Abstract

All-optical platforms for recurrent neural networks can offer higher computational speed and energy efficiency. To produce a major advance in comparison with currently available digital signal processing methods, the new system would need to have high bandwidth and operate both signal quadratures (power and phase). Here we propose a fiber echo state network analogue (FESNA) — the first optical technology that provides both high (beyond previous limits) bandwidth and dual-quadrature signal processing. We demonstrate applicability of the designed system for prediction tasks and for the mitigation of distortions in optical communication systems with multilevel dual-quadrature encoded signals.

© 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. M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett. 27387–390 (2015).
    [Crossref]
  2. E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
    [Crossref]
  3. M. Sorokina, S. Sygletos, and S. Turitsyn, “Sparse identification for nonlinear optical communication systems: SINO method, Opt. Express 24, 30433–30443 (2016)
    [Crossref]
  4. C. Hager and H. D. Pfister, “Nonlinear Interference Mitigation via Deep Neural Networks,” Optical Fiber Commun. Conf., paper W3A.4 (2018).
    [Crossref]
  5. T. S. R. Shen and A. P. T. Lau, “Fiber nonlinearity compensation using extreme learning machine for DSP-based coherent communication systems,” OECC816–817 (2011).
  6. S. Owaki and M. Nakamura, “Equalization of optical nonlinear waveform distortion using neural-network based digital signal processing,” Optoelectronics and Communications Conf. (Photon. Switching) paper WA2-40 (2016).
  7. M. Mahowald and R. Douglas, “A silicon neuron,” Nature 354, 515–518 (1991).
    [Crossref]
  8. C. Eliasmith, T. C. Stewart, X. Choo, T. Bekolay, T. DeWolf, Y. Tang, and D. Rasmussen, “A Large-Scale Model of the Functioning Brain,” Science 338, 1202–1205 (2012).
    [Crossref]
  9. T. A. Engel, N. A. Steinmetz, M. A. Gieselmann, A. Thiele, T. Moore, and K. Boahen, “Selective modulation of cortical state during spatial attention,” Science 354, 1140–1144 (2016).
    [Crossref]
  10. A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Rep. 7, 7430(2017).
    [Crossref] [PubMed]
  11. 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, 2401–2412 (2017).
    [Crossref]
  12. E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6, 29080 (2016).
    [Crossref] [PubMed]
  13. M. Lukosevicius and H. Jaeger, “Reservoir Computing Approaches to Recurrent Neural Network Training,” Computer Science Review 3, 127–149 (2009).
    [Crossref]
  14. M. Bauduin, S. Massar, and F. Horlin, “Non-linear satellite channel equalization based on a low complexity echo state network,” Information Science and Systems Conference, 99–104 (2016).
  15. K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwent, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
    [Crossref] [PubMed]
  16. A. Argyris, J. Bueno, and I. Fischer, “Photonic machine learning implementation for signal recovery in optical communications,” Sci. Rep. 8 (1), 8487 (2018).
    [Crossref]
  17. 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 (OSA) 5, 756–760 (2018).
    [Crossref]
  18. https://www.technologyreview.com/s/404874/smart-fibers/
  19. J. N. Kutz, X. Fu, and S. Brunton, “Self-tuning fiber lasers: machine learning applied to optical systems,” Advanced Photonics Conf. paper NTu4A.7. (2014).
  20. T. Baumeister, S. L. Brunton, and N. J. Kutz, “Deep learning and model predictive control for self-tuning mode-locked lasers,” J. Opt. Soc. Am. B 35, 617–626 (2018)
    [Crossref]
  21. Q. Ling, Z. Gu, and K. Gao, “Smart design of a long-period fiber grating refractive index sensor based on dual-peak resonance near the phase-matching turning point,” Appl. Opt. 57, 2693–2697 (2018).
    [Crossref] [PubMed]
  22. http://www.optonicus.com/infoco/
  23. 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]
  24. F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
    [Crossref]
  25. 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]
  26. 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]
  27. H. Jaeger, “Adaptive nonlinear system identification with echo state networks,” Advances in Neural Information Processing Systems 15, 593–600 (2003).
  28. A. Hideur, T. Chartier, C. Oezkul, and F. Sanchez, “Dynamics and stabilization of a high power side-pumped Yb-doped double-clad fiber laser,” Opt. Commun. 186, 311–317 (2000).
    [Crossref]
  29. M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).
  30. C. L. Guintrand, “Stimulated Brillouin scattering threshold variations due to bend-induced birefringence in a non-polarization-maintaining fiber amplifier,” CLEO JW2A-23 (2014).
  31. M. S. Sorokina and S. K. Turitsyn, “Regeneration limit of classical Shannon capacity,” Nat. Commun. 5, 3861 (2014).
    [Crossref]
  32. M. Sorokina, S. Sygletos, and S. Turitsyn, “Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM,” Opt. Lett. 40, 3117–3120 (2015).
    [Crossref] [PubMed]
  33. https://fiber-optic-catalog.ofsoptics.com/item/optical-fibers/highly-nonlinear-fiber-optical-fibers1/hnlf-pm-highly-non-linear-fiber-modules
  34. T. Okuno, M. Onishi, T. Kashiwada, S. Ishikawa, and M. Nishimura, “Silica-based functional fibers with enhanced nonlinearity and their applications,” IEEE J. Sel. Top. Quantum Electron. 51385–1391 (1999).
    [Crossref]
  35. A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photon. 9, 429–503 (2017).
    [Crossref]
  36. M. Sorokina, S. Sygletos, and S. Turitsyn, “Ripple distribution for nonlinear fiber-optic channels,” Opt. Express 25, 2228–2238 (2017)
    [Crossref]
  37. E. Agrell and M. Secondini, “Information-theoretic tools for optical communications engineers,” 2018 IEEE Photonics Conference (IPC) (2018).
  38. T. A. Eriksson, H. Buelow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Phot. Technol. Lett. 29, 2091–2094 (2017).
    [Crossref]
  39. W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

