Abstract

We experimentally investigate delay-based photonic reservoir computing using semiconductor lasers with optical feedback and injection. We apply different types of temporal mask signals, such as digital, chaos, and colored-noise mask signals, as the weights between the input signal and the virtual nodes in the reservoir. We evaluate the performance of reservoir computing by using a time-series prediction task for the different mask signals. The chaos mask signal shows superior performance than that of the digital mask signals. However, similar prediction errors can be achieved for the chaos and colored-noise mask signals. Mask signals with larger amplitudes result in better performance for all mask signals in the range of the amplitude accessible in our experiment. The performance of reservoir computing is strongly dependent on the cut-off frequency of the colored-noise mask signals, which is related to the resonance of the relaxation oscillation frequency of the laser used as the reservoir.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2017 (1)

2016 (2)

2015 (4)

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]

S. Ortín, M. C. Soriano, L. Pesquera, D. Brunner, D. San-Martín, I. Fischer, C. R. Mirasso, and J. M. Gutiérrez, “A unified framework for reservoir computing and extreme learning machines based on a single time-delayed Neuron,” Sci. Rep. 5(1), 14945 (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(1), 3629 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (3)

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]

2012 (4)

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]

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]

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

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)

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photonics Technol. Lett. 7(7), 709–711 (1995).
[Crossref]

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]

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(1), 3629 (2015).
[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]

Bienstman, P.

Brunner, D.

S. Ortín, M. C. Soriano, L. Pesquera, D. Brunner, D. San-Martín, I. Fischer, C. R. Mirasso, and J. M. Gutiérrez, “A unified framework for reservoir computing and extreme learning machines based on a single time-delayed Neuron,” Sci. Rep. 5(1), 14945 (2015).
[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]

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]

Dambre, J.

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, 468 (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]

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4(1), 3629 (2015).
[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]

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]

Dejonckheere, A.

Duport, F.

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.

Fischer, I.

S. Ortín, M. C. Soriano, L. Pesquera, D. Brunner, D. San-Martín, I. Fischer, C. R. Mirasso, and J. M. Gutiérrez, “A unified framework for reservoir computing and extreme learning machines based on a single time-delayed Neuron,” Sci. Rep. 5(1), 14945 (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(1), 3629 (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]

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]

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]

Gavrielides, A.

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photonics Technol. Lett. 7(7), 709–711 (1995).
[Crossref]

Guillet de Chatellus, H.

Gutierrez, J. M.

Gutiérrez, J. M.

S. Ortín, M. C. Soriano, L. Pesquera, D. Brunner, D. San-Martín, I. Fischer, C. R. Mirasso, and J. M. Gutiérrez, “A unified framework for reservoir computing and extreme learning machines based on a single time-delayed Neuron,” Sci. Rep. 5(1), 14945 (2015).
[Crossref] [PubMed]

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.

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]

Hugon, O.

Jacquin, O.

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]

Kanno, K.

Lacot, E.

Larger, L.

Liu, J. M.

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photonics Technol. Lett. 7(7), 709–711 (1995).
[Crossref]

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]

Mirasso, C. R.

S. Ortín, M. C. Soriano, L. Pesquera, D. Brunner, D. San-Martín, I. Fischer, C. R. Mirasso, and J. M. Gutiérrez, “A unified framework for reservoir computing and extreme learning machines based on a single time-delayed Neuron,” Sci. Rep. 5(1), 14945 (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]

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]

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]

Nakayama, J.

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.

Ortín, S.

S. Ortín, M. C. Soriano, L. Pesquera, D. Brunner, D. San-Martín, I. Fischer, C. R. Mirasso, and J. M. Gutiérrez, “A unified framework for reservoir computing and extreme learning machines based on a single time-delayed Neuron,” Sci. Rep. 5(1), 14945 (2015).
[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]

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(1), 287 (2012).
[Crossref] [PubMed]

Pesquera, L.

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]

San-Martín, D.

S. Ortín, M. C. Soriano, L. Pesquera, D. Brunner, D. San-Martín, I. Fischer, C. R. Mirasso, and J. M. Gutiérrez, “A unified framework for reservoir computing and extreme learning machines based on a single time-delayed Neuron,” Sci. Rep. 5(1), 14945 (2015).
[Crossref] [PubMed]

Schneider, B.

Schrauwen, B.

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

Simpson, T. B.

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photonics Technol. Lett. 7(7), 709–711 (1995).
[Crossref]

Smerieri, A.

