Abstract

Photonic implementations of reservoir computing (RC) have been receiving considerable attention due to their excellent performance, hardware, and energy efficiency as well as their speed. Here, we study a particularly attractive all-optical system using optical information injection into a semiconductor laser with delayed feedback. We connect its injection locking, consistency, and memory properties to the RC performance in a non-linear prediction task. We find that for partial injection locking we achieve a good combination of consistency and memory. Therefore, we are able to provide a physical basis identifying operational parameters suitable for prediction.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (6)

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van DenDriessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
[Crossref] [PubMed]

J. Qin, Q. Zhao, D. Xu, H. Yin, Y. Chang, and D. Huang, “Optical packet header identification utilizing an all-optical feedback chaotic reservoir computing,” Mod. Phys. Lett. B 30, 1650199 (2016).
[Crossref]

K. Kanno, A. Uchida, and M. Bunsen, “Complexity and bandwidth enhancement in unidirectionally coupled semiconductor lasers with time-delayed optical feedback,” Phys. Rev. E 93, 32206 (2016).
[Crossref]

A. Argyris, M. Bourmpos, and D. Syvridis, “Experimental synchrony of semiconductor lasers in coupled networks,” Opt. Express 24, 5600–5614 (2016).
[Crossref]

J. Nakayama, K. Kanno, and A. Uchida, “Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal,” Opt. Express 24, 8679–8692 (2016).
[Crossref] [PubMed]

2015 (5)

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, 438–446 (2015).
[Crossref]

N. Oliver, T. Jüngling, and I. Fischer, “Consistency properties of a chaotic semiconductor laser driven by optical feedback,” Phys. Rev. Lett. 114, 123902 (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 91, 020801 (2015).
[Crossref]

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

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
[Crossref] [PubMed]

2013 (5)

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

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

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

Y. H. Liao and F. Y. Lin, “Dynamical characteristics and their applications of semiconductor lasers subject to both optical injection and optical feedback.,” Opt. Express 21, 23568–23578 (2013).
[Crossref] [PubMed]

K. Hicke, M. Escalona, 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, 1501610 (2013).
[Crossref]

2012 (3)

K. Kanno and A. Uchida, “Consistency and complexity in coupled semiconductor lasers with time-delayed optical feedback,” Phys. Rev. E 86, 66202 (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, 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, 287 (2012).
[Crossref] [PubMed]

2011 (2)

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

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
[Crossref] [PubMed]

2009 (1)

V. Flunkert, O. D’Huys, J. Danckaert, I. Fischer, and E. Schöll, “Bubbling in delay-coupled lasers,” Phys. Rev. E 79, 065201 (2009).
[Crossref]

2008 (1)

A. Uchida, K. Yoshimura, P. Davis, S. Yoshimori, and R. Roy, “Local conditional Lyapunov exponent characterization of consistency of dynamical response of the driven Lorenz system,” Phys. Rev. E 78, 36203 (2008).
[Crossref]

2005 (1)

S. Wieczorek, B. Krauskopf, T.B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers”, Phys. Rep. 416, 1–128 (2005).
[Crossref]

2004 (1)

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

2002 (1)

H. Jaeger, “Short term memory in echo state networks,” GMD Rep. 152, pp. 60 (2002).

1998 (1)

V. Annovazzi-Lodi, A. Scire, M. Sorel, and S. Donati, “Dynamic behavior and locking of a semiconductor laser subjected to external injection,” IEEE J. Quantum Electron. 34, 2350–2356 (1998).
[Crossref]

1997 (1)

A. S. Pikovsky, M. G. Rosenblum, G. V. Osipov, and J. Kurths, “Phase synchronization of chaotic oscillators by external driving,” Phys. D non-linear Phenom. 104, 219–238 (1997).
[Crossref]

1995 (1)

G.H.M Van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quantum Semiclass. Opt. 7, 87–143 (1995).
[Crossref]

1991 (1)

L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals,” Phys. Rev. A 44, 2374–2383 (1991).
[Crossref] [PubMed]

1990 (1)

H. G. Winful and L. Rahman, “Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers,” Phys. Rev. Lett. 65, 1575–1578 (1990).
[Crossref] [PubMed]

1986 (1)

C. Henry and R. Kazarinov, “Instability of semiconductor lasers due to optical feedback from distant reflectors,” IEEE J. Quantum Electron. 22, 294–301 (1986).
[Crossref]

1985 (1)

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron. 21, 784–793 (1985).
[Crossref]

1982 (1)

R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976–983 (1982).
[Crossref]

1981 (1)

S. Kobayashi and T. Kimura, “Injection locking in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 17, 681–689 (1981).
[Crossref]

1977 (1)

M. C. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science 197, 287–289 (1977).
[Crossref] [PubMed]

Akrout, A.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
[Crossref] [PubMed]

Annovazzi-Lodi, V.