2018 (5)

A. Argyris, J. Bueno, and I. Fischer, “Photonic machine learning implementation for signal recovery in optical communications,” Sci. Rep. 8 (1), 8487 (2018).
[Crossref]

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 (OSA) 5, 756–760 (2018).
[Crossref]

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

T. Baumeister, S. L. Brunton, and N. J. Kutz, “Deep learning and model predictive control for self-tuning mode-locked lasers,” J. Opt. Soc. Am. B 35, 617–626 (2018)
[Crossref]

Q. Ling, Z. Gu, and K. Gao, “Smart design of a long-period fiber grating refractive index sensor based on dual-peak resonance near the phase-matching turning point,” Appl. Opt. 57, 2693–2697 (2018).
[Crossref] [PubMed]

2017 (5)

2016 (4)

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6, 29080 (2016).
[Crossref] [PubMed]

T. A. Engel, N. A. Steinmetz, M. A. Gieselmann, A. Thiele, T. Moore, and K. Boahen, “Selective modulation of cortical state during spatial attention,” Science 354, 1140–1144 (2016).
[Crossref]

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

M. Sorokina, S. Sygletos, and S. Turitsyn, “Sparse identification for nonlinear optical communication systems: SINO method, Opt. Express 24, 30433–30443 (2016)
[Crossref]

2015 (3)

M. Sorokina, S. Sygletos, and S. Turitsyn, “Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM,” Opt. Lett. 40, 3117–3120 (2015).
[Crossref] [PubMed]

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett. 27387–390 (2015).
[Crossref]

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

2014 (1)

M. S. Sorokina and S. K. Turitsyn, “Regeneration limit of classical Shannon capacity,” Nat. Commun. 5, 3861 (2014).
[Crossref]

2012 (3)

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]

C. Eliasmith, T. C. Stewart, X. Choo, T. Bekolay, T. DeWolf, Y. Tang, and D. Rasmussen, “A Large-Scale Model of the Functioning Brain,” Science 338, 1202–1205 (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]

2011 (2)

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

2009 (1)

M. Lukosevicius and H. Jaeger, “Reservoir Computing Approaches to Recurrent Neural Network Training,” Computer Science Review 3, 127–149 (2009).
[Crossref]

2003 (1)

H. Jaeger, “Adaptive nonlinear system identification with echo state networks,” Advances in Neural Information Processing Systems 15, 593–600 (2003).

