Abstract

Reservoir computing is a new bio-inspired computation paradigm. It exploits a dynamical system driven by a time-dependent input to carry out computation. For efficient information processing, only a few parameters of the reservoir needs to be tuned, which makes it a promising framework for hardware implementation. Recently, electronic, opto-electronic and all-optical experimental reservoir computers were reported. In those implementations, the nonlinear response of the reservoir is provided by active devices such as optoelectronic modulators or optical amplifiers. By contrast, we propose here the first reservoir computer based on a fully passive nonlinearity, namely the saturable absorption of a semiconductor mirror. Our experimental setup constitutes an important step towards the development of ultrafast low-consumption analog computers.

© 2014 Optical Society of America

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2014 (1)

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. BIenstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 4, 3541 (2014).

2013 (2)

C. Mesaritakis, V. Papataxiarhis, D. Syvridis, “Micro ring resonators as building blocks for an all-optical high-speed reservoir-computing bit-pattern-recognition system,” J. Opt. Soc. Am. B 30, 3048–3055 (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,” Nat. Commun. 4, 1364 (2013).
[CrossRef]

2012 (5)

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 468 (2012).
[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]

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

L. Bramerie, Q. Trung Le, M. Gay, A. O’Hare, S. Lobo, M. Joindot, J-C Simon, H-T. Nguyen, J-L. Oudar, “All-optical 2R regeneration with a vertical microcavity-based saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 18870–883 (2012).
[CrossRef]

J. Dambre, D. Verstraeten, B. Schrauwen, S. Massar, “Information processing capacity of dynamical systems,” Sci. Rep. 2, 514 (2012).
[CrossRef] [PubMed]

2011 (3)

A. Rodan, P. Tiňo, “Minimum complexity echo state network,” IEEE T. Neural Netw. 22131–144 (2011).
[CrossRef]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE T. Neural Netw. 221469–1481 (2011).
[CrossRef]

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 (2011).
[CrossRef] [PubMed]

2009 (1)

M. Lukoševičius, H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3127–149 (2009).
[CrossRef]

2008 (1)

2006 (2)

D. Massoubre, J.L. Oudar, J. Fatome, S. Pitois, G. Millot, J. Decobert, J. Landreau, “All-optical extinction ratio enhancement of a 160 Ghz pulse train by a saturable absorber vertical microcavity,” Opt. Lett. 31537–539 (2006).
[CrossRef] [PubMed]

D. Massoubre, J-L. Oudar, J. Dion, J-C Harmand, A. Shen, J. Landreau, L. Decobert, “Scaling of the saturation energy in microcavity saturable absorber devices,” Appl. Phys. Lett. 88153513 (2006).
[CrossRef]

2004 (1)

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

2002 (1)

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

Appeltant, L.

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 (2011).
[CrossRef] [PubMed]

Baets, R.

BIenstman, P.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. BIenstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 4, 3541 (2014).

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE T. Neural Netw. 221469–1481 (2011).
[CrossRef]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, J. Van Campenhout, “Toward optical signal processing using Photonic Reservoir Computing,” Opt. Express 16, 11182–11192 (2008).
[CrossRef] [PubMed]

Bramerie, L.

L. Bramerie, Q. Trung Le, M. Gay, A. O’Hare, S. Lobo, M. Joindot, J-C Simon, H-T. Nguyen, J-L. Oudar, “All-optical 2R regeneration with a vertical microcavity-based saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 18870–883 (2012).
[CrossRef]

Brunner, D.

Dambre, J.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. BIenstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 4, 3541 (2014).

J. Dambre, D. Verstraeten, B. Schrauwen, S. Massar, “Information processing capacity of dynamical systems,” Sci. Rep. 2, 514 (2012).
[CrossRef] [PubMed]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 468 (2012).
[CrossRef] [PubMed]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE T. Neural Netw. 221469–1481 (2011).
[CrossRef]

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 (2011).
[CrossRef] [PubMed]

Danckaert, J.

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 (2011).
[CrossRef] [PubMed]

Decobert, J.

Decobert, L.

D. Massoubre, J-L. Oudar, J. Dion, J-C Harmand, A. Shen, J. Landreau, L. Decobert, “Scaling of the saturation energy in microcavity saturable absorber devices,” Appl. Phys. Lett. 88153513 (2006).
[CrossRef]

Dierckx, W.

