Abstract

Semiconductor lasers subject to delayed optical feedback have recently shown great potential in solving computationally hard tasks. By optically implementing a neuro-inspired computational scheme, called reservoir computing, based on the transient response to optical data injection, high processing speeds have been demonstrated. While previous efforts have focused on signal bandwidths limited by the semiconductor laser’s relaxation oscillation frequency, we demonstrate numerically that the much faster phase response makes significantly higher processing speeds attainable. Moreover, this also leads to shorter external cavity lengths facilitating future on-chip implementations. We numerically benchmark our system on a chaotic time-series prediction task considering two different feedback configurations. The results show that a prediction error below 4% can be obtained when the data is processed at 0.25 GSamples/s. In addition, our insight into the phase dynamics of optical injection in a semiconductor laser also provides a clear understanding of the system performance at different pump current levels, even below solitary laser threshold. Considering spontaneous emission noise and noise in the readout layer, we obtain good prediction performance at fast processing speeds for realistic values of the noise strength.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. P. Crutchfield, L. D. William, S. Sudeshna, “Introduction to focus issue:intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony,” Chaos 20, 037101 (2010).
    [CrossRef]
  2. D. Woods, T. J. Naughton, “Optical computing: photonic neural networks,” Nat. Phys. 8257–259 (2012).
    [CrossRef]
  3. W. Maass, T. Natschläger, H. Markram, “Real-time computing without stable states: a new framework for neural computation based on perturbations,” Neural Comput. 14, 2531–2560 (2002).
    [CrossRef] [PubMed]
  4. H. Jaeger, H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304, 78–80 (2004).
    [CrossRef] [PubMed]
  5. D. Verstraeten, B. Schrauwen, M. D’Haene, D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Networks 20, 391–403 (2007).
    [CrossRef] [PubMed]
  6. J. J. Steil, “Backpropagation-decorrelation: Online recurrent learning with O(N) complexity,” In Proceedings of IJCNN ’04’ 1, 843–848 (2004).
  7. H. J. Caulfield, S. Dolev, “Why future supercomputing requires optics,” Nat. Photon. 4, 261–263 (2010).
    [CrossRef]
  8. K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, J. Campenhout, “Towards optical signal processing using photonic reservoir computing,” Opt. Express 16, 11182–11192 (2008).
    [CrossRef] [PubMed]
  9. L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
    [CrossRef] [PubMed]
  10. L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).
    [CrossRef] [PubMed]
  11. Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
    [CrossRef] [PubMed]
  12. R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev Lett. 108, 244101 (2012).
    [CrossRef] [PubMed]
  13. F. Duport, B. Schneider, A. Smerieri, M. Haelterman, Serge Massar, “All Optical Reservoir Computing” Optics Express 20, 22783–22795 (2012).
    [CrossRef]
  14. A. Smerieri, F. Duport, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems, Vol. 25, P. Bartlett, F. C. N. Pereira, C. J. C. Burges, L. Bottou, K.Q. Weinberger, eds. (MIT Press, 2012), pp. 953–961.
  15. D. Brunner, M. C. Soriano, C. R. Mirasso, I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nature Commun. 4, 1364 (2013).
    [CrossRef]
  16. K. Hicke, M. A. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
    [CrossRef]
  17. R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. 16, 347–355 (1980)
    [CrossRef]
  18. T. Heil, A. Uchida, P. Davis, T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated feedback,” Phys. Rev. A 68, 033811 (2003).
    [CrossRef]
  19. M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
    [CrossRef]
  20. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, X. Leijtens, J. Bolk, G. Van der Sande, “Fast random bit generation based on a single chaotic semiconductor ring laser,” Opt. Express 20, 28603–28613 (2012)
    [CrossRef] [PubMed]
  21. S. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, H. N. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightw. Technol. 292173–2179 (2011).
    [CrossRef]
  22. R. M. Nguimdo, M. C. Soriano, P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett. 36, 4332–4334 (2011).
    [CrossRef] [PubMed]
  23. D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, S. Ortin, “Time-Delay Identification in a Chaotic Semiconductor Laser With Optical Feedback: A Dynamical Point of View,” IEEE J. Quantum Electron. 45, 879–891 (2009).
    [CrossRef]
  24. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37, 2541–2544 (2012).
    [CrossRef] [PubMed]
  25. S. Wieczorek, B. Krauskopf, T. B. Simpson, D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 4161 (2005).
    [CrossRef]
  26. A. S. Weigend, N. A. Gershenfeld, “Time series prediction: Forecasting the future and understanding the past,” ftp://ftp.santafe.edu/pub/Time-Series/Competition (1993).
  27. M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, L. Pesquera, “Optoelectronic reservoir computing: Tackling noise-induced performance degradation,” Opt. Express 21, 12–20 (2013).
    [CrossRef] [PubMed]
  28. L. Appeltant, G. Van der Sande, J. Danckaert, I. Fischer, ”Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
    [CrossRef] [PubMed]
  29. M. C. Soriano, S. Ortín, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van der Sande, ”Delay-based Reservoir Computing: noise effects in a combined analog and digital implementation,” accepted to IEEE Trans. Neural Netw. Learn. Syst. (2014).