Soriano, M. C.

S. Ortín, M. C. Soriano, L. Pesquera, D. Brunner, D. San-Martín, I. Fischer, C. R. Mirasso, and J. M. Gutiérrez, “A unified framework for reservoir computing and extreme learning machines based on a single time-delayed Neuron,” Sci. Rep. 5(1), 14945 (2015).
[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]

Uchida, A.

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]

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 der Sande, G.

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]

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(1), 3629 (2015).
[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]

Vandoorne, K.

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.

Vinckier, Q.

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 Photonics Technol. Lett. (1)

T. B. Simpson, J. M. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photonics Technol. Lett. 7(7), 709–711 (1995).
[Crossref]

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. (2)

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]

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 (7)

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]

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]

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, “Fast photonic information processing using semiconductor lasers with delayed optical feedback: Role of phase dynamics,” Opt. Express 22(7), 8672–8686 (2014).
[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]

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]

Opt. Lett. (1)

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. Lett. (2)

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. (3)

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, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4(1), 3629 (2015).
[Crossref] [PubMed]

S. Ortín, M. C. Soriano, L. Pesquera, D. Brunner, D. San-Martín, I. Fischer, C. R. Mirasso, and J. M. Gutiérrez, “A unified framework for reservoir computing and extreme learning machines based on a single time-delayed Neuron,” Sci. Rep. 5(1), 14945 (2015).
[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)

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).

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Figures (11)

Fig. 1
Fig. 1 Schematic of delay-based photonic reservoir computing with two semiconductor lasers. The processing scheme consists of the input layer, the reservoir, and the output layer.
Fig. 2
Fig. 2 Experimental setup for delay-based photonic reservoir computing with two semiconductor lasers.
Fig. 3
Fig. 3 Temporal input mask signals: (a) binary mask, (b) random-level mask, and (c) chaos mask signal. The digital mask interval θ = 0.2 ns corresponds to the virtual node interval. (d) The fast Fourier transform of the chaos mask signal of (c).
Fig. 4
Fig. 4 Temporal waveforms of the mask signals and the response laser outputs for (a) digital random-level mask signal and (b) analog chaos mask signal. Blue dots indicate node states.
Fig. 5
Fig. 5 Experimental results of the Santa Fe time-series prediction task using reservoir computing with (a) digital random-level mask signal and (b) analog chaos mask signal. Original signals (black lines), prediction results (red lines), and error signals (blue lines) are shown. The normalized mean-square errors (NMSEs) are (a) 0.305 and (b) 0.154, respectively. The feedback strength of the response laser is set to zero.
Fig. 6
Fig. 6 NMSEs of the time-series prediction task as a function of the feedback strength of the response laser using reservoir computing with analog chaos mask signal.
Fig. 7
Fig. 7 NMSEs of the time-series prediction task for the binary (black curve with circles), six-level (red curve with squares), random-level (blue curve with triangles), and chaos mask signals (green curve with diamonds) as the standard deviation of the mask signal is varied.
Fig. 8
Fig. 8 (a), (c) Temporal input mask signals of colored-noise signals and (b), (d) corresponding fast Fourier transforms. (a), (b) Cut-off frequencies of fc = 3 GHz, and (c), (d) fc = 12 GHz.
Fig. 9
Fig. 9 Temporal waveforms of the colored-noise mask signals with the cut-off frequencies of (a) fc = 3 GHz and (b) fc = 12 GHz, and the corresponding response laser outputs. Blue dots indicate node states.
Fig. 10
Fig. 10 Experimental results of the Santa Fe time-series prediction task using the colored-noise mask signals with the cut-off frequencies of (a) fc = 3 GHz and (b) fc = 12 GHz. Original signals (black lines), prediction results (red lines), and error signals (blue lines) are shown. The NMSEs are (a) 0.243 and (b) 0.146, respectively.
Fig. 11
Fig. 11 NMSEs for the four colored-noise mask signals with the cut-off frequencies of fc = 1.5 GHz (black curve with circles), fc = 3 GHz (red curve with squares), fc = 6 GHz (green curve with triangles), and fc = 12 GHz (blue curve with diamonds) as the standard deviation of the mask signal is varied. The results of NMSEs for the chaos mask signal (purple curve with crosses) is also plotted for comparison. CNmask indicates the colored-noise mask.

Equations (1)

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N M S E = 1 L n = 1 L { y ¯ ( n ) y ( n ) } 2 var ( y ¯ ) ,

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