V. Annovazzi-Lodi, A. Scire, M. Sorel, and S. Donati, “Dynamic behavior and locking of a semiconductor laser subjected to external injection,” IEEE J. Quantum Electron. 34, 2350–2356 (1998).
[Crossref]

Antonoglou, I.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van DenDriessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[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, 3241–3249 (2012).
[Crossref] [PubMed]

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

Argyris, A.

Bengio, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
[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, 438–446 (2015).
[Crossref]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
[Crossref] [PubMed]

Bourmpos, M.

Brunner, D.

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

K. Hicke, M. Escalona, 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, 1501610 (2013).
[Crossref]

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

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

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

Bunsen, M.

K. Kanno, A. Uchida, and M. Bunsen, “Complexity and bandwidth enhancement in unidirectionally coupled semiconductor lasers with time-delayed optical feedback,” Phys. Rev. E 93, 32206 (2016).
[Crossref]

Carroll, T. L.

L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals,” Phys. Rev. A 44, 2374–2383 (1991).
[Crossref] [PubMed]

Chang, Y.

J. Qin, Q. Zhao, D. Xu, H. Yin, Y. Chang, and D. Huang, “Optical packet header identification utilizing an all-optical feedback chaotic reservoir computing,” Mod. Phys. Lett. B 30, 1650199 (2016).
[Crossref]

D’Huys, O.

V. Flunkert, O. D’Huys, J. Danckaert, I. Fischer, and E. Schöll, “Bubbling in delay-coupled lasers,” Phys. Rev. E 79, 065201 (2009).
[Crossref]

Dambre, J.

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

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
[Crossref] [PubMed]

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

Danckaert, J.

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

V. Flunkert, O. D’Huys, J. Danckaert, I. Fischer, and E. Schöll, “Bubbling in delay-coupled lasers,” Phys. Rev. E 79, 065201 (2009).
[Crossref]

Davis, P.

A. Uchida, K. Yoshimura, P. Davis, S. Yoshimori, and R. Roy, “Local conditional Lyapunov exponent characterization of consistency of dynamical response of the driven Lorenz system,” Phys. Rev. E 78, 36203 (2008).
[Crossref]

Dieleman, S.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van DenDriessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Donati, S.

V. Annovazzi-Lodi, A. Scire, M. Sorel, and S. Donati, “Dynamic behavior and locking of a semiconductor laser subjected to external injection,” IEEE J. Quantum Electron. 34, 2350–2356 (1998).
[Crossref]

Duport, F.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
[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, 438–446 (2015).
[Crossref]

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

Erneux, T.

T. Erneux and P. Glorieux, Laser Dynamics (Cambridge University, 2010).
[Crossref]

Escalona, M.

K. Hicke, M. Escalona, 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, 1501610 (2013).
[Crossref]

Escalona-Moran, M.

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

Fischer, I.

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

N. Oliver, T. Jüngling, and I. Fischer, “Consistency properties of a chaotic semiconductor laser driven by optical feedback,” Phys. Rev. Lett. 114, 123902 (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 91, 020801 (2015).
[Crossref]

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K. Hicke, M. Escalona, 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, 1501610 (2013).
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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).
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M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
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M. C. Soriano, S. Ortin, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, and L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21, 12–20 (2013).
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L. Appeltant, M. C. Soriano, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, and G. Van Der Sande, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
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Sutskever, I.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van DenDriessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
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Syvridis, D.

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J. Schumacher, H. Toutounji, and G. Pipa, “An introduction to delay-coupled reservoir computing,” in Artificial Neural Networks, P. Koprinkova-Hristova, V. Mladenov, and N. K. Kasabov, eds. (Springer International Publishing, 1985).

Uchida, A.

K. Kanno, A. Uchida, and M. Bunsen, “Complexity and bandwidth enhancement in unidirectionally coupled semiconductor lasers with time-delayed optical feedback,” Phys. Rev. E 93, 32206 (2016).
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Van Der Sande, G.

