Abstract

We numerically investigate reservoir computing based on the consistency of a semiconductor laser subjected to optical feedback and injection. We introduce a chaos mask signal as an input temporal mask for reservoir computing and perform a time-series prediction task. We compare the errors of the task obtained from the chaos mask signal with those obtained from other digital and analog masks. The performance of the prediction task can be improved by using the chaos mask signal due to complex dynamical response.

© 2016 Optical Society of America

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References

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  1. H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4(5), 261–263 (2010).
    [Crossref]
  2. B. A. Pearlmutter, “Gradient calculations for dynamic recurrent neural networks: a survey,” IEEE Trans. Neural Netw. 6(5), 1212–1228 (1995).
    [Crossref] [PubMed]
  3. W. Maass, T. Natschläger, and H. Markram, “Real-time computing without stable states: a new framework for neural computation based on perturbations,” Neural Comput. 14(11), 2531–2560 (2002).
    [Crossref] [PubMed]
  4. H. Jaeger and H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304(5667), 78–80 (2004).
    [Crossref] [PubMed]
  5. M. C. Soriano, D. Brunner, M. Escalona-Morán, C. R. Mirasso, and I. Fischer, “Minimal approach to neuro-inspired information processing,” Front. Comput. Neurosci. 9(68), 68 (2015).
    [PubMed]
  6. K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, and J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16(15), 11182–11192 (2008).
    [Crossref] [PubMed]
  7. K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
    [Crossref] [PubMed]
  8. 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, 3541 (2014).
    [Crossref] [PubMed]
  9. 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, 468 (2011).
    [Crossref] [PubMed]
  10. L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
    [Crossref] [PubMed]
  11. Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
    [Crossref] [PubMed]
  12. R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
    [Crossref] [PubMed]
  13. F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and S. Massar, “All-optical reservoir computing,” Opt. Express 20(20), 22783–22795 (2012).
    [Crossref] [PubMed]
  14. 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]
  15. 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]
  16. 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, 1364 (2013).
    [Crossref] [PubMed]
  17. N. D. Haynes, M. C. Soriano, D. P. Rosin, I. Fischer, and D. J. Gauthier, “Reservoir computing with a single time-delay autonomous Boolean node,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 020801 (2015).
    [Crossref] [PubMed]
  18. 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]
  19. 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]
  20. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26(12), 3301–3307 (2015).
    [Crossref] [PubMed]
  21. H. Zhang, X. Feng, B. Li, Y. Wang, K. Cui, F. Liu, W. Dou, and Y. Huang, “Integrated photonic reservoir computing based on hierarchical time-multiplexing structure,” Opt. Express 22(25), 31356–31370 (2014).
    [Crossref] [PubMed]
  22. A. Uchida, R. McAllister, and R. Roy, “Consistency of nonlinear system response to complex drive signals,” Phys. Rev. Lett. 93(24), 244102 (2004).
    [Crossref] [PubMed]
  23. K. Kanno and A. Uchida, “Consistency and complexity in coupled semiconductor lasers with time-delayed optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(6), 066202 (2012).
    [Crossref] [PubMed]
  24. N. Oliver, T. Jüngling, and I. Fischer, “Consistency properties of a chaotic semiconductor laser driven by optical feedback,” Phys. Rev. Lett. 114(12), 123902 (2015).
    [Crossref] [PubMed]
  25. 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]
  26. L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
    [Crossref] [PubMed]
  27. F. Duport, A. Akrout, A. Smerieri, M. Haelterman, and S. Massar, “Analog input layer for optical reservoir computers,” arXiv:1406, 3238 (2014).
  28. A. Rodan and P. Tiňo, “Minimum complexity echo state network,” IEEE Trans. Neural Netw. 22(1), 131–144 (2011).
    [Crossref] [PubMed]
  29. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
    [Crossref]
  30. A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).
  31. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Reducing the phase sensitivity of laser-based optical reservoir computing systems,” Opt. Express 24(2), 1238–1252 (2016).
    [Crossref] [PubMed]
  32. 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).
  33. S. Haykin, J. C. Principe, T. J. Sejnowski, and J. Mcwhirter, “What makes a dynamical system computationally powerful,” in New Directions in Statistical Signal Processing: From Systems to Brain, (MIT press, 2007), pp. 127–154.
  34. R. F. Fox, I. R. Gatland, R. Roy, and G. Vemuri, “Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise,” Phys. Rev. A Gen. Phys. 38(11), 5938–5940 (1988).
    [Crossref] [PubMed]
  35. K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
    [Crossref] [PubMed]

