Abstract

A reservoir computing (RC) system based on a semiconductor laser (SL) with double optical feedback and optical injection is proposed, and the prediction performance of such a system is numerically investigated via Santa Fe Time-Series Prediction task. The simulation results indicate that the RC system can yield a good prediction performance. Through optimizing some relevant operating parameters, ultra-fast information processing rates up to Gb/s level can be realized for the prediction error is below 3%.

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

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2017 (3)

2016 (1)

2015 (4)

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 (2015).
[Crossref] [PubMed]

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

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]

2014 (5)

2013 (2)

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)

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

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

D. Woods and T. J. Naughton, “Optical computing: photonic neural networks,” Nat. Phys. 8(4), 257–259 (2012).
[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]

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]

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]

2010 (3)

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[Crossref] [PubMed]

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

J. P. Crutchfield, W. L. Ditto, and S. Sinha, “Introduction to focus issue: intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony,” Chaos 20(3), 037101 (2010).
[Crossref] [PubMed]

2009 (1)

2007 (1)

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

2005 (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[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]

1989 (1)

U. Hübner, N. B. Abraham, and C. O. Weiss, “Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser,” Phys. Rev. A Gen. Phys. 40(11), 6354–6365 (1989).
[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]

Abraham, N. B.

U. Hübner, N. B. Abraham, and C. O. Weiss, “Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser,” Phys. Rev. A Gen. Phys. 40(11), 6354–6365 (1989).
[Crossref] [PubMed]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Appeltant, L.

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]

Argyris, A.

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[Crossref] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

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]

Bloch, M.

Bogris, A.

Brunner, D.

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

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

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]

Bueno, J.

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]

Chizhevsky, V. N.

Citrin, D. S.

Colet, P.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Crutchfield, J. P.

J. P. Crutchfield, W. L. Ditto, and S. Sinha, “Introduction to focus issue: intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony,” Chaos 20(3), 037101 (2010).
[Crossref] [PubMed]

Cui, K.

D’Haene, M.

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

Dambre, J.

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(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, “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.

Deligiannidis, S.

Ditto, W. L.

J. P. Crutchfield, W. L. Ditto, and S. Sinha, “Introduction to focus issue: intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony,” Chaos 20(3), 037101 (2010).
[Crossref] [PubMed]

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 (2015).
[Crossref] [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.

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

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

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]

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]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

García-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[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]

Guillet de Chatellus, H.

Gutierrez, J. M.

Haelterman, M.

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]

Hou, Y. S.

Y. S. Hou, L. L. Yi, G. Q. Xia, and Z. M. Wu, “Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor laser system,” IEEE Photonics J. 9(5), 1505110 (2017).
[Crossref]

Huang, Y.

Hübner, U.

U. Hübner, N. B. Abraham, and C. O. Weiss, “Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser,” Phys. Rev. A Gen. Phys. 40(11), 6354–6365 (1989).
[Crossref] [PubMed]

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]

Kanno, K.

Kim, B.

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]

Lacot, E.

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.

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]

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]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Li, B.

Li, N.

Liu, F.

Locquet, A.

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.

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 (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]

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]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Morthier, G.

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

Naughton, T. J.

D. Woods and T. J. Naughton, “Optical computing: photonic neural networks,” Nat. Phys. 8(4), 257–259 (2012).
[Crossref]

Nguimdo, R. M.

Oudar, J. L.

Pan, W.

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]

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.

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]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Pikasis, E.

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]

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(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]

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

Shore, K. A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Sinha, S.

J. P. Crutchfield, W. L. Ditto, and S. Sinha, “Introduction to focus issue: intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony,” Chaos 20(3), 037101 (2010).
[Crossref] [PubMed]

Smerieri, A.

Soriano, M. C.

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

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 (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]

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]

Stroobandt, D.

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

Syvridis, D.

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[Crossref] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Uchida, A.

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, “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]

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]

Verschaffelt, G.

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]

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]

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

Vinckier, Q.

Wang, Y.

Weiss, C. O.

U. Hübner, N. B. Abraham, and C. O. Weiss, “Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser,” Phys. Rev. A Gen. Phys. 40(11), 6354–6365 (1989).
[Crossref] [PubMed]

Woods, D.

D. Woods and T. J. Naughton, “Optical computing: photonic neural networks,” Nat. Phys. 8(4), 257–259 (2012).
[Crossref]

Wu, J. G.

Wu, Z. M.