2014 (1)

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

2013 (4)

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

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

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

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

2012 (7)

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

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

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

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, Serge Massar, “All Optical Reservoir Computing” Optics Express 20, 22783–22795 (2012).
[CrossRef]

D. Woods, T. J. Naughton, “Optical computing: photonic neural networks,” Nat. Phys. 8257–259 (2012).
[CrossRef]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, X. Leijtens, J. Bolk, G. Van der Sande, “Fast random bit generation based on a single chaotic semiconductor ring laser,” Opt. Express 20, 28603–28613 (2012)
[CrossRef] [PubMed]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37, 2541–2544 (2012).
[CrossRef] [PubMed]

2011 (3)

S. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, H. N. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightw. Technol. 292173–2179 (2011).
[CrossRef]

R. M. Nguimdo, M. C. Soriano, P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett. 36, 4332–4334 (2011).
[CrossRef] [PubMed]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
[CrossRef] [PubMed]

2010 (2)

J. P. Crutchfield, L. D. William, S. Sudeshna, “Introduction to focus issue:intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony,” Chaos 20, 037101 (2010).
[CrossRef]

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

2009 (1)

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, S. Ortin, “Time-Delay Identification in a Chaotic Semiconductor Laser With Optical Feedback: A Dynamical Point of View,” IEEE J. Quantum Electron. 45, 879–891 (2009).
[CrossRef]

2008 (1)

2007 (1)

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

2005 (1)

S. Wieczorek, B. Krauskopf, T. B. Simpson, D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 4161 (2005).
[CrossRef]

2004 (2)

J. J. Steil, “Backpropagation-decorrelation: Online recurrent learning with O(N) complexity,” In Proceedings of IJCNN ’04’ 1, 843–848 (2004).

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

2003 (1)

T. Heil, A. Uchida, P. Davis, T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

2002 (1)

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

1980 (1)

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. 16, 347–355 (1980)
[CrossRef]

Aida, T.

T. Heil, A. Uchida, P. Davis, T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Appeltant, L.

L. Appeltant, G. Van der Sande, J. Danckaert, 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, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 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, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
[CrossRef] [PubMed]

M. C. Soriano, S. Ortín, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van der Sande, ”Delay-based Reservoir Computing: noise effects in a combined analog and digital implementation,” accepted to IEEE Trans. Neural Netw. Learn. Syst. (2014).

Baets, R.

Bienstman, P.

Bolk, J.

Brunner, D.

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

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

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

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

Campenhout, J.

Caulfield, H. J.

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

Chembo, Y. K.

