 8(1), 2204 (2017).
[Crossref] [PubMed]

Cemlyn, B. R.

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

D’Haene, M.

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Netw. 20(3), 391–403 (2007).
[Crossref] [PubMed]

Dambre, J.

B. Schneider, J. Dambre, and P. Bienstman, “Using digital masks to enhance the bandwidth tolerance and improve the performance of on-chip reservoir computing systems,” IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2748–2753 (2016).
[Crossref] [PubMed]

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
[Crossref] [PubMed]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref] [PubMed]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref] [PubMed]

Danckaert, J.

L. Keuninckx, J. Danckaert, and G. Van der Sande, “Real-time audio processing with a cascade of discrete-time delay line-based reservoir computers,” Cognit. Comput. 9(3), 315–326 (2017).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and 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).
[Crossref] [PubMed]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref] [PubMed]

Dejonckheere, A.

Deng, T.

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

T. Deng, J. Robertson, and 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).
[Crossref]

Du, C.

C. Du, F. Cai, M. A. Zidan, W. Ma, S. H. Lee, and W. D. Lu, “Reservoir computing using dynamic memristors for temporal information processing,” Nat. Commun. 8(1), 2204 (2017).
[Crossref] [PubMed]

Duport, F.

Erneux, T.

Escalona-Morán, M. A.

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

Fang, L.

Fiers, M.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
[Crossref] [PubMed]

Fischer, I.

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

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, and L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21(1), 12–20 (2013).
[Crossref] [PubMed]

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref] [PubMed]

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref] [PubMed]

Girvan, M.

J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, “Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach,” Phys. Rev. Lett. 120(2), 024102 (2018).
[Crossref] [PubMed]

Guillet de Chatellus, H.

Guo, X.

Haas, H.

H. Jaeger and H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304(5667), 78–80 (2004).
[Crossref] [PubMed]

Haelterman, M.

Henning, I. D.

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

A. Hurtado, D. Labukhin, I. D. Henning, and 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).
[Crossref]

Hicke, K.

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

Hou, Y.

Hou, Y. S.

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

Hu, C.

Hugon, O.

Hunt, B.

J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, “Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach,” Phys. Rev. Lett. 120(2), 024102 (2018).
[Crossref] [PubMed]

Hurtado, A.

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

T. Deng, J. Robertson, and 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).
[Crossref]

A. Hurtado, D. Labukhin, I. D. Henning, and 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).
[Crossref]

Jacquin, O.

Jaeger, H.

M. Lukoševičius, H. Jaeger, and B. Schrauwen, “Reservoir computing trends,” Künstl. Intell 26(4), 365–371 (2012).

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3(3), 127–149 (2009).
[Crossref]

H. Jaeger, W. Maass, and J. Principe, “Special issue on echo state networks and liquid state machines,” Neural Netw. 20(3), 287–289 (2007).
[Crossref] [PubMed]

H. Jaeger and H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304(5667), 78–80 (2004).
[Crossref] [PubMed]

Jayaprasath, E.

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

Y. Hou, G. Xia, W. Yang, D. Wang, E. Jayaprasath, Z. Jiang, C. Hu, and Z. 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).
[Crossref] [PubMed]

Jiang, N.

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

Jiang, Z.

Kanno, K.

Keuninckx, L.

L. Keuninckx, J. Danckaert, and G. Van der Sande, “Real-time audio processing with a cascade of discrete-time delay line-based reservoir computers,” Cognit. Comput. 9(3), 315–326 (2017).
[Crossref]

Koyama, F.

Labukhin, D.

A. Hurtado, D. Labukhin, I. D. Henning, and 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).
[Crossref]

Lacot, E.

Larger, L.

Lee, S. H.

C. Du, F. Cai, M. A. Zidan, W. Ma, S. H. Lee, and W. D. Lu, “Reservoir computing using dynamic memristors for temporal information processing,” Nat. Commun. 8(1), 2204 (2017).
[Crossref] [PubMed]

Li, N.

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

Li, N. Q.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and 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).
[Crossref]

Lin, X.

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

Lu, W. D.

C. Du, F. Cai, M. A. Zidan, W. Ma, S. H. Lee, and W. D. Lu, “Reservoir computing using dynamic memristors for temporal information processing,” Nat. Commun. 8(1), 2204 (2017).
[Crossref] [PubMed]

Lu, Z.

J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, “Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach,” Phys. Rev. Lett. 120(2), 024102 (2018).
[Crossref] [PubMed]

Lukoševicius, M.

M. Lukoševičius, H. Jaeger, and B. Schrauwen, “Reservoir computing trends,” Künstl. Intell 26(4), 365–371 (2012).

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3(3), 127–149 (2009).
[Crossref]

Luo, B.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and 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).
[Crossref]

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

Ma, W.