L. Appeltant, M. C. Soriano, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, and G. Van Der Sande, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
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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, 438–446 (2015).
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J. Qin, Q. Zhao, D. Xu, H. Yin, Y. Chang, and D. Huang, “Optical packet header identification utilizing an all-optical feedback chaotic reservoir computing,” Mod. Phys. Lett. B 30, 1650199 (2016).
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J. Qin, Q. Zhao, D. Xu, H. Yin, Y. Chang, and D. Huang, “Optical packet header identification utilizing an all-optical feedback chaotic reservoir computing,” Mod. Phys. Lett. B 30, 1650199 (2016).
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Yoshimura, K.

A. Uchida, K. Yoshimura, P. Davis, S. Yoshimori, and R. Roy, “Local conditional Lyapunov exponent characterization of consistency of dynamical response of the driven Lorenz system,” Phys. Rev. E 78, 36203 (2008).
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Front. Comput. Neurosci. (1)

M. C. Soriano, D. Brunner, M. Escalona-Moran, M. C. Mirasso, and I. Fischer, “Minimal approach to neuro-inspired information processing,” Front. Comput. Neurosci. 9, 68 (2015).
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K. Hicke, M. Escalona, 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, 1501610 (2013).
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IEEE Trans. Neural Netw. (1)

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
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J. Qin, Q. Zhao, D. Xu, H. Yin, Y. Chang, and D. Huang, “Optical packet header identification utilizing an all-optical feedback chaotic reservoir computing,” Mod. Phys. Lett. B 30, 1650199 (2016).
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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. Appeltant, M. C. Soriano, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, and G. Van Der Sande, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
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D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van DenDriessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
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Optica (1)

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S. Wieczorek, B. Krauskopf, T.B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers”, Phys. Rep. 416, 1–128 (2005).
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[Crossref]

K. Kanno and A. Uchida, “Consistency and complexity in coupled semiconductor lasers with time-delayed optical feedback,” Phys. Rev. E 86, 66202 (2012).
[Crossref]

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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 91, 020801 (2015).
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Quantum Semiclass. Opt. (1)

G.H.M Van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quantum Semiclass. Opt. 7, 87–143 (1995).
[Crossref]

Rev. Mod. Phys. (1)

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

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Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
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J. Schumacher, H. Toutounji, and G. Pipa, “An introduction to delay-coupled reservoir computing,” in Artificial Neural Networks, P. Koprinkova-Hristova, V. Mladenov, and N. K. Kasabov, eds. (Springer International Publishing, 1985).

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Figures (5)

Fig. 1
Fig. 1

Scheme of the experimental setup. Blue (light gray) lines are optical fibres. Orange (dark gray) lines are electrical cables. Thick red lines represent the optical path for the optical feedback, and the circular arrow represents the propagation direction of light.

Fig. 2
Fig. 2

(a) Optical spectra of the injected signal detuned at −30 GHz (black), and response laser spectra with η = 0 dB and no injection (gray). (b) Examples of response spectra for different spectral detunings: full locking for Δν = −15 GHz (light gray), partial locking for Δν = −25 GHz (black), and unlocking for Δν = −45 GHz (dark gray). (c) Locking categories in the (Δν, η) plane for Ibias = 11.10 mA and Pinj = 0.7 mW.

Fig. 3
Fig. 3

Persistence plots of the response for full locking (a) and partial locking (b) conditions. Parameters are Ibias = 11.10 mA, Pinj = 0.7 mW, η = 5 dB. Frequency detuning are Δν = −10 GHz and Δν = −30 GHz, respectively. Gray levels indicate the level of consistency. (c) Consistency correlation dependence in the (Δν, η) plane for Ibias = 11.10 mA and Pinj = 0.7 mW.

Fig. 4
Fig. 4

(a) Memory correlation mi dependence on Δν from 0 to 19 time steps for Ibias = 11.10 mA and Pinj = 0.7 mW at η = 5 dB. (b) Memory capacity MC dependence in the (Δν, η) plane for Ibias = 11.10 mA and Pinj = 0.7 mW. Panel (a) corresponds to η = 5 dB in panel (b).

Fig. 5
Fig. 5

NMSE for δ = 1 (a), δ = 2 (b), and for δ = 3 (c) in the (Δν, η) plane using Ibias = 11.10 mA and Pinj = 0.7 mW. All panels share the gray scale.

Equations (6)

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

Δ ν = ν i ν r
C C i , j = < | I i ( t ) I ¯ i | | I j ( t ) I ¯ j | > σ i σ j
m i = c o r r ( y ¯ i ( k ) , y ( k i ) )
M C = i = 0 n m i
d y ( t ) d t = α y ( t τ ) 1 + y β ( t τ ) γ y ( t )
N M S E = k = 1 N ( y ¯ k y k ) 2 N σ y 2

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