Y. S. Hou, L. L. Yi, G. Q. Xia, and Z. M. Wu, “Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor laser system,” IEEE Photonics J. 9(5), 1505110 (2017).
[Crossref]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[Crossref] [PubMed]

Xia, G. Q.

Y. S. Hou, L. L. Yi, G. Q. Xia, and Z. M. Wu, “Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor laser system,” IEEE Photonics J. 9(5), 1505110 (2017).
[Crossref]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[Crossref] [PubMed]

Yi, L. L.

Y. S. Hou, L. L. Yi, G. Q. Xia, and Z. M. Wu, “Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor laser system,” IEEE Photonics J. 9(5), 1505110 (2017).
[Crossref]

Zhang, H.

Chaos (1)

J. P. Crutchfield, W. L. Ditto, and S. Sinha, “Introduction to focus issue: intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony,” Chaos 20(3), 037101 (2010).
[Crossref] [PubMed]

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 (2015).
[Crossref] [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 Photonics J. (1)

Y. S. Hou, L. L. Yi, G. Q. Xia, and Z. M. Wu, “Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor laser system,” IEEE Photonics J. 9(5), 1505110 (2017).
[Crossref]

IEEE Trans. Neural Netw. (1)

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

Nat. Phys. (1)

D. Woods and T. J. Naughton, “Optical computing: photonic neural networks,” Nat. Phys. 8(4), 257–259 (2012).
[Crossref]

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[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]

Neural Netw. (1)

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

Opt. Express (10)

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]

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[Crossref] [PubMed]

N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (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]

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

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

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]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[Crossref] [PubMed]

Opt. Lett. (1)

Optica (1)

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

U. Hübner, N. B. Abraham, and C. O. Weiss, “Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser,” Phys. Rev. A Gen. Phys. 40(11), 6354–6365 (1989).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

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]

Phys. Rev. Lett. (1)

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. (1)

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

Other (3)

H. Jaeger, “The ‘echo state’ approach to analyzing and training recurrent neural networks,” Technical Report GMD Report 148, German National Research Center for Information Technology (2001).

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).

L. Appeltant, “Reservoir computing based on delay-dynamical systems,” http://www.tdx.cat/handle/10803/ 84144 (2012).

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of RC for predicating based on a response SL (R-SL) under double optical feedback and optical injection from a drive SL (D-SL).
Fig. 2
Fig. 2 NMSEs as a function of the virtual node interval θ (a) and the number of virtual nodes N (b) under T ( = ) fixed at 40 ns. Red lines are for single optical feedback with k1 = 15.53 ns−1 and τ1 = T + θ, and blue lines are for double optical feedback with k1 = k2 = 7.765 ns−1 under τ1 = T + θ and τ2τ1 = 0.335 ns.
Fig. 3
Fig. 3 NMSEs as a function of T for the RC system with double feedback loops under τ2τ1 = 0.335 ns and N = 100, 200, 400, respectively.
Fig. 4
Fig. 4 NMSE as a function of the delayed time τ2 for the RC with double feedback loops under 1 Gb/s data processing rate in a relatively large scale (a) and a much smaller scale (b).
Fig. 5
Fig. 5 NMSE as a function of the scaling factor γ in the RC system with double feedback loops under 1 Gb/s data processing rate for τ1 = 1.01 ns, τ2 = 1.17 ns.
Fig. 6
Fig. 6 Mapping of NMSE in the parameter space of τ2 and γ for the RC system with double feedback loops under k1 = k2 = 7.765 ns−1, N = 100 and θ = 10 ps.
Fig. 7
Fig. 7 NMSE as a function of the delayed time τ2 for the RC with double feedback loops under 1 Gb/s data processing rate in a much smaller scale of (a) ɵ1 = π/4, ɵ2 = π, (b) ɵ1 = π/4, ɵ2 = π/3 and (c) ɵ1 = 7π/4, ɵ2 = π/3.

Equations (5)

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dE(t) dt = 1 2 (1+iα)[ g( N r ( t ) N 0 ) 1+ε | E(t) | 2 1 τ p ]E(t)+ k 1 E( t τ 1 ) e i2πν τ 1 +i θ 1 + k 2 E( t τ 2 ) e i2πν τ 2 +i θ 2 + k inj E inj ( t ) e i2πΔνt +F(t)
dN(t) dt =J N(t) τ s g( N( t ) N 0 ) 1+ε | E(t) | 2 | E(t) | 2
E inj ( t )= I d e (iπS(t)) ,
S( t )=M( t )×u( n )×γ,
NMSE= 1 L n=1 L (y(n) y ¯ (n)) 2 /var(y),

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