C. Du, F. Cai, M. A. Zidan, W. Ma, S. H. Lee, and W. D. Lu, “Reservoir computing using dynamic memristors for temporal information processing,” Nat. Commun. 8(1), 2204 (2017).
[Crossref] [PubMed]

Maass, W.

H. Jaeger, W. Maass, and J. Principe, “Special issue on echo state networks and liquid state machines,” Neural Netw. 20(3), 287–289 (2007).
[Crossref] [PubMed]

Martin-Regalado, J.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

Masoller, C.

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59(4), 3021–3031 (1999).
[Crossref]

Massar, S.

Q. Vinckier, F. Duport, A. Smerieri, K. Vandoorne, P. Bienstman, M. Haelterman, and S. Massar, “High-performance photonic reservoir computer based on a coherently driven passive cavity,” Optica 2(5), 438–446 (2015).
[Crossref]

A. Dejonckheere, F. Duport, A. Smerieri, L. Fang, J. L. Oudar, M. Haelterman, and S. Massar, “All-optical reservoir computer based on saturation of absorption,” Opt. Express 22(9), 10868–10881 (2014).
[Crossref] [PubMed]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref] [PubMed]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref] [PubMed]

Mechet, P.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
[Crossref] [PubMed]

Mirasso, C. R.

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref] [PubMed]

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, and L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21(1), 12–20 (2013).
[Crossref] [PubMed]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref] [PubMed]

Morthier, G.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
[Crossref] [PubMed]

Nakayama, J.

Nguimdo, R. M.

Ortín, S.

Ott, E.

J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, “Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach,” Phys. Rev. Lett. 120(2), 024102 (2018).
[Crossref] [PubMed]

Oudar, J. L.

Pan, W.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and 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).
[Crossref]

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

Paquot, Y.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref] [PubMed]

Pathak, J.

J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, “Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach,” Phys. Rev. Lett. 120(2), 024102 (2018).
[Crossref] [PubMed]

Pesquera, L.

Prati, F.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

Principe, J.

H. Jaeger, W. Maass, and J. Principe, “Special issue on echo state networks and liquid state machines,” Neural Netw. 20(3), 287–289 (2007).
[Crossref] [PubMed]

Robertson, J.

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

T. Deng, J. Robertson, and 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).
[Crossref]

Rontani, D.

San Miguel, M.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

Schneider, B.

B. Schneider, J. Dambre, and P. Bienstman, “Using digital masks to enhance the bandwidth tolerance and improve the performance of on-chip reservoir computing systems,” IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2748–2753 (2016).
[Crossref] [PubMed]

Schrauwen, B.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
[Crossref] [PubMed]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref] [PubMed]

M. Lukoševičius, H. Jaeger, and B. Schrauwen, “Reservoir computing trends,” Künstl. Intell 26(4), 365–371 (2012).

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref] [PubMed]

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Netw. 20(3), 391–403 (2007).
[Crossref] [PubMed]

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. Van Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95(6), 521–528 (2005).
[Crossref]

Sciamanna, M.

Smerieri, A.

Soriano, M. C.

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

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, and L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21(1), 12–20 (2013).
[Crossref] [PubMed]

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref] [PubMed]

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref] [PubMed]

Stroobandt, D.

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Netw. 20(3), 391–403 (2007).
[Crossref] [PubMed]

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. Van Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95(6), 521–528 (2005).
[Crossref]

Susanto, H.

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

Tang, X.

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

Uchida, A.

Van Campenhout, J.

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. Van Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95(6), 521–528 (2005).
[Crossref]

Van der Sande, G.

Van Vaerenbergh, T.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
[Crossref] [PubMed]

Vandoorne, K.

Q. Vinckier, F. Duport, A. Smerieri, K. Vandoorne, P. Bienstman, M. Haelterman, and S. Massar, “High-performance photonic reservoir computer based on a coherently driven passive cavity,” Optica 2(5), 438–446 (2015).
[Crossref]

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
[Crossref] [PubMed]

Vatin, J.

Verschaffelt, G.

Verstraeten, D.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
[Crossref] [PubMed]

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Netw. 20(3), 391–403 (2007).
[Crossref] [PubMed]

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. Van Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95(6), 521–528 (2005).
[Crossref]

Vinckier, Q.

Wang, D.

Wang, Z.

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

Wu, Z.

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

Y. Hou, G. Xia, W. Yang, D. Wang, E. Jayaprasath, Z. Jiang, C. Hu, and Z. 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).
[Crossref] [PubMed]

Wu, Z. M.

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

Xia, G.