Dion, J.

D. Massoubre, J-L. Oudar, J. Dion, J-C Harmand, A. Shen, J. Landreau, L. Decobert, “Scaling of the saturation energy in microcavity saturable absorber devices,” Appl. Phys. Lett. 88153513 (2006).
[CrossRef]

Duport, F.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 468 (2012).
[CrossRef] [PubMed]

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

Fatome, J.

Fiers, M.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. BIenstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 4, 3541 (2014).

Fischer, I.

D. Brunner, M. C. Soriano, C. R. Mirasso, I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. 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]

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 (2011).
[CrossRef] [PubMed]

Gay, M.

L. Bramerie, Q. Trung Le, M. Gay, A. O’Hare, S. Lobo, M. Joindot, J-C Simon, H-T. Nguyen, J-L. Oudar, “All-optical 2R regeneration with a vertical microcavity-based saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 18870–883 (2012).
[CrossRef]

Gutierrez, J. M.

Haas, H.

H. Jaeger, H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304(5667), 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, 468 (2012).
[CrossRef] [PubMed]

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

Harmand, J-C

D. Massoubre, J-L. Oudar, J. Dion, J-C Harmand, A. Shen, J. Landreau, L. Decobert, “Scaling of the saturation energy in microcavity saturable absorber devices,” Appl. Phys. Lett. 88153513 (2006).
[CrossRef]

Jaeger, H.

M. Lukoševičius, H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3127–149 (2009).
[CrossRef]

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

H. Jaeger, “The ’echo state’ approach to analysing and training recurrent neural networks - with an Erratum note,” GMD Report 148: German National Research Centre for Information Technology (2001).

H. Jaeger, “Short-term memory in echo states networks,” GMD Report 152, German National Research Center for Information Technology (2002).

Joindot, M.

L. Bramerie, Q. Trung Le, M. Gay, A. O’Hare, S. Lobo, M. Joindot, J-C Simon, H-T. Nguyen, J-L. Oudar, “All-optical 2R regeneration with a vertical microcavity-based saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 18870–883 (2012).
[CrossRef]

Landreau, J.

D. Massoubre, J-L. Oudar, J. Dion, J-C Harmand, A. Shen, J. Landreau, L. Decobert, “Scaling of the saturation energy in microcavity saturable absorber devices,” Appl. Phys. Lett. 88153513 (2006).
[CrossRef]

D. Massoubre, J.L. Oudar, J. Fatome, S. Pitois, G. Millot, J. Decobert, J. Landreau, “All-optical extinction ratio enhancement of a 160 Ghz pulse train by a saturable absorber vertical microcavity,” Opt. Lett. 31537–539 (2006).
[CrossRef] [PubMed]

Larger, L.

Lobo, S.

L. Bramerie, Q. Trung Le, M. Gay, A. O’Hare, S. Lobo, M. Joindot, J-C Simon, H-T. Nguyen, J-L. Oudar, “All-optical 2R regeneration with a vertical microcavity-based saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 18870–883 (2012).
[CrossRef]

Lukoševicius, M.

M. Lukoševičius, H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3127–149 (2009).
[CrossRef]

Lyon, R.

R. Lyon, “A computational model of filtering, detection, and compression in the cochlea,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, 1282–1285 (1982).
[CrossRef]

Maass, W.

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

Markram, H.

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

Massar, S.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 468 (2012).
[CrossRef] [PubMed]

J. Dambre, D. Verstraeten, B. Schrauwen, S. Massar, “Information processing capacity of dynamical systems,” Sci. Rep. 2, 514 (2012).
[CrossRef] [PubMed]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795 (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 (2011).
[CrossRef] [PubMed]

Massoubre, D.

D. Massoubre, J-L. Oudar, J. Dion, J-C Harmand, A. Shen, J. Landreau, L. Decobert, “Scaling of the saturation energy in microcavity saturable absorber devices,” Appl. Phys. Lett. 88153513 (2006).
[CrossRef]

D. Massoubre, J.L. Oudar, J. Fatome, S. Pitois, G. Millot, J. Decobert, J. Landreau, “All-optical extinction ratio enhancement of a 160 Ghz pulse train by a saturable absorber vertical microcavity,” Opt. Lett. 31537–539 (2006).
[CrossRef] [PubMed]

Mechet, P.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. BIenstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 4, 3541 (2014).