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

Citrin, D. S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, S. Ortin, “Time-Delay Identification in a Chaotic Semiconductor Laser With Optical Feedback: A Dynamical Point of View,” IEEE J. Quantum Electron. 45, 879–891 (2009).
[CrossRef]

Colet, P.

Crutchfield, J. P.

J. P. Crutchfield, L. D. William, S. Sudeshna, “Introduction to focus issue:intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony,” Chaos 20, 037101 (2010).
[CrossRef]

D’Haene, M.

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

Dambre, J.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, 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, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
[CrossRef] [PubMed]

Danckaert, J.

L. Appeltant, G. Van der Sande, J. Danckaert, 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, G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37, 2541–2544 (2012).
[CrossRef] [PubMed]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, X. Leijtens, J. Bolk, G. Van der Sande, “Fast random bit generation based on a single chaotic semiconductor ring laser,” Opt. Express 20, 28603–28613 (2012)
[CrossRef] [PubMed]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
[CrossRef] [PubMed]

M. C. Soriano, S. Ortín, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van der Sande, ”Delay-based Reservoir Computing: noise effects in a combined analog and digital implementation,” accepted to IEEE Trans. Neural Netw. Learn. Syst. (2014).

Davis, P.

T. Heil, A. Uchida, P. Davis, T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Dierckx, W.

Dolev, S.

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

Duport, F.

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

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, Serge Massar, “All Optical Reservoir Computing” Optics Express 20, 22783–22795 (2012).
[CrossRef]

A. Smerieri, F. Duport, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems, Vol. 25, P. Bartlett, F. C. N. Pereira, C. J. C. Burges, L. Bottou, K.Q. Weinberger, eds. (MIT Press, 2012), pp. 953–961.

Escalona-Moran, M. A.

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

Fischer, I.

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

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

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

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

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

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 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, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
[CrossRef] [PubMed]

García-Ojalvo, J.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

Gershenfeld, N. A.

A. S. Weigend, N. A. Gershenfeld, “Time series prediction: Forecasting the future and understanding the past,” ftp://ftp.santafe.edu/pub/Time-Series/Competition (1993).

Gutierrez, J. M.

Haas, H.

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

Haelterman, M.

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

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, Serge Massar, “All Optical Reservoir Computing” Optics Express 20, 22783–22795 (2012).
[CrossRef]

A. Smerieri, F. Duport, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems, Vol. 25, P. Bartlett, F. C. N. Pereira, C. J. C. Burges, L. Bottou, K.Q. Weinberger, eds. (MIT Press, 2012), pp. 953–961.

Heil, T.

T. Heil, A. Uchida, P. Davis, T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Hicke, K.

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

Jacquot, M.

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

Jaeger, H.

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

Jiang, N.

S. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, H. N. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightw. Technol. 292173–2179 (2011).
[CrossRef]

Keuninckx, L.

M. C. Soriano, S. Ortín, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van der Sande, ”Delay-based Reservoir Computing: noise effects in a combined analog and digital implementation,” accepted to IEEE Trans. Neural Netw. Learn. Syst. (2014).

Kobayashi, K.

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. 16, 347–355 (1980)
[CrossRef]

Krauskopf, B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 4161 (2005).
[CrossRef]

Lang, R.

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. 16, 347–355 (1980)
[CrossRef]

Larger, L.

Leijtens, X.

Lenstra, D.

S. Wieczorek, B. Krauskopf, T. B. Simpson, D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 4161 (2005).
[CrossRef]

Locquet, A.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, S. Ortin, “Time-Delay Identification in a Chaotic Semiconductor Laser With Optical Feedback: A Dynamical Point of View,” IEEE J. Quantum Electron. 45, 879–891 (2009).
[CrossRef]

Luo, B.

S. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, H. N. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightw. Technol. 292173–2179 (2011).
[CrossRef]

Maass, W.

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

Markram, H.

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

Martinenghi, R.