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

Y. Hou, G. Xia, W. Yang, D. Wang, E. Jayaprasath, Z. Jiang, C. Hu, and Z. 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).
[Crossref] [PubMed]

Xia, G. Q.

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

Xiang, S.

Xiang, S. Y.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and 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).
[Crossref]

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

Yan, L. S.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and 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).
[Crossref]

Yang, L.

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

Yang, W.

Yang, W. Y.

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

Yue, D. Z.

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

Zhang, H.

Zhang, Y.

Zidan, M. A.

C. Du, F. Cai, M. A. Zidan, W. Ma, S. H. Lee, and W. D. Lu, “Reservoir computing using dynamic memristors for temporal information processing,” Nat. Commun. 8(1), 2204 (2017).
[Crossref] [PubMed]

Zou, X. H.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and 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).
[Crossref]

Appl. Opt. (1)

Cognit. Comput. (2)

S. Ortín and L. Pesquera, “Reservoir computing with an ensemble of time-delay reservoirs,” Cognit. Comput. 9(3), 327–336 (2017).
[Crossref]

L. Keuninckx, J. Danckaert, and G. Van der Sande, “Real-time audio processing with a cascade of discrete-time delay line-based reservoir computers,” Cognit. Comput. 9(3), 315–326 (2017).
[Crossref]

Comput. Sci. Rev. (1)

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3(3), 127–149 (2009).
[Crossref]

IEEE Access (1)

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

IEEE J. Quantum Electron. (1)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (4)

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

A. Hurtado, D. Labukhin, I. D. Henning, and 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).
[Crossref]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and 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).
[Crossref]

T. Deng, J. Robertson, and 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).
[Crossref]

IEEE Photonics Technol. Lett. (1)

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

IEEE Trans. Neural Netw. Learn. Syst. (1)

B. Schneider, J. Dambre, and P. Bienstman, “Using digital masks to enhance the bandwidth tolerance and improve the performance of on-chip reservoir computing systems,” IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2748–2753 (2016).
[Crossref] [PubMed]

Inf. Process. Lett. (1)

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. Van Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95(6), 521–528 (2005).
[Crossref]

J. Lightwave Technol. (1)

Künstl. Intell (1)

M. Lukoševičius, H. Jaeger, and B. Schrauwen, “Reservoir computing trends,” Künstl. Intell 26(4), 365–371 (2012).

Nat. Commun. (4)

C. Du, F. Cai, M. A. Zidan, W. Ma, S. H. Lee, and W. D. Lu, “Reservoir computing using dynamic memristors for temporal information processing,” Nat. Commun. 8(1), 2204 (2017).
[Crossref] [PubMed]

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
[Crossref] [PubMed]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref] [PubMed]

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref] [PubMed]

Neural Netw. (2)

H. Jaeger, W. Maass, and J. Principe, “Special issue on echo state networks and liquid state machines,” Neural Netw. 20(3), 287–289 (2007).
[Crossref] [PubMed]

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Netw. 20(3), 391–403 (2007).
[Crossref] [PubMed]

Opt. Commun. (1)

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

Opt. Express (6)

Opt. Lett. (4)

Optica (1)

Phys. Rev. A (1)

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59(4), 3021–3031 (1999).
[Crossref]

Phys. Rev. A (Coll. Park) (1)

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

Phys. Rev. Lett. (1)

J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, “Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach,” Phys. Rev. Lett. 120(2), 024102 (2018).
[Crossref] [PubMed]

Sci. Rep. (1)

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref] [PubMed]

Science (1)

H. Jaeger and H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304(5667), 78–80 (2004).
[Crossref] [PubMed]

Other (3)

D. Verstraeten, B. Schrauwen, and D. Stroobandt, “Reservoir-based techniques for speech recognition,” in Proceedings of IJCNN06, International Joint Conference on Neural Networks, ed. (Academic), 1050–1053 (2006).