Mesaritakis, C.

Millot, G.

Mirasso, C. R.

Mirasso, C.R.

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 (2011).
[CrossRef] [PubMed]

Morthier, G.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. BIenstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 4, 3541 (2014).

Natschläger, T.

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

Nguyen, H-T.

L. Bramerie, Q. Trung Le, M. Gay, A. O’Hare, S. Lobo, M. Joindot, J-C Simon, H-T. Nguyen, J-L. Oudar, “All-optical 2R regeneration with a vertical microcavity-based saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 18870–883 (2012).
[CrossRef]

O’Hare, A.

L. Bramerie, Q. Trung Le, M. Gay, A. O’Hare, S. Lobo, M. Joindot, J-C Simon, H-T. Nguyen, J-L. Oudar, “All-optical 2R regeneration with a vertical microcavity-based saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 18870–883 (2012).
[CrossRef]

Oudar, J.L.

Oudar, J-L.

L. Bramerie, Q. Trung Le, M. Gay, A. O’Hare, S. Lobo, M. Joindot, J-C Simon, H-T. Nguyen, J-L. Oudar, “All-optical 2R regeneration with a vertical microcavity-based saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 18870–883 (2012).
[CrossRef]

D. Massoubre, J-L. Oudar, J. Dion, J-C Harmand, A. Shen, J. Landreau, L. Decobert, “Scaling of the saturation energy in microcavity saturable absorber devices,” Appl. Phys. Lett. 88153513 (2006).
[CrossRef]

Papataxiarhis, V.

Paquot, Y.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 468 (2012).
[CrossRef] [PubMed]

Pesquera, L.

Pitois, S.

Rodan, A.

A. Rodan, P. Tiňo, “Minimum complexity echo state network,” IEEE T. Neural Netw. 22131–144 (2011).
[CrossRef]

A. Rodan, P. Tiňo, “Simple deterministically constructed recurrent neural networks,” in Intelligent Data Engineering and Automated Learning (IDEAL, 2010), pp. 267–274.

Schneider, B.

Schrauwen, B.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. BIenstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 4, 3541 (2014).

J. Dambre, D. Verstraeten, B. Schrauwen, S. Massar, “Information processing capacity of dynamical systems,” Sci. Rep. 2, 514 (2012).
[CrossRef] [PubMed]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 468 (2012).
[CrossRef] [PubMed]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE T. Neural Netw. 221469–1481 (2011).
[CrossRef]

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 (2011).
[CrossRef] [PubMed]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, J. Van Campenhout, “Toward optical signal processing using Photonic Reservoir Computing,” Opt. Express 16, 11182–11192 (2008).
[CrossRef] [PubMed]

D. Verstraeten, B. Schrauwen, D. Stroobandt, “Isolated word recognition using a liquid state machine,” in Proceedings of the 13th European Symposium on Artificial Neural Networks(ESANN), 435–440 (2005).

Shen, A.

D. Massoubre, J-L. Oudar, J. Dion, J-C Harmand, A. Shen, J. Landreau, L. Decobert, “Scaling of the saturation energy in microcavity saturable absorber devices,” Appl. Phys. Lett. 88153513 (2006).
[CrossRef]

Simon, J-C

L. Bramerie, Q. Trung Le, M. Gay, A. O’Hare, S. Lobo, M. Joindot, J-C Simon, H-T. Nguyen, J-L. Oudar, “All-optical 2R regeneration with a vertical microcavity-based saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 18870–883 (2012).
[CrossRef]

Smerieri, A.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 468 (2012).
[CrossRef] [PubMed]

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Soriano, M.C.

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 (2011).
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Syvridis, D.

Tino, P.

A. Rodan, P. Tiňo, “Minimum complexity echo state network,” IEEE T. Neural Netw. 22131–144 (2011).
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A. Rodan, P. Tiňo, “Simple deterministically constructed recurrent neural networks,” in Intelligent Data Engineering and Automated Learning (IDEAL, 2010), pp. 267–274.

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L. Bramerie, Q. Trung Le, M. Gay, A. O’Hare, S. Lobo, M. Joindot, J-C Simon, H-T. Nguyen, J-L. Oudar, “All-optical 2R regeneration with a vertical microcavity-based saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 18870–883 (2012).
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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 (2011).
[CrossRef] [PubMed]

Van Vaerenbergh, T.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. BIenstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 4, 3541 (2014).