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

Massar, S.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, 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, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
[CrossRef] [PubMed]

A. Smerieri, F. Duport, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems, Vol. 25, P. Bartlett, F. C. N. Pereira, C. J. C. Burges, L. Bottou, K.Q. Weinberger, eds. (MIT Press, 2012), pp. 953–961.

Massar, Serge

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, Serge Massar, “All Optical Reservoir Computing” Optics Express 20, 22783–22795 (2012).
[CrossRef]

Mirasso, C. R.

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

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

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

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

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 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, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
[CrossRef] [PubMed]

Natschläger, T.

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

Naughton, T. J.

D. Woods, T. J. Naughton, “Optical computing: photonic neural networks,” Nat. Phys. 8257–259 (2012).
[CrossRef]

Nguimdo, R. M.

Ortin, S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, S. Ortin, “Time-Delay Identification in a Chaotic Semiconductor Laser With Optical Feedback: A Dynamical Point of View,” IEEE J. Quantum Electron. 45, 879–891 (2009).
[CrossRef]

Ortín, S.

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

M. C. Soriano, S. Ortín, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van der Sande, ”Delay-based Reservoir Computing: noise effects in a combined analog and digital implementation,” accepted to IEEE Trans. Neural Netw. Learn. Syst. (2014).

Pan, W.

S. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, H. N. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightw. Technol. 292173–2179 (2011).
[CrossRef]

Paquot, Y.

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

Pesquera, L.

Rontani, D.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, S. Ortin, “Time-Delay Identification in a Chaotic Semiconductor Laser With Optical Feedback: A Dynamical Point of View,” IEEE J. Quantum Electron. 45, 879–891 (2009).
[CrossRef]

Rybalko, S.

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

Schneider, B.

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, Serge Massar, “All Optical Reservoir Computing” Optics Express 20, 22783–22795 (2012).
[CrossRef]

Schrauwen, B.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, 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, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
[CrossRef] [PubMed]

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

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

Sciamanna, M.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, S. Ortin, “Time-Delay Identification in a Chaotic Semiconductor Laser With Optical Feedback: A Dynamical Point of View,” IEEE J. Quantum Electron. 45, 879–891 (2009).
[CrossRef]

Simpson, T. B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 4161 (2005).
[CrossRef]

Smerieri, A.

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, Serge Massar, “All Optical Reservoir Computing” Optics Express 20, 22783–22795 (2012).
[CrossRef]

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

A. Smerieri, F. Duport, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems, Vol. 25, P. Bartlett, F. C. N. Pereira, C. J. C. Burges, L. Bottou, K.Q. Weinberger, eds. (MIT Press, 2012), pp. 953–961.

Soriano, M. C.

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

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

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

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 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, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
[CrossRef] [PubMed]

R. M. Nguimdo, M. C. Soriano, P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett. 36, 4332–4334 (2011).
[CrossRef] [PubMed]

M. C. Soriano, S. Ortín, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van der Sande, ”Delay-based Reservoir Computing: noise effects in a combined analog and digital implementation,” accepted to IEEE Trans. Neural Netw. Learn. Syst. (2014).

Steil, J. J.

J. J. Steil, “Backpropagation-decorrelation: Online recurrent learning with O(N) complexity,” In Proceedings of IJCNN ’04’ 1, 843–848 (2004).

Stroobandt, D.

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

Sudeshna, S.

J. P. Crutchfield, L. D. William, S. Sudeshna, “Introduction to focus issue:intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony,” Chaos 20, 037101 (2010).
[CrossRef]

Uchida, A.

T. Heil, A. Uchida, P. Davis, T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Van der Sande, G.

L. Appeltant, G. Van der Sande, J. Danckaert, 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, X. Leijtens, J. Bolk, G. Van der Sande, “Fast random bit generation based on a single chaotic semiconductor ring laser,” Opt. Express 20, 28603–28613 (2012)
[CrossRef] [PubMed]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37, 2541–2544 (2012).
[CrossRef] [PubMed]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
[CrossRef] [PubMed]

M. C. Soriano, S. Ortín, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van der Sande, ”Delay-based Reservoir Computing: noise effects in a combined analog and digital implementation,” accepted to IEEE Trans. Neural Netw. Learn. Syst. (2014).