2016 (1)

2015 (5)

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]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26(12), 3301–3307 (2015).
[Crossref] [PubMed]

M. C. Soriano, D. Brunner, M. Escalona-Morán, C. R. Mirasso, and I. Fischer, “Minimal approach to neuro-inspired information processing,” Front. Comput. Neurosci. 9(68), 68 (2015).
[PubMed]

N. D. Haynes, M. C. Soriano, D. P. Rosin, I. Fischer, and D. J. Gauthier, “Reservoir computing with a single time-delay autonomous Boolean node,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 020801 (2015).
[Crossref] [PubMed]

N. Oliver, T. Jüngling, and I. Fischer, “Consistency properties of a chaotic semiconductor laser driven by optical feedback,” Phys. Rev. Lett. 114(12), 123902 (2015).
[Crossref] [PubMed]

2014 (5)

2013 (3)

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, 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]

2012 (5)

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

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

K. Kanno and A. Uchida, “Consistency and complexity in coupled semiconductor lasers with time-delayed optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(6), 066202 (2012).
[Crossref] [PubMed]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
[Crossref] [PubMed]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and S. Massar, “All-optical reservoir computing,” Opt. Express 20(20), 22783–22795 (2012).
[Crossref] [PubMed]

2011 (3)

A. Rodan and P. Tiňo, “Minimum complexity echo state network,” IEEE Trans. Neural Netw. 22(1), 131–144 (2011).
[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, 468 (2011).
[Crossref] [PubMed]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

2010 (2)

2008 (1)

2004 (2)

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

A. Uchida, R. McAllister, and R. Roy, “Consistency of nonlinear system response to complex drive signals,” Phys. Rev. Lett. 93(24), 244102 (2004).
[Crossref] [PubMed]

2002 (1)

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

1995 (1)

B. A. Pearlmutter, “Gradient calculations for dynamic recurrent neural networks: a survey,” IEEE Trans. Neural Netw. 6(5), 1212–1228 (1995).
[Crossref] [PubMed]

1988 (1)

R. F. Fox, I. R. Gatland, R. Roy, and G. Vemuri, “Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise,” Phys. Rev. A Gen. Phys. 38(11), 5938–5940 (1988).
[Crossref] [PubMed]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Aida, H.

Appeltant, L.

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
[Crossref] [PubMed]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (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, 468 (2011).
[Crossref] [PubMed]

Baets, R.

Bienstman, P.

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, 3541 (2014).
[Crossref] [PubMed]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, and J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16(15), 11182–11192 (2008).
[Crossref] [PubMed]

Brunner, D.

M. C. Soriano, D. Brunner, M. Escalona-Morán, C. R. Mirasso, and I. Fischer, “Minimal approach to neuro-inspired information processing,” Front. Comput. Neurosci. 9(68), 68 (2015).
[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, 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]

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. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
[Crossref] [PubMed]

Caulfield, H. J.

H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4(5), 261–263 (2010).
[Crossref]

Chembo, Y. K.

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

Cui, K.

Dambre, J.

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, 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, 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, 468 (2011).
[Crossref] [PubMed]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

Danckaert, J.

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

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26(12), 3301–3307 (2015).
[Crossref] [PubMed]

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
[Crossref] [PubMed]

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, 468 (2011).
[Crossref] [PubMed]

Davis, P.

Dejonckheere, A.

Dierckx, W.

Dolev, S.

H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4(5), 261–263 (2010).
[Crossref]

Dou, W.

Duport, F.

Escalona-Morán, M.

M. C. Soriano, D. Brunner, M. Escalona-Morán, C. R. Mirasso, and I. Fischer, “Minimal approach to neuro-inspired information processing,” Front. Comput. Neurosci. 9(68), 68 (2015).
[PubMed]

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.

Feng, X.

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, 3541 (2014).
[Crossref] [PubMed]

Fischer, I.

