Abstract

We propose a new design for a passive photonic reservoir computer on a silicon photonics chip which can be used in the context of optical communication applications, and study it through detailed numerical simulations. The design consists of a photonic crystal cavity with a quarter-stadium shape, which is known to foster interesting mixing dynamics. These mixing properties turn out to be very useful for memory-dependent optical signal processing tasks, such as header recognition. The proposed, ultra-compact photonic crystal cavity exhibits a memory of up to 6 bits, while simultaneously accepting bitrates in a wide region of operation. Moreover, because of the inherent low losses in a high-Q photonic crystal cavity, the proposed design is very power efficient.

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

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References

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  1. H. Jaeger, “The echo state approach to analyzing and training recurrent neural networks,” Bonn, Germany: German National Research Center for Information Technology GMD Technical Report 148(34), 13 (2001).
  2. 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]
  3. D. Verstraeten, B. Schrauwen, M. d’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural networks 20(3), 391–403 (2007).
    [Crossref] [PubMed]
  4. 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]
  5. 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]
  6. 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]
  7. L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutiérrez, 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]
  8. 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]
  9. 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).
  10. K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, and J. V. Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16(15), 11182–11192 (2008).
    [Crossref] [PubMed]
  11. 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]
  12. H.-J. Stöckmann and J. Stein, “Quantum chaos in billiards studied by microwave absorption,” Phys. Rev. Lett. 64(19), 2215–2218 (1990).
    [Crossref] [PubMed]
  13. M. Sieber, U. Smilansky, S. Creagh, and R. Littlejohn, “Non-generic spectral statistics in the quantized stadium billiard,” J. Phys. A: Mathematical and General 26(22), 6217 (1993).
    [Crossref]
  14. C. Liu, R. E. Van Der Wel, N. Rotenberg, L. Kuipers, T. F. Krauss, A. Di Falco, and A. Fratalocchi, “Triggering extreme events at the nanoscale in photonic seas,” Nature Physics 11(4), 358–363 (2015).
    [Crossref]
  15. A. J. Izenman, “Linear discriminant analysis,” in Modern multivariate statistical techniques (Springer, 2013) pp. 237–280.
    [Crossref]
  16. M. Jeruchim, “Techniques for estimating the bit error rate in the simulation of digital communication systems,” J-SAC 2(1), 153–170 (1984).

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 (2)

C. Liu, R. E. Van Der Wel, N. Rotenberg, L. Kuipers, T. F. Krauss, A. Di Falco, and A. Fratalocchi, “Triggering extreme events at the nanoscale in photonic seas,” Nature Physics 11(4), 358–363 (2015).
[Crossref]

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]

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 (1)

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]

2012 (2)

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]

2008 (1)

2007 (1)

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

2001 (1)

H. Jaeger, “The echo state approach to analyzing and training recurrent neural networks,” Bonn, Germany: German National Research Center for Information Technology GMD Technical Report 148(34), 13 (2001).

1993 (1)

M. Sieber, U. Smilansky, S. Creagh, and R. Littlejohn, “Non-generic spectral statistics in the quantized stadium billiard,” J. Phys. A: Mathematical and General 26(22), 6217 (1993).
[Crossref]

1990 (1)

H.-J. Stöckmann and J. Stein, “Quantum chaos in billiards studied by microwave absorption,” Phys. Rev. Lett. 64(19), 2215–2218 (1990).
[Crossref] [PubMed]

1984 (1)

M. Jeruchim, “Techniques for estimating the bit error rate in the simulation of digital communication systems,” J-SAC 2(1), 153–170 (1984).

Appeltant, L.

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutiérrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
[Crossref] [PubMed]

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

Baets, R.

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).

Bienstman, P.

Brunner, D.

Campenhout, J. V.

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).

Creagh, S.

M. Sieber, U. Smilansky, S. Creagh, and R. Littlejohn, “Non-generic spectral statistics in the quantized stadium billiard,” J. Phys. A: Mathematical and General 26(22), 6217 (1993).
[Crossref]

d’Haene, M.

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

Dambre, J.

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

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 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.

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]

Di Falco, A.

C. Liu, R. E. Van Der Wel, N. Rotenberg, L. Kuipers, T. F. Krauss, A. Di Falco, and A. Fratalocchi, “Triggering extreme events at the nanoscale in photonic seas,” Nature Physics 11(4), 358–363 (2015).
[Crossref]

Dierckx, W.

Duport, F.

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.

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. Gutiérrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
[Crossref] [PubMed]

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

Fratalocchi, A.