Vandoorne, K.

Verschaffelt, G.

Verstraeten, D.

Weigend, A. S.

A. S. Weigend, N. A. Gershenfeld, “Time series prediction: Forecasting the future and understanding the past,” ftp://ftp.santafe.edu/pub/Time-Series/Competition (1993).

Wieczorek, S.

S. Wieczorek, B. Krauskopf, T. B. Simpson, D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 4161 (2005).
[CrossRef]

William, L. D.

J. P. Crutchfield, L. D. William, S. Sudeshna, “Introduction to focus issue:intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony,” Chaos 20, 037101 (2010).
[CrossRef]

Woods, D.

D. Woods, T. J. Naughton, “Optical computing: photonic neural networks,” Nat. Phys. 8257–259 (2012).
[CrossRef]

Xiang, S.

S. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, H. N. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightw. Technol. 292173–2179 (2011).
[CrossRef]

Yan, L. S.

S. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, H. N. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightw. Technol. 292173–2179 (2011).
[CrossRef]

Yang, L.

S. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, H. N. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightw. Technol. 292173–2179 (2011).
[CrossRef]

Zhu, H. N.

S. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, H. N. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightw. Technol. 292173–2179 (2011).
[CrossRef]

Zou, X. H.

S. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, H. N. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightw. Technol. 292173–2179 (2011).
[CrossRef]

Chaos (1)

J. P. Crutchfield, L. D. William, S. Sudeshna, “Introduction to focus issue:intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony,” Chaos 20, 037101 (2010).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. 16, 347–355 (1980)
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, S. Ortin, “Time-Delay Identification in a Chaotic Semiconductor Laser With Optical Feedback: A Dynamical Point of View,” IEEE J. Quantum Electron. 45, 879–891 (2009).
[CrossRef]

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

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

J. Lightw. Technol. (1)

S. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, H. N. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightw. Technol. 292173–2179 (2011).
[CrossRef]

Nat. Commun. (1)

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468–472 (2011).
[CrossRef] [PubMed]

Nat. Photon. (1)

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

Nat. Phys. (1)

D. Woods, T. J. Naughton, “Optical computing: photonic neural networks,” Nat. Phys. 8257–259 (2012).
[CrossRef]

Nature Commun. (1)

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

Neural Comput. (1)

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

Neural Networks (1)

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

Opt. Express (4)

Opt. Lett. (2)

Optics Express (1)

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, Serge Massar, “All Optical Reservoir Computing” Optics Express 20, 22783–22795 (2012).
[CrossRef]

Phys. Rep. (1)

S. Wieczorek, B. Krauskopf, T. B. Simpson, D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 4161 (2005).
[CrossRef]

Phys. Rev Lett. (1)

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

Phys. Rev. A (1)

T. Heil, A. Uchida, P. Davis, T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Proceedings of IJCNN ’04’ (1)

J. J. Steil, “Backpropagation-decorrelation: Online recurrent learning with O(N) complexity,” In Proceedings of IJCNN ’04’ 1, 843–848 (2004).

Rev. Mod. Phys. (1)

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[CrossRef]

Sci. Rep. (2)

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

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

Science (1)

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

Other (3)

A. Smerieri, F. Duport, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems, Vol. 25, P. Bartlett, F. C. N. Pereira, C. J. C. Burges, L. Bottou, K.Q. Weinberger, eds. (MIT Press, 2012), pp. 953–961.

M. C. Soriano, S. Ortín, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van der Sande, ”Delay-based Reservoir Computing: noise effects in a combined analog and digital implementation,” accepted to IEEE Trans. Neural Netw. Learn. Syst. (2014).