N. D. Haynes, M. C. Soriano, D. P. Rosin, I. Fischer, and D. J. Gauthier, “Reservoir computing with a single time-delay autonomous Boolean node,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 020801 (2015).
[Crossref] [PubMed]

M. C. Soriano, D. Brunner, M. Escalona-Morán, C. R. Mirasso, and I. Fischer, “Minimal approach to neuro-inspired information processing,” Front. Comput. Neurosci. 9(68), 68 (2015).
[PubMed]

N. Oliver, T. Jüngling, and I. Fischer, “Consistency properties of a chaotic semiconductor laser driven by optical feedback,” Phys. Rev. Lett. 114(12), 123902 (2015).
[Crossref] [PubMed]

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
[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, 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. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (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, 468 (2011).
[Crossref] [PubMed]

Fox, R. F.

R. F. Fox, I. R. Gatland, R. Roy, and G. Vemuri, “Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise,” Phys. Rev. A Gen. Phys. 38(11), 5938–5940 (1988).
[Crossref] [PubMed]

Gatland, I. R.

R. F. Fox, I. R. Gatland, R. Roy, and G. Vemuri, “Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise,” Phys. Rev. A Gen. Phys. 38(11), 5938–5940 (1988).
[Crossref] [PubMed]

Gauthier, D. J.

N. D. Haynes, M. C. Soriano, D. P. Rosin, I. Fischer, and D. J. Gauthier, “Reservoir computing with a single time-delay autonomous Boolean node,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 020801 (2015).
[Crossref] [PubMed]

Gutierrez, J. M.

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.

Harayama, T.

Haynes, N. D.

N. D. Haynes, M. C. Soriano, D. P. Rosin, I. Fischer, and D. J. Gauthier, “Reservoir computing with a single time-delay autonomous Boolean node,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 020801 (2015).
[Crossref] [PubMed]

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]

Hirano, K.

Huang, Y.

Jacquot, M.

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

Jaeger, 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]

Jüngling, T.

N. Oliver, T. Jüngling, and I. Fischer, “Consistency properties of a chaotic semiconductor laser driven by optical feedback,” Phys. Rev. Lett. 114(12), 123902 (2015).
[Crossref] [PubMed]

Kanno, K.

K. Kanno and A. Uchida, “Consistency and complexity in coupled semiconductor lasers with time-delayed optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(6), 066202 (2012).
[Crossref] [PubMed]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Larger, L.

Li, B.

Liu, F.

Maass, W.

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

Markram, H.

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

Martinenghi, R.

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

Massar, S.

McAllister, R.

A. Uchida, R. McAllister, and R. Roy, “Consistency of nonlinear system response to complex drive signals,” Phys. Rev. Lett. 93(24), 244102 (2004).
[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, 3541 (2014).
[Crossref] [PubMed]

Mirasso, C. R.

M. C. Soriano, D. Brunner, M. Escalona-Morán, C. R. Mirasso, and I. Fischer, “Minimal approach to neuro-inspired information processing,” Front. Comput. Neurosci. 9(68), 68 (2015).
[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, 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]

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. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (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, 468 (2011).
[Crossref] [PubMed]

Morikatsu, S.

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, 3541 (2014).
[Crossref] [PubMed]

Natschläger, T.

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

Nguimdo, R. M.

Okumura, H.

Oliver, N.

N. Oliver, T. Jüngling, and I. Fischer, “Consistency properties of a chaotic semiconductor laser driven by optical feedback,” Phys. Rev. Lett. 114(12), 123902 (2015).
[Crossref] [PubMed]

Ortín, S.

Oudar, J. L.

Paquot, Y.

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

Pearlmutter, B. A.

B. A. Pearlmutter, “Gradient calculations for dynamic recurrent neural networks: a survey,” IEEE Trans. Neural Netw. 6(5), 1212–1228 (1995).
[Crossref] [PubMed]

Pesquera, L.

Rodan, A.

A. Rodan and P. Tiňo, “Minimum complexity echo state network,” IEEE Trans. Neural Netw. 22(1), 131–144 (2011).
[Crossref] [PubMed]

Rosin, D. P.

N. D. Haynes, M. C. Soriano, D. P. Rosin, I. Fischer, and D. J. Gauthier, “Reservoir computing with a single time-delay autonomous Boolean node,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 020801 (2015).
[Crossref] [PubMed]

Roy, R.

A. Uchida, R. McAllister, and R. Roy, “Consistency of nonlinear system response to complex drive signals,” Phys. Rev. Lett. 93(24), 244102 (2004).
[Crossref] [PubMed]

R. F. Fox, I. R. Gatland, R. Roy, and G. Vemuri, “Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise,” Phys. Rev. A Gen. Phys. 38(11), 5938–5940 (1988).
[Crossref] [PubMed]

Rybalko, S.

