Abstract

Photonic reservoir computing is a new paradigm for performing high-speed prediction and classification tasks in an efficient manner. The major challenge for the miniaturization of photonic reservoir computing is the need for the use of photonic integrated circuits. Herein, we experimentally demonstrate reservoir computing using a photonic integrated circuit with a semiconductor laser and a short external cavity. We propose a method to increase the number of virtual nodes in delayed feedback using short node intervals and outputs from multiple delay times. We perform time-series prediction and nonlinear channel equalization tasks using reservoir computing with the photonic integrated circuit. We show that the photonic integrated circuit with optical feedback outperforms the photonic integrated circuit without optical feedback for prediction tasks. To enhance the memory effect we feed past input signals in the current input data and demonstrate successful performance in an n-step-ahead prediction task.

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

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References

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2018 (3)

2017 (8)

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

A. Karsaklian Dal Bosco, N. Sato, Y. Terashima, S. Ohara, A. Uchida, T. Harayama, and M. Inubushi, “Random number generation from intermittent optical chaos,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1801208 (2017).

T. Sasaki, I. Kakesu, Y. Mitsui, D. Rontani, A. Uchida, S. Sunada, K. Yoshimura, and M. Inubushi, “Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution,” Opt. Express 25(21), 26029–26044 (2017).
[Crossref] [PubMed]

L. Larger, A. Baylón-Fuentes, R. Martinenghi, V. S. Udaltsov, Y. K. Chembo, and M. Jacquot, “High-speed photonic reservoir computing using a time-delay-based architecture: Million words per second classification,” Phys. Rev. X 7(1), 011015 (2017).
[Crossref]

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]

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: mapping the short cavity regime,” IEEE Photonics J. 9(2), 6600512 (2017).

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]

M. Inubushi and K. Yoshimura, “Reservoir computing beyond memory-nonlinearity trade-off,” Sci. Rep. 7(1), 10199 (2017).
[Crossref] [PubMed]

2016 (2)

2015 (3)

2014 (4)

2013 (4)

J.-G. Wu, L.-J. Zhao, Z.-M. Wu, D. Lu, X. Tang, Z.-Q. Zhong, and G.-Q. Xia, “Direct generation of broadband chaos by a monolithic integrated semiconductor laser chip,” Opt. Express 21(20), 23358–23364 (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]

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(1), 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]

2012 (4)

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

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]

2011 (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(1), 468 (2011).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83, 031803 (R) (2011).

2010 (2)

2008 (1)

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

2004 (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]

H. Jaeger and 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, 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]

Akizawa, Y.

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(1), 468 (2011).
[Crossref] [PubMed]

Arai, K.

Argyris, A.

Baylón-Fuentes, A.

L. Larger, A. Baylón-Fuentes, R. Martinenghi, V. S. Udaltsov, Y. K. Chembo, and M. Jacquot, “High-speed photonic reservoir computing using a time-delay-based architecture: Million words per second classification,” Phys. Rev. X 7(1), 011015 (2017).
[Crossref]

Bienstman, P.

A. Katumba, J. Heyvaert, B. Schneider, S. Uvin, J. Dambre, and P. Bienstman, “Low-loss photonic reservoir computing with multimode photonic integrated circuits,” Sci. Rep. 8(1), 2653 (2018).
[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]

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(1), 3541 (2014).
[Crossref] [PubMed]

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]

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]

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(1), 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.

Chembo, Y. K.

L. Larger, A. Baylón-Fuentes, R. Martinenghi, V. S. Udaltsov, Y. K. Chembo, and M. Jacquot, “High-speed photonic reservoir computing using a time-delay-based architecture: Million words per second classification,” Phys. Rev. X 7(1), 011015 (2017).
[Crossref]

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]

Chlouverakis, K. E.

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

Dambre, J.

A. Katumba, J. Heyvaert, B. Schneider, S. Uvin, J. Dambre, and P. Bienstman, “Low-loss photonic reservoir computing with multimode photonic integrated circuits,” Sci. Rep. 8(1), 2653 (2018).
[Crossref] [PubMed]

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(1), 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(1), 468 (2011).
[Crossref] [PubMed]

Danckaert, J.

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(1), 468 (2011).
[Crossref] [PubMed]

Davis, P.

Dejonckheere, A.

Deligiannidis, S.

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.

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(1), 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]

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]

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(1), 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(1), 468 (2011).
[Crossref] [PubMed]

Gershenfeld, N. A.

A. S. Weigend and N. A. Gershenfeld, “Results of the time series prediction competition at the Santa Fe Institute,” IEEE International Conference on Neural Networks3, 1786–1793 (1993).
[Crossref]

Grivas, E.