A. S. Weigend, N. A. Gershenfeld, “Time series prediction: Forecasting the future and understanding the past,” ftp://ftp.santafe.edu/pub/Time-Series/Competition (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 (11)

Fig. 1
Fig. 1

Illustration of the masking procedure. (a) The discrete input data. (b) The temporal mask constructed for N = 3 and with a node separation of θ. (c) The full preprocessed signal to be injected into the reservoir computer.

Fig. 2
Fig. 2

(a) Spectra computed from intensity |E1(t)|2(black) and from phase φ1(t) (gray, blue); (b) autocorrelation. The parameters are I0 = 1.3Ith, TD = 4 ns, β1,2 = 10−6, η1 = 20 ns−1, kinj = 0 ns−1 and η2 = 0 ns−1 (i.e PMOF configuration)

Fig. 3
Fig. 3

Same as in Fig. 2 for I0 = 0.9Ith.

Fig. 4
Fig. 4

(a) Phase spectra computed from phase φ1(t) for η1 = 20 ns−1 (gray, blue in color) and η1 = 30 ns−1 (black); (b)corresponding autocorrelation function computed from the same φ1(t). Other parameters are in Fig. 2.

Fig. 5
Fig. 5

Autocorrelation function showing the (a) intensity relaxation and (b) the carrier relaxation considering η1 = 10 ns−1 for the PMOF configuration.

Fig. 6
Fig. 6

Temporal profiles of the data input at the rf electrode of the MZM (back) and the SL response in the intensity (red) and in the phase (blue) for (a) Θ = 200 ps and (b) Θ = 20 ps considering η1 = 10 ns−1 (PMOF configuration), β1,2 = 10−6 and I0 = 1.1Ith.

Fig. 7
Fig. 7

(a) NMSE for PMOF considering η1 = 10 ns−1, (b) PROF considering η2 = 10 ns−1 when the data are input and read out in the dominant mode which provides feedback to the other mode. The injection strength considered for both cases is kinj = 50 ns−1.

Fig. 8
Fig. 8

NMSE for SL with (a) PMOF and (b) PROF considering Θ = 20 ps for different values of feedback strengths η = η1 for PMOF or η = η2 for PROF. The parameters are TD = NΘ, N=200 and kinj = 50 ns−1.

Fig. 9
Fig. 9

NMSE as a function of Θ for a SL with (a) PMOF considering η1 = 10 ns−1 and (b) PROF considering η2 = 30 ns−1.

Fig. 10
Fig. 10

NMSE as a function of the intrinsic noise strength for (a) I0 = 1.1Ith and (b) for I0 = 0.9Ith. Other parameters are as in Fig. 7

Fig. 11
Fig. 11

NMSE as a function of I0/Ith without (•) and with (★) noise in the readout layer for (a) PMOF configuration with η1 = 10 ns−1 and (b) PROF configuration with η2 = 30 ns−1. The noise strength in the readout layer is chosen such that it yiels to the signal-to-noise ratio of ≈ 20 dB at I0 = 1.1Ith for PMOF configuration. β1,2 = 10−6

Tables (1)

Tables Icon

Table 1 Values used for numerical simulations

Equations (5)

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

E ˙ 1 = 1 2 ( 1 + i α ) [ 𝒢 1 γ 1 ] E 1 + η 1 E 1 ( t T D ) e i Ω 0 T D + ξ 1 ( t ) + k inj inj ( t ) ,
E ˙ 2 = i Δ Ω E 2 + 1 2 ( 1 + i α ) [ 𝒢 2 γ 2 ] E 2 + η 2 E 1 ( t T D ) e i Ω 0 T D + ξ 2 ( t ) ,
N ˙ = I 0 e γ e N 𝒢 1 | E 1 | 2 𝒢 2 | E 2 | 2 ,
inj ( t ) = | 0 | 2 { 1 + e i [ S ( t ) + Φ 0 ] } e i Δ ω t ,
NMSE ( y , y target ) = y ( n ) y target ( n ) 2 y target ( n ) y target ( n ) 2 ,

Metrics