Vandoorne, K.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. BIenstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 4, 3541 (2014).

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE T. Neural Netw. 221469–1481 (2011).
[CrossRef]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, J. Van Campenhout, “Toward optical signal processing using Photonic Reservoir Computing,” Opt. Express 16, 11182–11192 (2008).
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K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. BIenstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 4, 3541 (2014).

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[CrossRef] [PubMed]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE T. Neural Netw. 221469–1481 (2011).
[CrossRef]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, J. Van Campenhout, “Toward optical signal processing using Photonic Reservoir Computing,” Opt. Express 16, 11182–11192 (2008).
[CrossRef] [PubMed]

D. Verstraeten, B. Schrauwen, D. Stroobandt, “Isolated word recognition using a liquid state machine,” in Proceedings of the 13th European Symposium on Artificial Neural Networks(ESANN), 435–440 (2005).

Appl. Phys. Lett. (1)

D. Massoubre, J-L. Oudar, J. Dion, J-C Harmand, A. Shen, J. Landreau, L. Decobert, “Scaling of the saturation energy in microcavity saturable absorber devices,” Appl. Phys. Lett. 88153513 (2006).
[CrossRef]

Comput. Sci. Rev. (1)

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[CrossRef]

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

L. Bramerie, Q. Trung Le, M. Gay, A. O’Hare, S. Lobo, M. Joindot, J-C Simon, H-T. Nguyen, J-L. Oudar, “All-optical 2R regeneration with a vertical microcavity-based saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 18870–883 (2012).
[CrossRef]

IEEE T. Neural Netw. (2)

A. Rodan, P. Tiňo, “Minimum complexity echo state network,” IEEE T. Neural Netw. 22131–144 (2011).
[CrossRef]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE T. Neural Netw. 221469–1481 (2011).
[CrossRef]

J. Opt. Soc. Am. B (1)

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 (2011).
[CrossRef] [PubMed]

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

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. BIenstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 4, 3541 (2014).

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Opt. Express (3)

Opt. Lett. (1)

Sci. Rep. (2)

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 468 (2012).
[CrossRef] [PubMed]

J. Dambre, D. Verstraeten, B. Schrauwen, S. Massar, “Information processing capacity of dynamical systems,” Sci. Rep. 2, 514 (2012).
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H. Jaeger, “Short-term memory in echo states networks,” GMD Report 152, German National Research Center for Information Technology (2002).

http://soma.ece.mcmaster.ca/ipix/dartmouth/datasets.html

D. Verstraeten, B. Schrauwen, D. Stroobandt, “Isolated word recognition using a liquid state machine,” in Proceedings of the 13th European Symposium on Artificial Neural Networks(ESANN), 435–440 (2005).

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[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Principle of the delay dynamical system reservoir computer. The states xi(n) of the reservoir are multiplexed in time. Each input u(n) is held for a time T = and is divided in N time windows of length θ during which it is multiplied by the value mi. All these inputs miu(n) are multiplied by the input gain β and fed into the delay loop where they are processed by an element applying a nonlinear transformation FNL. Part of the signal is extracted for readout while the remaining signal is sent back into the dynamical system after multiplication by the feedback gain α. The period of the loop T′ is desynchronized with respect to the input time T through the relation T′ = (N + k)θ, which allows for coupling between neighboring states. In this work, we choose k = 1 which means that each internal state is coupled to its direct neighbor.

Fig. 2
Fig. 2

Comparison of the experimentally measured output-input nonlinear relations of the SOA used in our previous work [8] pumped by a 200 mA current (blue, top and left axes) and of the SESAM used in the current work (red, bottom and right axes). The SOA exhibits a nonlinear behavior at high input power and is mainly linear at low input powers. The situation is reversed for the SESAM. Dashed lines show where a linear approximation holds, i.e. for high input and low input powers for the SESAM and the SOA, respectively.

Fig. 3
Fig. 3

The SESAM structure consists of 4 different layers deposited on a copper substrate. A saturable absorber layer (InGaAs) is sandwiched between two InP phase layers. More information about this type of structure can be found in ref. [15].