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.

Hamacher, M.

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010).
[Crossref] [PubMed]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

Harayama, T.

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: mapping the short cavity regime,” IEEE Photonics J. 9(2), 6600512 (2017).

A. Karsaklian Dal Bosco, N. Sato, Y. Terashima, S. Ohara, A. Uchida, T. Harayama, and M. Inubushi, “Random number generation from intermittent optical chaos,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1801208 (2017).

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

A. Karsaklian Dal Bosco, Y. Akizawa, K. Kanno, A. Uchida, T. Harayama, and K. Yoshimura, “Photonic integrated circuits unveil crisis-induced intermittency,” Opt. Express 24(19), 22198–22209 (2016).
[Crossref] [PubMed]

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83, 031803 (R) (2011).

Heyvaert, J.

A. Katumba, J. Heyvaert, B. Schneider, S. Uvin, J. Dambre, and P. Bienstman, “Low-loss photonic reservoir computing with multimode photonic integrated circuits,” Sci. Rep. 8(1), 2653 (2018).
[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.

Hu, C.

Hugon, O.

Inubushi, M.

T. Sasaki, I. Kakesu, Y. Mitsui, D. Rontani, A. Uchida, S. Sunada, K. Yoshimura, and M. Inubushi, “Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution,” Opt. Express 25(21), 26029–26044 (2017).
[Crossref] [PubMed]

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: mapping the short cavity regime,” IEEE Photonics J. 9(2), 6600512 (2017).

A. Karsaklian Dal Bosco, N. Sato, Y. Terashima, S. Ohara, A. Uchida, T. Harayama, and M. Inubushi, “Random number generation from intermittent optical chaos,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1801208 (2017).

M. Inubushi and K. Yoshimura, “Reservoir computing beyond memory-nonlinearity trade-off,” Sci. Rep. 7(1), 10199 (2017).
[Crossref] [PubMed]

Iwakawa, K.

Jacquin, O.

Jacquot, M.

L. Larger, A. Baylón-Fuentes, R. Martinenghi, V. S. Udaltsov, Y. K. Chembo, and M. Jacquot, “High-speed photonic reservoir computing using a time-delay-based architecture: Million words per second classification,” Phys. Rev. X 7(1), 011015 (2017).
[Crossref]

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]

Jayaprasath, E.

Jiang, Z.

Kakesu, I.

Kane, D. M.

Kanno, K.

Karsaklian Dal Bosco, A.

A. Karsaklian Dal Bosco, N. Sato, Y. Terashima, S. Ohara, A. Uchida, T. Harayama, and M. Inubushi, “Random number generation from intermittent optical chaos,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1801208 (2017).

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: mapping the short cavity regime,” IEEE Photonics J. 9(2), 6600512 (2017).

A. Karsaklian Dal Bosco, Y. Akizawa, K. Kanno, A. Uchida, T. Harayama, and K. Yoshimura, “Photonic integrated circuits unveil crisis-induced intermittency,” Opt. Express 24(19), 22198–22209 (2016).
[Crossref] [PubMed]

Katumba, A.

A. Katumba, J. Heyvaert, B. Schneider, S. Uvin, J. Dambre, and P. Bienstman, “Low-loss photonic reservoir computing with multimode photonic integrated circuits,” Sci. Rep. 8(1), 2653 (2018).
[Crossref] [PubMed]

Kuriki, Y.

Lacot, E.

Larger, L.

L. Larger, A. Baylón-Fuentes, R. Martinenghi, V. S. Udaltsov, Y. K. Chembo, and M. Jacquot, “High-speed photonic reservoir computing using a time-delay-based architecture: Million words per second classification,” Phys. Rev. X 7(1), 011015 (2017).
[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]

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]

Lu, D.

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.

L. Larger, A. Baylón-Fuentes, R. Martinenghi, V. S. Udaltsov, Y. K. Chembo, and M. Jacquot, “High-speed photonic reservoir computing using a time-delay-based architecture: Million words per second classification,” Phys. Rev. X 7(1), 011015 (2017).
[Crossref]

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]

McMahon, C.

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(1), 3541 (2014).
[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]

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, and L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21(1), 12–20 (2013).
[Crossref] [PubMed]

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 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(1), 468 (2011).
[Crossref] [PubMed]

Mitsui, Y.

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(1), 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]

Nguimdo, R. M.

Ohara, S.

A. Karsaklian Dal Bosco, N. Sato, Y. Terashima, S. Ohara, A. Uchida, T. Harayama, and M. Inubushi, “Random number generation from intermittent optical chaos,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1801208 (2017).