C. Liu, R. E. Van Der Wel, N. Rotenberg, L. Kuipers, T. F. Krauss, A. Di Falco, and A. Fratalocchi, “Triggering extreme events at the nanoscale in photonic seas,” Nature Physics 11(4), 358–363 (2015).
[Crossref]

Gutiérrez, J. M.

Haelterman, M.

Izenman, A. J.

A. J. Izenman, “Linear discriminant analysis,” in Modern multivariate statistical techniques (Springer, 2013) pp. 237–280.
[Crossref]

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, 011015 (2017).

Jaeger, H.

H. Jaeger, “The echo state approach to analyzing and training recurrent neural networks,” Bonn, Germany: German National Research Center for Information Technology GMD Technical Report 148(34), 13 (2001).

Jeruchim, M.

M. Jeruchim, “Techniques for estimating the bit error rate in the simulation of digital communication systems,” J-SAC 2(1), 153–170 (1984).

Krauss, T. F.

C. Liu, R. E. Van Der Wel, N. Rotenberg, L. Kuipers, T. F. Krauss, A. Di Falco, and A. Fratalocchi, “Triggering extreme events at the nanoscale in photonic seas,” Nature Physics 11(4), 358–363 (2015).
[Crossref]

Kuipers, L.

C. Liu, R. E. Van Der Wel, N. Rotenberg, L. Kuipers, T. F. Krauss, A. Di Falco, and A. Fratalocchi, “Triggering extreme events at the nanoscale in photonic seas,” Nature Physics 11(4), 358–363 (2015).
[Crossref]

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, 011015 (2017).

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutiérrez, 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]

Littlejohn, R.

M. Sieber, U. Smilansky, S. Creagh, and R. Littlejohn, “Non-generic spectral statistics in the quantized stadium billiard,” J. Phys. A: Mathematical and General 26(22), 6217 (1993).
[Crossref]

Liu, C.

C. Liu, R. E. Van Der Wel, N. Rotenberg, L. Kuipers, T. F. Krauss, A. Di Falco, and A. Fratalocchi, “Triggering extreme events at the nanoscale in photonic seas,” Nature Physics 11(4), 358–363 (2015).
[Crossref]

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, 011015 (2017).

Massar, S.

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]

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]

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]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutiérrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
[Crossref] [PubMed]

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

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.

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]

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.

Rotenberg, N.

C. Liu, R. E. Van Der Wel, N. Rotenberg, L. Kuipers, T. F. Krauss, A. Di Falco, and A. Fratalocchi, “Triggering extreme events at the nanoscale in photonic seas,” Nature Physics 11(4), 358–363 (2015).
[Crossref]

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]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, and J. V. Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16(15), 11182–11192 (2008).
[Crossref] [PubMed]

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

Sieber, M.

M. Sieber, U. Smilansky, S. Creagh, and R. Littlejohn, “Non-generic spectral statistics in the quantized stadium billiard,” J. Phys. A: Mathematical and General 26(22), 6217 (1993).
[Crossref]

Smerieri, A.

Smilansky, U.

M. Sieber, U. Smilansky, S. Creagh, and R. Littlejohn, “Non-generic spectral statistics in the quantized stadium billiard,” J. Phys. A: Mathematical and General 26(22), 6217 (1993).
[Crossref]

Soriano, M. C.

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. Gutiérrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
[Crossref] [PubMed]

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

Stein, J.

H.-J. Stöckmann and J. Stein, “Quantum chaos in billiards studied by microwave absorption,” Phys. Rev. Lett. 64(19), 2215–2218 (1990).
[Crossref] [PubMed]

Stöckmann, H.-J.

H.-J. Stöckmann and J. Stein, “Quantum chaos in billiards studied by microwave absorption,” Phys. Rev. Lett. 64(19), 2215–2218 (1990).
[Crossref] [PubMed]

Stroobandt, D.

D. Verstraeten, B. Schrauwen, M. d’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural networks 20(3), 391–403 (2007).
[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, 011015 (2017).

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 Der Wel, R. E.

C. Liu, R. E. Van Der Wel, N. Rotenberg, L. Kuipers, T. F. Krauss, A. Di Falco, and A. Fratalocchi, “Triggering extreme events at the nanoscale in photonic seas,” Nature Physics 11(4), 358–363 (2015).
[Crossref]

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.

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]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, and J. V. Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16(15), 11182–11192 (2008).
[Crossref] [PubMed]

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

Vinckier, Q.