2000 (1)

A. Hideur, T. Chartier, C. Oezkul, and F. Sanchez, “Dynamics and stabilization of a high power side-pumped Yb-doped double-clad fiber laser,” Opt. Commun. 186, 311–317 (2000).
[Crossref]

1999 (1)

T. Okuno, M. Onishi, T. Kashiwada, S. Ishikawa, and M. Nishimura, “Silica-based functional fibers with enhanced nonlinearity and their applications,” IEEE J. Sel. Top. Quantum Electron. 51385–1391 (1999).
[Crossref]

1991 (1)

M. Mahowald and R. Douglas, “A silicon neuron,” Nature 354, 515–518 (1991).
[Crossref]

Agrell, E.

E. Agrell and M. Secondini, “Information-theoretic tools for optical communications engineers,” 2018 IEEE Photonics Conference (IPC) (2018).

Akrout, A.

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

Al Khateeb, M. A. Z.

Aldaya, I.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett. 27387–390 (2015).
[Crossref]

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[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]

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]

Argyris, A.

A. Argyris, J. Bueno, and I. Fischer, “Photonic machine learning implementation for signal recovery in optical communications,” Sci. Rep. 8 (1), 8487 (2018).
[Crossref]

Bauduin, M.

M. Bauduin, S. Massar, and F. Horlin, “Non-linear satellite channel equalization based on a low complexity echo state network,” Information Science and Systems Conference, 99–104 (2016).

Baumeister, T.

Becker, J.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Bekolay, T.

C. Eliasmith, T. C. Stewart, X. Choo, T. Bekolay, T. DeWolf, Y. Tang, and D. Rasmussen, “A Large-Scale Model of the Functioning Brain,” Science 338, 1202–1205 (2012).
[Crossref]

Bienstman, P.

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

Boahen, K.

T. A. Engel, N. A. Steinmetz, M. A. Gieselmann, A. Thiele, T. Moore, and K. Boahen, “Selective modulation of cortical state during spatial attention,” Science 354, 1140–1144 (2016).
[Crossref]

Bock, V.

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

Brunner, D.

Brunton, S.

J. N. Kutz, X. Fu, and S. Brunton, “Self-tuning fiber lasers: machine learning applied to optical systems,” Advanced Photonics Conf. paper NTu4A.7. (2014).

Brunton, S. L.

Buelow, H.

T. A. Eriksson, H. Buelow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Phot. Technol. Lett. 29, 2091–2094 (2017).
[Crossref]

Bueno, J.

A. Argyris, J. Bueno, and I. Fischer, “Photonic machine learning implementation for signal recovery in optical communications,” Sci. Rep. 8 (1), 8487 (2018).
[Crossref]

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 (OSA) 5, 756–760 (2018).
[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, 2401–2412 (2017).
[Crossref]

Chartier, T.

A. Hideur, T. Chartier, C. Oezkul, and F. Sanchez, “Dynamics and stabilization of a high power side-pumped Yb-doped double-clad fiber laser,” Opt. Commun. 186, 311–317 (2000).
[Crossref]

Choo, X.

C. Eliasmith, T. C. Stewart, X. Choo, T. Bekolay, T. DeWolf, Y. Tang, and D. Rasmussen, “A Large-Scale Model of the Functioning Brain,” Science 338, 1202–1205 (2012).
[Crossref]

Cohen, E.

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6, 29080 (2016).
[Crossref] [PubMed]

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]

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, J. Dambre, D. Verstraeten, B. Schrauwent, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (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]

DeWolf, T.

C. Eliasmith, T. C. Stewart, X. Choo, T. Bekolay, T. DeWolf, Y. Tang, and D. Rasmussen, “A Large-Scale Model of the Functioning Brain,” Science 338, 1202–1205 (2012).
[Crossref]

Doran, N. J.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photon. 9, 429–503 (2017).
[Crossref]

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett. 27387–390 (2015).
[Crossref]

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

Douglas, R.