R. Michalzik, VCSELs: Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers (Springer-Verlag, 2013).

A. S. Weigend and N. A. Gershenfeld, “Time series prediction: Forecasting the future and understanding the past,” http://www-psych.stanford.edu/~andreas/Time-Series/SantaFe.html (1993).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1 System design and operation principle diagram of the Four-channels RC based on MDC-VCSELs with three layers: input layer, reservoir and output layer. VCSEL: vertical cavity surface emitting laser, MZMs: Mach–Zehnder modulators, the pink lines indicate the electric path and the black lines represent the optical path.
Fig. 2
Fig. 2 The virtual node states matrix for each channel.
Fig. 3
Fig. 3 The polarization-resolved intensities as a function of the normalized injection current μ for free-running VCSEL.
Fig. 4
Fig. 4 Numerical bifurcation diagrams as a function of μ for (the first column) VCSEL1 and (the second column) VCSEL2, for (a1, a2) XP mode, for (b1, b2) YP mode, with k r =10ns 1 and k inj =30 ns -1 .
Fig. 5
Fig. 5 The NMSE values of RC system based on MDC-VCSELs as a function of μ for Four-channels RC with Z=20 and R 4 =2Gbps, for One-channel RC with Z=80and R 1 =0.5Gbps, with k r =10ns 1 and k inj =30 ns -1 .
Fig. 6
Fig. 6 The transient responses of the XP and YP modes of Four-channels RC based on MDC-VCSELs, with k inj =30 ns -1 , k d =10 ns -1 and μ=1.2.
Fig. 7
Fig. 7 Two dimensional maps of the NMSE values of Four-channels RC system based on MDC-VCSELs in the parameter space of Δ f and k inj ,with μ=1.01. (a1, a2, a3) for k r =5 ns -1 , k r =10 ns -1 , k r =20 ns -1 with Δ f 12 =0GHz; (b1, b2, b3) for k r =5 ns -1 , k r =10 ns -1 , k r =20 ns -1 with Δ f 12 =5GHz.
Fig. 8
Fig. 8 Two dimensional maps of the NMSE values of Four-channels RC system based on MDC-VCSELs in the parameter space of k r and k inj ,with μ=1.01and Δ f 12 =0. (a) for Δf=15GHz, (b) for Δf=0GHz, (c) Δ f =15GHz.
Fig. 9
Fig. 9 The NMSE values of Four-channels RC system based on MDC-VCSELs as a function of the k r for different k inj , with Δ f =0and Δ f 12 =0, (a) for μ=1.01, (b) for μ=1.2, (c) for μ=1.5.
Fig. 10
Fig. 10 The NMSE values of Four-channels RC system based on MDC-VCSELs as a function of k r for different internal parameters with μ=1.01, k inj =30 ns -1 , Δ f 12 =0, Δ f =0,, (a) for γ a =0.1 ns -1 ,0.1 ns -1 ,1 ns -1 , (b) for γ p =3 ns -1 ,6 ns -1 ,10 ns -1 .
Fig. 11
Fig. 11 The NMSE values of Four-channels RC system based on MDC-VCSELs as a function of the T for different θfor (a) τ=T, (b) τ=0.5ns, (c) τ=10ns, with μ=1.01, k inj =30 ns -1 , k r =10 ns -1 , Δ f 12 =0, Δf=0.
Fig. 12
Fig. 12 The NMSE values of Four-channels RC system based on MDC-VCSELs as a function of Z for T=Zθ= τ =0 .05ns with μ=1.01, k inj =30 ns -1 , k r =10 ns -1 , Δ f 12 =0, Δf=0.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

d E 1x dt =κ(1+iα)( N 1 E 1x E 1x +i n 1 E 1 y )( γ a +i γ p ) E 1 x + k 21x E 2x (t τ 21 ) e i ω 2 τ 21 e iΔ ω 21 t + k inj1x ε 1x (t)+ F 1x
d E 1y dt =κ(1+iα)( N 1 E 1y E 1y i n 1 E 1x )+( γ a +i γ p ) E 1y + k 21y E 2y (t τ 21 ) e i ω 2 τ 21 e iΔ ω 21 t + k inj1y ε 1y (t)+ F 1y
d E 2x dt =κ(1+iα)( N 2 E 2x E 2x +i n 2 E 2y )( γ a +i γ p ) E 2x + k 12x E 1x (t τ 12 ) e i ω 1 τ 12 e iΔ ω 12 t + k inj2x ε 2x (t)+ F 2x
d E 2y dt =κ(1+iα)( N 2 E 2y E 2y i n 2 E 2x )+( γ a +i γ p ) E 2y + k 21y E 1y (t τ 12 ) e i ω 1 τ 12 e iΔ ω 12 t + k inj2y ε 2y (t)+ F 2y
d n 1,2 dt = γ s n 1,2 γ N [ n 1,2 (| E 1x,2x | 2 +| E 1y,2y | 2 ) +i N 1,2 ( E 1y,2y E 1x,2x * E 1x,2x E 1y,2y * )]
d N 1,2 dt = γ N [ μ 1,2 N 1,2 (1+| E 1x,2x | 2 +| E 1y,2y | 2 ) +i n 1,2 ( E 1x,2x E 1y,2y * E 1y,2y E 1x,2x * )],
ε 1x,1y,2x,2y (t)= | ε 0 | 2 e iΔ ω 1x,1y,2x,2y t {1+ e i[ s 1x,1y,2x,2y (t)+ Φ 0 ] },
NMSE= Y( L ) Y ¯ (L) 2 σ 2

Metrics