Fig. 4
Fig. 4

Reflectivity of the SESAM structure as a function of its input power. The reflectivity is measured relatively to a gold mirror to remove the intrinsic losses of the experimental setup. For input powers lower than −13dBm (50μW), the reflectivity is almost constant and the response of the SESAM is essentially linear. For input powers varying between −13dBm (50μW) and 10dBm (10 mW), there is a strong variation of the reflectivity with power. Consequently, the absorber is nonlinear in this region. For higher input powers, the reflectivity is stable around a value of 0.7, meaning that the absorber acts again as a linear medium. Note the logarithmic axis used for the input power. Arrows show the average powers focused on the absorber for which interesting performances were obtained: (a) −9.20 dBm (120 μW) for nonlinear memory capacities and channel equalization, (b) −2.2 dBm (600 μW) for the radar task and (c) 0.80 dBm (1.2 mW) for the linear memory capacity and the radar task.

Fig. 5
Fig. 5

Schematic of the experimental setup of the all-optical reservoir. Optical components are depicted in red whereas electronic components are depicted in green. The all-optical loop is driven by the input optical signal. A superluminescent light emitting diode (SLED) generates a 40nm-wide spectrum centered around 1560 nm. An electronic signal corresponding to the time dependent input multiplied by the input mask is generated by the Arbitrary Waveform Generator (AWG). This electronic signal drives an integrated Lithium niobate Mach-Zehnder intensity modulator (MZ), which produces a time dependent input optical signal whose intensity is adjusted with a variable attenuator. The input optical signal is injected into the cavity by means of a 90/10 fiber coupler. The cavity itself consists of an erbium-doped fiber amplifier, a circulator, a SESAM and a fiber spool used as a delay line. A 80/20 fiber coupler is used to send 20% of the cavity intensity to the readout photodiode and then to a digitizer. Two polarization controllers are used to match the polarizations input and feedback signals with the polarization state of the amplifier. The amplifier is used in a linear regime (no saturation) to compensate for the losses in the cavity.

Fig. 6
Fig. 6

Results for channel equalization task. The signal-to-noise ratio (SNR) varies between 12 and 32 dB by steps of 4 dB. The average Symbol Error Rate (SER - the fraction of misclassified symbols) obtained on 5 experiments of 6000 inputs test sequences is presented with statistical error bars and compared with the results of our two previous opto-electronic and all-optical reservoirs of refs. [6] and [8] with the same number of internal states (N = 50).

Fig. 7
Fig. 7

Results for the radar task. The NMSE is presented for prediction delays ranging from 1 to 10. Our results are slightly better than the ones obtained with our previous opto-electronic and all-optical reservoirs for high sea state. For low sea state, our results are slightly better for small prediction delays but get slightly degraded for larger delays. On average, our results are comparable to the ones obtained by our previous hardware realizations.

Tables (1)

Tables Icon

Table 1 Comparison of the linear, quadratic, cross and total memory capacities of our optoelectronic reservoir and our two all-optical reservoirs, using N = 50 internal variables. Our new reservoir computer based on saturable absorption shows increased linear, cross and total memory capacities with respect to our first all-optical reservoir based on a SOA. For each of the different memory capacities, the optimum input gain β is determined (while α is kept fixed at 0.85, see text). The total memory capacity corresponds to the sum of the linear, quadratic and cross memory capacities for a fixed value of the parameters α, β. Only the best values are reported in the table.

Equations (5)

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x i ( n + 1 ) = F N L ( α j = 1 N A i j x j ( n ) + β m i u ( n + 1 ) )
y ( n ) = i = 1 N W i x i ( n )
N M S E = ( y y ^ ) 2 n ( y y ^ n ) 2 n
x i ( n + 1 ) = { F N L ( α x i 1 ( n ) + β m i u ( n + 1 ) ) if 2 i N F N L ( α x N + i 1 ( n 1 ) + β m i u ( n + 1 ) ) if i = 1
q ( n ) = 0.08 d ( n + 2 ) 0.12 d ( n + 1 ) + d ( n ) + 0.18 d ( n 1 ) 0.1 d ( n 2 ) + 0.091 d ( n 3 ) 0.05 d ( n 4 ) + 0.04 d ( n 5 ) + 0.03 d ( n 6 ) + 0.01 d ( n 7 ) u ( n ) = q ( n ) + 0.036 q 2 ( n ) 0.011 q 3 ( n ) + ν ( n )

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