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

Schneider, B.

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, 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, 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, 468 (2011).
[Crossref] [PubMed]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, and J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16(15), 11182–11192 (2008).
[Crossref] [PubMed]

Smerieri, A.

Soriano, M. C.

M. C. Soriano, D. Brunner, M. Escalona-Morán, C. R. Mirasso, and I. Fischer, “Minimal approach to neuro-inspired information processing,” Front. Comput. Neurosci. 9(68), 68 (2015).
[PubMed]

N. D. Haynes, M. C. Soriano, D. P. Rosin, I. Fischer, and D. J. Gauthier, “Reservoir computing with a single time-delay autonomous Boolean node,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 020801 (2015).
[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]

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, 1364 (2013).
[Crossref] [PubMed]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (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, 468 (2011).
[Crossref] [PubMed]

Tino, P.

A. Rodan and P. Tiňo, “Minimum complexity echo state network,” IEEE Trans. Neural Netw. 22(1), 131–144 (2011).
[Crossref] [PubMed]

Uchida, A.

K. Kanno and A. Uchida, “Consistency and complexity in coupled semiconductor lasers with time-delayed optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(6), 066202 (2012).
[Crossref] [PubMed]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

A. Uchida, R. McAllister, and R. Roy, “Consistency of nonlinear system response to complex drive signals,” Phys. Rev. Lett. 93(24), 244102 (2004).
[Crossref] [PubMed]

Van Campenhout, J.

Van der Sande, G.

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

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26(12), 3301–3307 (2015).
[Crossref] [PubMed]

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
[Crossref] [PubMed]

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, 468 (2011).
[Crossref] [PubMed]

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, 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, 3541 (2014).
[Crossref] [PubMed]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, and J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16(15), 11182–11192 (2008).
[Crossref] [PubMed]

Vemuri, G.

R. F. Fox, I. R. Gatland, R. Roy, and G. Vemuri, “Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise,” Phys. Rev. A Gen. Phys. 38(11), 5938–5940 (1988).
[Crossref] [PubMed]

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, 3541 (2014).
[Crossref] [PubMed]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, and J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16(15), 11182–11192 (2008).
[Crossref] [PubMed]

Vinckier, Q.

Wang, Y.

Yamazaki, T.

Yoshimori, S.

Yoshimura, K.

Zhang, H.

Front. Comput. Neurosci. (1)

M. C. Soriano, D. Brunner, M. Escalona-Morán, C. R. Mirasso, and I. Fischer, “Minimal approach to neuro-inspired information processing,” Front. Comput. Neurosci. 9(68), 68 (2015).
[PubMed]

IEEE J. Quantum Electron. (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

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]

IEEE Trans. Neural Netw. (3)

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

B. A. Pearlmutter, “Gradient calculations for dynamic recurrent neural networks: a survey,” IEEE Trans. Neural Netw. 6(5), 1212–1228 (1995).
[Crossref] [PubMed]

A. Rodan and P. Tiňo, “Minimum complexity echo state network,” IEEE Trans. Neural Netw. 22(1), 131–144 (2011).
[Crossref] [PubMed]

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

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26(12), 3301–3307 (2015).
[Crossref] [PubMed]

Nat. Commun. (3)

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, 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, 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, 1364 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4(5), 261–263 (2010).
[Crossref]

Neural Comput. (1)

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

Opt. Express (9)

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, and J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16(15), 11182–11192 (2008).
[Crossref] [PubMed]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
[Crossref] [PubMed]

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

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]

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]

H. Zhang, X. Feng, B. Li, Y. Wang, K. Cui, F. Liu, W. Dou, and Y. Huang, “Integrated photonic reservoir computing based on hierarchical time-multiplexing structure,” Opt. Express 22(25), 31356–31370 (2014).
[Crossref] [PubMed]

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

Optica (1)

Phys. Rev. A Gen. Phys. (1)

R. F. Fox, I. R. Gatland, R. Roy, and G. Vemuri, “Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise,” Phys. Rev. A Gen. Phys. 38(11), 5938–5940 (1988).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

N. D. Haynes, M. C. Soriano, D. P. Rosin, I. Fischer, and D. J. Gauthier, “Reservoir computing with a single time-delay autonomous Boolean node,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 020801 (2015).
[Crossref] [PubMed]