Bonn, Germany: German National Research Center for Information Technology GMD Technical Report (1)

H. Jaeger, “The echo state approach to analyzing and training recurrent neural networks,” Bonn, Germany: German National Research Center for Information Technology GMD Technical Report 148(34), 13 (2001).

J-SAC (1)

M. Jeruchim, “Techniques for estimating the bit error rate in the simulation of digital communication systems,” J-SAC 2(1), 153–170 (1984).

J. Phys. A: Mathematical and General (1)

M. Sieber, U. Smilansky, S. Creagh, and R. Littlejohn, “Non-generic spectral statistics in the quantized stadium billiard,” J. Phys. A: Mathematical and General 26(22), 6217 (1993).
[Crossref]

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).
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Nature Physics (1)

C. Liu, R. E. Van Der Wel, N. Rotenberg, L. Kuipers, T. F. Krauss, A. Di Falco, and A. Fratalocchi, “Triggering extreme events at the nanoscale in photonic seas,” Nature Physics 11(4), 358–363 (2015).
[Crossref]

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

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Figures (11)

Fig. 1
Fig. 1 Waveguides connected to the photonic crystal cavity. (a) Snapshot of the field profile in the cavity. The mixing of the signal can clearly be witnessed by inspecting the field profiles. (b) Close up of the entrance waveguide. Some scattering losses can be observed at the waveguide-W1 transition.
Fig. 2
Fig. 2 Block diagram of the simulation.
Fig. 3
Fig. 3 (a) Waveforms detected at two of the exit waveguides as the result of a certain 50 Gbps bit sequence input. The outputs get sampled once per bit period. (b) After the readout, the prediction approximates the desired XOR target. The prediction and the target were aligned by shifting the prediction backwards in time according to the optimal latency of 0.8 bit periods.
Fig. 4
Fig. 4 The accumulated power exiting the cavity via the output waveguides adds up to about 83 % of the total energy introduced in the system. This corresponds to a 0.8 dB loss.
Fig. 5
Fig. 5 The XOR and AND of two neighboring bits at 50 Gbps can easily be performed by the reservoir. The latency represents the time shift with respect to the input, after which the output should give the desired value. The correct result of bn XOR bn−1 can be retained until a new bit is sent in, while the AND of two bits can be retained until 2 new bits are sent in. Since the BER is cropped at 10−3, we often look how well the output continuously approximates the target function by looking at the Mean Squared Error (MSE).
Fig. 6
Fig. 6 By performing the performance vs latency sweep for every bitrate and looking at the minimal error for each sweep, the operating range of the reservoir can be determined. (a) The optimal bitrate - looking at the MSE - for the XOR task lies at 50 Gbps. However, there is a full band of frequencies the reservoir can work with between 25 Gbps and 67 Gbps. (b) The fact that the linear AND task is easier is again reflected in the the region of operation for the AND, which starts at lower bitrates.
Fig. 7
Fig. 7 Error Rate (ER) for the worst performing header at each latency. The reservoir can distinguish headers of up to L=6 bits without error at the optimal bitrate of 50 Gbps. To reduce simulation times, the sweep over the latencies was stopped when the ER became higher than 10−1.
Fig. 8
Fig. 8 We can visualize the separation of three bit headers by projecting on the two primary LDA axes. We see nice separation for all different headers, while similar headers are located closer together.
Fig. 9
Fig. 9 By sweeping over the bitrate to find the operation range, we find that the reservoir can distinguish headers up to a header length of L = 6 bits without error at a bitrate of up to 100Gbps.
Fig. 10
Fig. 10 Decay of the power inside the cavity. The envelope decays with a half-life of 10 ps, yielding a Q factor of 16400.
Fig. 11
Fig. 11 The Q-factor decays harmonically with the number of connected waveguides

Equations (8)

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x n = W in u n 1 + W res x n 1
y n = W out f ( x n )
u ( t ) = ( E 0 ( t ) H 0 ( t ) ) with u ( t ) = 0 if t < 0 or t > T ,
x ( t ) = ( E in ( t ) H in ( t ) ) = n = 1 N b n u ( t n T ) = b k u ( t k T ) with k = t T
X i ( t ) = ( E out i ( t ) H out i ( t ) ) = n = 1 N b n U i ( t n T ) .
I n = I tn 2 + I sn 2 = ( 4 k T f c R L ) 2 + 2 q I f c .
Q = 2 π c λ m = 16400 .
T 1 / 2 = log ( 2 ) m = 10 ps .

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