Abstract

We realize an experimental setup of a time-delay reservoir using a VCSEL with optical feedback and optical injection. The VCSEL is operated in the injection-locking regime. This allows us to solve different information processing tasks, such as chaotic time-series prediction with a NMSE of 1.6×102 and nonlinear channel equalization with a SER of 1.5×102, improving state-of-the-art performance. We also demonstrate experimentally, through a careful statistical analysis, the impact of the VCSEL polarization dynamics on the performance of our architecture. More specifically, we confirm recent theoretical prediction stating that a polarization rotated feedback allows for the enhancement of the calculation performance compared to an isotropic feedback.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. L. K. Grover, “Quantum computers can search arbitrarily large databases by a single query,” Phys. Rev. Lett. 79, 4709–4712 (1997).
    [Crossref]
  2. J. P. Crutchfield, W. L. Ditto, and S. Sinha, “Introduction to focus issue: Intrinsic and designed computation: Information processing in dynamical systems-beyond the digital hegemony,” Chaos 20, 037101 (2010).
    [Crossref]
  3. H. Jaeger and H. Haas, “Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication,” Science 304, 78–80 (2004).
    [Crossref] [PubMed]
  4. K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
    [Crossref] [PubMed]
  5. 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, 011015 (2017).
  6. J. Bueno, S. Maktoobi, L. Froehly, I. Fischer, M. Jacquot, L. Larger, and D. Brunner, “Reinforcement learning in a large-scale photonic recurrent neural network,” Optica 5, 756–760 (2018).
    [Crossref]
  7. L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
    [Crossref] [PubMed]
  8. 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]
  9. 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]
  10. F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795 (2012).
    [Crossref] [PubMed]
  11. 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]
  12. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. V. der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26, 3301–3307 (2015).
    [Crossref] [PubMed]
  13. K. Takano, C. Sugano, M. Inubushi, K. Yoshimura, S. Sunada, K. Kanno, and A. Uchida, “Compact reservoir computing with a photonic integrated circuit,” Opt. Express 26, 29424–29439 (2018).
    [Crossref] [PubMed]
  14. 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, 1501610 (2013).
    [Crossref]
  15. J. Vatin, D. Rontani, and M. Sciamanna, “Enhanced performance of a reservoir computer using polarization dynamics in VCSELs,” Opt. Lett. 43, 4497–4500 (2018).
    [Crossref] [PubMed]
  16. K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481 (2009).
    [Crossref]
  17. N. Bertschinger and T. Natschläger, “Real-time computation at the edge of chaos in recurrent neural networks,” Neural Comput. 16, 1413–1436 (2004).
    [Crossref] [PubMed]
  18. C. Chatfield and A. S. Weigend, “The future of time series,” in Time series prediction: Forecasting the future and understanding the past, C. Chatfield and A. S. Weigend, eds. (Addison-Wesley, 1993).
  19. V. J. Mathews and J. Lee, “Adaptive algorithms for bilinear filtering,” Proc. SPIE2296, 317–327 (1994).
    [Crossref]
  20. N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions (Wiley-Interscience, 1995). Ed. 2, Vol. 2.

2018 (3)

2017 (1)

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, 011015 (2017).

2015 (1)

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. V. der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26, 3301–3307 (2015).
[Crossref] [PubMed]

2014 (1)

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

2013 (2)

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

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
[Crossref]

2012 (3)

2011 (1)

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

2010 (1)

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

2009 (1)

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481 (2009).
[Crossref]

2004 (2)

N. Bertschinger and T. Natschläger, “Real-time computation at the edge of chaos in recurrent neural networks,” Neural Comput. 16, 1413–1436 (2004).
[Crossref] [PubMed]

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

1997 (1)

L. K. Grover, “Quantum computers can search arbitrarily large databases by a single query,” Phys. Rev. Lett. 79, 4709–4712 (1997).
[Crossref]

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

Balakrishnan, N.

N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions (Wiley-Interscience, 1995). Ed. 2, Vol. 2.

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, 011015 (2017).

Bertschinger, N.

N. Bertschinger and T. Natschläger, “Real-time computation at the edge of chaos in recurrent neural networks,” Neural Comput. 16, 1413–1436 (2004).
[Crossref] [PubMed]

Bienstman, P.