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: mapping the short cavity regime,” IEEE Photonics J. 9(2), 6600512 (2017).

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.

Pikasis, E.

Rontani, D.

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]

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]

Sasaki, T.

Sato, N.

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: mapping the short cavity regime,” IEEE Photonics J. 9(2), 6600512 (2017).

A. Karsaklian Dal Bosco, N. Sato, Y. Terashima, S. Ohara, A. Uchida, T. Harayama, and M. Inubushi, “Random number generation from intermittent optical chaos,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1801208 (2017).

Schneider, B.

A. Katumba, J. Heyvaert, B. Schneider, S. Uvin, J. Dambre, and P. Bienstman, “Low-loss photonic reservoir computing with multimode photonic integrated circuits,” Sci. Rep. 8(1), 2653 (2018).
[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]

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(1), 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(1), 468 (2011).
[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]

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]

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(1), 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(1), 468 (2011).
[Crossref] [PubMed]

Sunada, S.

Syvridis, D.

Takahashi, R.

Takano, K.

Tang, X.

Terashima, Y.

A. Karsaklian Dal Bosco, N. Sato, Y. Terashima, S. Ohara, A. Uchida, T. Harayama, and M. Inubushi, “Random number generation from intermittent optical chaos,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1801208 (2017).

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

Toomey, J. P.

Tsuzuki, K.

Uchida, A.

Y. Kuriki, J. Nakayama, K. Takano, and A. Uchida, “Impact of input mask signals on delay-based photonic reservoir computing with semiconductor lasers,” Opt. Express 26(5), 5777–5788 (2018).
[Crossref] [PubMed]

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

T. Sasaki, I. Kakesu, Y. Mitsui, D. Rontani, A. Uchida, S. Sunada, K. Yoshimura, and M. Inubushi, “Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution,” Opt. Express 25(21), 26029–26044 (2017).
[Crossref] [PubMed]

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: mapping the short cavity regime,” IEEE Photonics J. 9(2), 6600512 (2017).

A. Karsaklian Dal Bosco, N. Sato, Y. Terashima, S. Ohara, A. Uchida, T. Harayama, and M. Inubushi, “Random number generation from intermittent optical chaos,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1801208 (2017).

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. Karsaklian Dal Bosco, Y. Akizawa, K. Kanno, A. Uchida, T. Harayama, and K. Yoshimura, “Photonic integrated circuits unveil crisis-induced intermittency,” Opt. Express 24(19), 22198–22209 (2016).
[Crossref] [PubMed]

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83, 031803 (R) (2011).

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]

Udaltsov, V. S.

L. Larger, A. Baylón-Fuentes, R. Martinenghi, V. S. Udaltsov, Y. K. Chembo, and M. Jacquot, “High-speed photonic reservoir computing using a time-delay-based architecture: Million words per second classification,” Phys. Rev. X 7(1), 011015 (2017).
[Crossref]

Ugajin, K.

Uvin, S.

A. Katumba, J. Heyvaert, B. Schneider, S. Uvin, J. Dambre, and P. Bienstman, “Low-loss photonic reservoir computing with multimode photonic integrated circuits,” Sci. Rep. 8(1), 2653 (2018).
[Crossref] [PubMed]

Van der Sande, G.

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(1), 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(1), 3541 (2014).
[Crossref] [PubMed]

Verschaffelt, G.

Verstraeten, D.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5(1), 3541 (2014).
[Crossref] [PubMed]

Vinckier, Q.

Wang, D.

Weigend, A. S.

A. S. Weigend and N. A. Gershenfeld, “Results of the time series prediction competition at the Santa Fe Institute,” IEEE International Conference on Neural Networks3, 1786–1793 (1993).
[Crossref]

Wu, J.-G.

Wu, Z.

Wu, Z.-M.

Xia, G.

Xia, G.-Q.

Yang, W.

Yoshimura, K.

Zhao, L.-J.

Zhong, Z.-Q.

IEEE J. Sel. Top. Quantum Electron. (2)

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]

A. Karsaklian Dal Bosco, N. Sato, Y. Terashima, S. Ohara, A. Uchida, T. Harayama, and M. Inubushi, “Random number generation from intermittent optical chaos,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1801208 (2017).

IEEE Photonics J. (1)

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: mapping the short cavity regime,” IEEE Photonics J. 9(2), 6600512 (2017).