K. Kanno and A. Uchida, “Consistency and complexity in coupled semiconductor lasers with time-delayed optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(6), 066202 (2012).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

N. Oliver, T. Jüngling, and I. Fischer, “Consistency properties of a chaotic semiconductor laser driven by optical feedback,” Phys. Rev. Lett. 114(12), 123902 (2015).
[Crossref] [PubMed]

A. Uchida, R. McAllister, and R. Roy, “Consistency of nonlinear system response to complex drive signals,” Phys. Rev. Lett. 93(24), 244102 (2004).
[Crossref] [PubMed]

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

Sci. Rep. (2)

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

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
[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 (4)

F. Duport, A. Akrout, A. Smerieri, M. Haelterman, and S. Massar, “Analog input layer for optical reservoir computers,” arXiv:1406, 3238 (2014).

A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).

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).

S. Haykin, J. C. Principe, T. J. Sejnowski, and J. Mcwhirter, “What makes a dynamical system computationally powerful,” in New Directions in Statistical Signal Processing: From Systems to Brain, (MIT press, 2007), pp. 127–154.

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Figures (12)

Fig. 1
Fig. 1 Schematics of reservoir computing using a semiconductor laser (Response) with time-delayed optical feedback and injection from another semiconductor laser (Drive).
Fig. 2
Fig. 2 Temporal waveforms of the masked input signal M(t) and response laser output for (a) the binary mask signal and (b) the chaos mask signal for the first input signal u(1) = 0.33. Blue dots indicate the node states. (c) Frequency spectra of the chaos mask signal (blue curve) and the response laser output without the input mask signal under optical injection (black curve).
Fig. 3
Fig. 3 Temporal waveforms of the original signal (black curve) and the RC prediction signal (red curve) for (a) the binary mask signal and (b) the chaotic mask signal. Figures in the bottom show the error signals between the original signal and the RC prediction signal.
Fig. 4
Fig. 4 Histograms of the node states for the first input data with (a) the binary mask signal and (b) the chaos mask signal.
Fig. 5
Fig. 5 Temporal waveforms of the masked input signal and the response laser output for (a) the six-level mask signal and (b) the random-level mask signal. Blue dots indicate the node states.
Fig. 6
Fig. 6 NMSEs of the time-series prediction task as a function of the standard deviation of the amplitude of the binary, six-level, random-level, and chaos mask signals.
Fig. 7
Fig. 7 NMSEs of the time-series prediction task as a function of the feedback strength κ for the binary, six-level, random-level, and chaos mask signals.
Fig. 8
Fig. 8 (a) Cross correlation values between the two response lasers with the same optical injection under the condition of different initial conditions and different noise signals and (b) conditional Lyapunov exponents of the response laser as a function of the feedback strength. The dotted line indicates zero conditional Lyapunov exponent.
Fig. 9
Fig. 9 Temporal waveforms of the masked input signal M(t) and the response laser output for (a) the white Gaussian noise mask signal and (b) the colored-noise mask signal with the cut-off frequency of 6.0 GHz. Blue dots indicate the node states.
Fig. 10
Fig. 10 NMSEs of the time-series prediction task as a function of the standard deviation of the amplitude of the white Gaussian noise, colored-noise, and chaos mask signals.
Fig. 11
Fig. 11 NMSEs of the time-series prediction task as a function of the feedback strength κ for the white Gaussian noise, colored-noise, and chaos mask signals.
Fig. 12
Fig. 12 NMSEs of the time-series prediction task as a function of (a) the peak frequency of chaos mask signal and (b) the cut-off frequency of the colored-noise mask signal.

Tables (1)

Tables Icon

Table 1 Laser parameter values used in numerical simulations.

Equations (7)

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

y(n)= i=1 N W i x i (n)
1 L n=1 L ( y(n) y ¯ (n) ) 2 min
d E r (t) dt = 1+iα 2 { G N ( N r (t) N 0 ) 1+ε | E r (t) | 2 1 τ p } E r (t)+ξ(t) +κ E r (tτ)exp(i ω r τ)+ κ inj E d (t)exp(iΔω t)
d N r (t) dt = J r N r (t) τ s G N ( N r (t) N 0 ) 1+ε | E r (t) | 2 | E r (t) | 2
M(t)=mask(t)×u(n)×γ
E d (t)= I d exp(iπM(t))
NMSE= 1 L n=1 L ( y ¯ (n)y(n) ) 2 var( y ¯ )

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