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

Brunner, D.

J. Bueno, S. Maktoobi, L. Froehly, I. Fischer, M. Jacquot, L. Larger, and D. Brunner, “Reinforcement learning in a large-scale photonic recurrent neural network,” Optica 5, 756–760 (2018).
[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]

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, 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, 3241–3249 (2012).
[Crossref] [PubMed]

Bueno, J.

Chatfield, C.

C. Chatfield and A. S. Weigend, “The future of time series,” in Time series prediction: Forecasting the future and understanding the past, C. Chatfield and A. S. Weigend, eds. (Addison-Wesley, 1993).

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, 011015 (2017).

Crutchfield, J. P.

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

Dambre, J.

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

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

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

Danckaert, J.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. V. der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26, 3301–3307 (2015).
[Crossref] [PubMed]

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

der Sande, G. V.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. V. der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26, 3301–3307 (2015).
[Crossref] [PubMed]

Ditto, W. L.

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

Duport, F.

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]

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

Escalona-Morán, M. A.

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
[Crossref]

Fiers, M.

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

Fischer, I.

J. Bueno, S. Maktoobi, L. Froehly, I. Fischer, M. Jacquot, L. Larger, and D. Brunner, “Reinforcement learning in a large-scale photonic recurrent neural network,” Optica 5, 756–760 (2018).
[Crossref]

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, 1501610 (2013).
[Crossref]

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

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

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

Froehly, L.

Gatare, I.

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481 (2009).
[Crossref]

Grover, L. K.

L. K. Grover, “Quantum computers can search arbitrarily large databases by a single query,” Phys. Rev. Lett. 79, 4709–4712 (1997).
[Crossref]

Gutierrez, J. M.

Haas, H.

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

Haelterman, M.

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]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795 (2012).
[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, 1501610 (2013).
[Crossref]

Inubushi, M.

Jacquot, M.

J. Bueno, S. Maktoobi, L. Froehly, I. Fischer, M. Jacquot, L. Larger, and D. Brunner, “Reinforcement learning in a large-scale photonic recurrent neural network,” Optica 5, 756–760 (2018).
[Crossref]

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, 011015 (2017).

Jaeger, H.

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

Johnson, N. L.

N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions (Wiley-Interscience, 1995). Ed. 2, Vol. 2.

Kanno, K.

Kotz, S.

N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions (Wiley-Interscience, 1995). Ed. 2, Vol. 2.

Larger, L.

Lee, J.

V. J. Mathews and J. Lee, “Adaptive algorithms for bilinear filtering,” Proc. SPIE2296, 317–327 (1994).
[Crossref]

Maktoobi, S.

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, 011015 (2017).

Massar, S.

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]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and 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, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref] [PubMed]

Mathews, V. J.

V. J. Mathews and J. Lee, “Adaptive algorithms for bilinear filtering,” Proc. SPIE2296, 317–327 (1994).
[Crossref]

Mechet, P.

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

Mirasso, C. R.

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

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 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, 3241–3249 (2012).
[Crossref] [PubMed]

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

Morthier, G.

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

Natschläger, T.

N. Bertschinger and T. Natschläger, “Real-time computation at the edge of chaos in recurrent neural networks,” Neural Comput. 16, 1413–1436 (2004).
[Crossref] [PubMed]

Nguimdo, R. M.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. V. der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26, 3301–3307 (2015).
[Crossref] [PubMed]

Panajotov, K.

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481 (2009).
[Crossref]

Paquot, Y.

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]

Pesquera, L.

Rontani, D.

Schneider, B.

Schrauwen, B.

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

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

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

Sciamanna, M.

J. Vatin, D. Rontani, and M. Sciamanna, “Enhanced performance of a reservoir computer using polarization dynamics in VCSELs,” Opt. Lett. 43, 4497–4500 (2018).
[Crossref] [PubMed]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481 (2009).
[Crossref]

Sinha, S.

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

Smerieri, A.

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]

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

Soriano, M. C.

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, 1501610 (2013).
[Crossref]

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

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

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

Sugano, C.

Sunada, S.

Takano, K.