Nat. Commun. (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(1), 1364 (2013).
[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(1), 468 (2011).
[Crossref] [PubMed]

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(1), 3541 (2014).
[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 (17)

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. 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]

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Figures (11)

Fig. 1
Fig. 1 (a) Experimental setup for reservoir computing using a photonic integrated circuit. (b) Structure of photonic integrated circuit. Amp, electric amplifier; ATT, optical attenuator; DFB laser, distributed-feedback semiconductor laser; FC, fiber coupler; ISO, optical isolator; LD, semiconductor laser diode; PD, photodetector; PIC, photonic integrated circuit; PM, phase modulator; SOA, semiconductor optical amplifier.
Fig. 2
Fig. 2 (a) Time-series prediction task for different node intervals θ and different number of delay times k used as virtual nodes. (a) θ = 40 ps, k = 1, (b) θ = 10 ps, k = 1, (c) θ = 40 ps, k = 5, and (d) θ = 10 ps, k = 5. The numbers of the virtual nodes are (a) N = 6, (b) N = 24, (c) N = 31, and (d) N = 124, respectively. The mask interval is set to θM = 40 ps.
Fig. 3
Fig. 3 Prediction errors (NMSEs) as a function of (a) the number of the delay times k and (b) the number of virtual nodes N. The node intervals θ are set to 10 ps (black circles), 20 ps (red squares), and 40 ps (blue diamonds). The mean NMSE values for ten different repetitions of the experiments are plotted, and the maximum and minimum values of the ten repetitions are shown as error bars. The injection power is 62.3 μW.
Fig. 4
Fig. 4 NMSEs with (red curve) and without (black curve) optical feedback in the PIC as a function of the delay times k. The SOA injection currents with and without the optical feedback are respectively set to 4 and 0 mA. The mean NMSE values for ten different repetitions of the experiments are plotted, and the maximum and minimum values of the ten repetitions are shown as error bars.
Fig. 5
Fig. 5 (a) Variations of NMSE values (black curve) and cross-correlation (red curve) as a function of SOA injection current (feedback strength). (b) Variations of NMSE values as a function of normalized injection current of the PIC with (red curve) and without (black curve) optical feedback. The SOA injection currents with and without the optical feedback are respectively set to 4 and 0 mA. The number of delay times is set to k = 5. The mean NMSE values for ten different repetitions of the experiments are plotted, and the maximum and minimum values of the ten repetitions are shown as error bars.
Fig. 6
Fig. 6 (a) Memory capacity MC as a function of the number of delay times k with (red curve) and without (black curve) optical feedback. The SOA injection currents are respectively set to 4 and 0 mA with and without the optical feedback. (b) Memory capacity as a function of the SOA injection current (the feedback strength) in the cases where three (black curve), four (red), and five (blue) delay times are used.
Fig. 7
Fig. 7 NMSEs as a function of the number of past inputs with (red curve) and without (black curve) optical feedback. The SOA injection currents with and without optical feedback are respectively set to 4 and 0 mA. The number of delay times is set to k = 5. The node interval is set to θ = 10 ps.
Fig. 8
Fig. 8 NMSEs as a function of the number of past input signals P (a) without and (b) with optical feedback for different prediction steps n. The SOA injection currents in the cases with and without the optical feedback are respectively set to 4 and 0 mA. The prediction steps include n = 1 (black circles), n = 2 (red squares), n = 3 (green diamonds), and n = 7 (blue triangles).
Fig. 9
Fig. 9 NMSEs as a function of the prediction step n (a) without and (b) with optical feedback for different past input signals P. The SOA injection currents with and without the optical feedback are respectively set to 4 and 0 mA. The numbers of past input signals include P = 0 (black circles), P = 2 (red squares), P = 6 (green diamonds), and P = 15 (blue triangles).
Fig. 10
Fig. 10 Auto-correlation function of the Santa Fe time series of the laser chaos [35] used for the prediction task.
Fig. 11
Fig. 11 Results of nonlinear channel equalization task. (a) Signal error rate (SER) as a function of the signal-to-noise ratio (SNR) of the nonlinear channel signal. (b) SER as a function of the SOA injection current (the feedback strength) for different past input signals. The numbers of past input signals are P = 0 (black), P = 1 (red), and P = 7 (blue).

Equations (7)

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N=[ (int){ (int) kτ θ M } θ M θ ]
m(i)= ( y(ni) )( o i (n) ) 2 σ 2 ( y(n) ) σ 2 ( o i (n) )
MC= i=1 m(i)
U(t)= i=0 P g i m i (t)u(ni)
g i =1 i P+1
q(n)=0.08d(n+2)0.12d(n+1)+d(n)+0.18d(n1)0.1d(n2)        +0.091d(n3)0.05d(n4)+0.04d(n5)        +0.03d(n6)+0.01d(n7)
u(n)=q(n)+0.036q (n) 2 0.011q (n) 3 +v(n)

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