Thienpont, H.

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481 (2009).
[Crossref]

Uchida, A.

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, 011015 (2017).

Valle, A.

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481 (2009).
[Crossref]

Van der Sande, G.

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

Van Vaerenbergh, T.

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

Vandoorne, K.

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

Vatin, J.

Verschaffelt, G.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. V. der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26, 3301–3307 (2015).
[Crossref] [PubMed]

Verstraeten, D.

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

Weigend, A. S.

C. Chatfield and A. S. Weigend, “The future of time series,” in Time series prediction: Forecasting the future and understanding the past, C. Chatfield and A. S. Weigend, eds. (Addison-Wesley, 1993).

Yoshimura, K.

Chaos (1)

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

IEEE J. Quantum Electron. (1)

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481 (2009).
[Crossref]

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

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
[Crossref]

IEEE Trans. Neural Netw. Learn. Syst. (1)

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. V. der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Netw. Learn. Syst. 26, 3301–3307 (2015).
[Crossref] [PubMed]

Nat. Commun. (3)

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

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

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

Neural Comput. (1)

N. Bertschinger and T. Natschläger, “Real-time computation at the edge of chaos in recurrent neural networks,” Neural Comput. 16, 1413–1436 (2004).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Optica (1)

Phys. Rev. Lett. (1)

L. K. Grover, “Quantum computers can search arbitrarily large databases by a single query,” Phys. Rev. Lett. 79, 4709–4712 (1997).
[Crossref]

Phys. Rev. X (1)

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, 011015 (2017).

Sci. Rep. (1)

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]

Science (1)

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

Other (3)

C. Chatfield and A. S. Weigend, “The future of time series,” in Time series prediction: Forecasting the future and understanding the past, C. Chatfield and A. S. Weigend, eds. (Addison-Wesley, 1993).

V. J. Mathews and J. Lee, “Adaptive algorithms for bilinear filtering,” Proc. SPIE2296, 317–327 (1994).
[Crossref]

N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions (Wiley-Interscience, 1995). Ed. 2, Vol. 2.

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Figures (4)

Fig. 1
Fig. 1 (a) Scheme of the setup. The signal loaded in the AWG is made by multiplying the input signal by a mask. MZ: Mach-Zehnder madolator, P.C.: polarization Controller, AWG: Arbitrary Waveform Generator, att: attenuator, Oscillo: Oscilloscope, ampl: amplificator, PD: photodiode. (b) masked signal for the input of the reservoir computer. (c) corresponding response of the reservoir.
Fig. 2
Fig. 2 Experimental optical spectra in different conditions. (a) free running VCSEL, (b) System with feedback and injection (50 μW injection, 18 dB attenuation), (c) VCSEL with parallel feedback, 10 dB attenuation, (d) VCSEL with rotated feedback, 10 dB attenuation.
Fig. 3
Fig. 3 Example of Santa Fe series prediction: the original Santa-Fe series (blue line and circles), and the predicted series (red line and crosses).
Fig. 4
Fig. 4 Results for channel equalization task. (a) experimental prediction for the channel equalization task: the target signal (blue lines and circles) and the predicted signal (red crosses) in case of polarization rotated feedback. arrow points out the error (b) Theoretical SER for different SNR added in the readout layer, for parallel feedback (blue) and perpendicular feedback (red). The green line is set at the experimental level of SNR, green squares show the experimental performance. (c) Experimental results: The shortest strips shows the different SER obtained over different measurement series, the biggest strips shows the mean value, for the parallel feedback (blue) and the perpendicular feedback (red).

Equations (3)

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N M S E = 1 N i = 1 N ( y ( i ) y ˜ ( i ) ) 2 σ y ,
q ( i ) = 0.08 d ( i + 2 ) 0.12 d ( i + 1 ) + d ( i ) + 0.18 d ( i 1 ) 0.1 d ( i 2 ) + 0.091 d ( i 3 ) 0.05 d ( i 4 ) + 0.04 d ( i 5 ) + 0.03 d ( i 6 ) + 0.01 d ( i 7 ) .
u ( i ) = q ( i ) + 0.026 q ( i ) 2 0.011 q ( i ) 3 ,

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