M. Mahowald and R. Douglas, “A silicon neuron,” Nature 354, 515–518 (1991).
[Crossref]

Dreschmann, M.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Duport, F.

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

Eggleton, B. J.

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

Eliasmith, C.

C. Eliasmith, T. C. Stewart, X. Choo, T. Bekolay, T. DeWolf, Y. Tang, and D. Rasmussen, “A Large-Scale Model of the Functioning Brain,” Science 338, 1202–1205 (2012).
[Crossref]

Ellis, A. D.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photon. 9, 429–503 (2017).
[Crossref]

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

Engel, T. A.

T. A. Engel, N. A. Steinmetz, M. A. Gieselmann, A. Thiele, T. Moore, and K. Boahen, “Selective modulation of cortical state during spatial attention,” Science 354, 1140–1144 (2016).
[Crossref]

Eriksson, T. A.

T. A. Eriksson, H. Buelow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Phot. Technol. Lett. 29, 2091–2094 (2017).
[Crossref]

Fischer, I.

A. Argyris, J. Bueno, and I. Fischer, “Photonic machine learning implementation for signal recovery in optical communications,” Sci. Rep. 8 (1), 8487 (2018).
[Crossref]

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 (OSA) 5, 756–760 (2018).
[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, 2401–2412 (2017).
[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]

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]

Freude, W.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Froehly, L.

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 (OSA) 5, 756–760 (2018).
[Crossref]

Fu, X.

J. N. Kutz, X. Fu, and S. Brunton, “Self-tuning fiber lasers: machine learning applied to optical systems,” Advanced Photonics Conf. paper NTu4A.7. (2014).

Gao, K.

Ghanbarisabagh, M.

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

Ghassemlooy, Z.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett. 27387–390 (2015).
[Crossref]

Giacoumidis, E.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett. 27387–390 (2015).
[Crossref]

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

Gieselmann, M. A.

T. A. Engel, N. A. Steinmetz, M. A. Gieselmann, A. Thiele, T. Moore, and K. Boahen, “Selective modulation of cortical state during spatial attention,” Science 354, 1140–1144 (2016).
[Crossref]

Goebel, T. A.

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

Gu, Z.

Guintrand, C. L.

C. L. Guintrand, “Stimulated Brillouin scattering threshold variations due to bend-induced birefringence in a non-polarization-maintaining fiber amplifier,” CLEO JW2A-23 (2014).

Gutierrez, J. M.

Haelterman, M.

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

Hager, C.

C. Hager and H. D. Pfister, “Nonlinear Interference Mitigation via Deep Neural Networks,” Optical Fiber Commun. Conf., paper W3A.4 (2018).
[Crossref]

Haigh, P. A.

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

Heck, M.

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

Hideur, A.

A. Hideur, T. Chartier, C. Oezkul, and F. Sanchez, “Dynamics and stabilization of a high power side-pumped Yb-doped double-clad fiber laser,” Opt. Commun. 186, 311–317 (2000).
[Crossref]

Hillerkuss, D.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Horlin, F.

M. Bauduin, S. Massar, and F. Horlin, “Non-linear satellite channel equalization based on a low complexity echo state network,” Information Science and Systems Conference, 99–104 (2016).

Huebner, M.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Ishikawa, S.

T. Okuno, M. Onishi, T. Kashiwada, S. Ishikawa, and M. Nishimura, “Silica-based functional fibers with enhanced nonlinearity and their applications,” IEEE J. Sel. Top. Quantum Electron. 51385–1391 (1999).
[Crossref]

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 (OSA) 5, 756–760 (2018).
[Crossref]

Jaeger, H.

M. Lukosevicius and H. Jaeger, “Reservoir Computing Approaches to Recurrent Neural Network Training,” Computer Science Review 3, 127–149 (2009).
[Crossref]

H. Jaeger, “Adaptive nonlinear system identification with echo state networks,” Advances in Neural Information Processing Systems 15, 593–600 (2003).

Jarajreh, M. A.

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett. 27387–390 (2015).
[Crossref]

Josten, A.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Kashiwada, T.

T. Okuno, M. Onishi, T. Kashiwada, S. Ishikawa, and M. Nishimura, “Silica-based functional fibers with enhanced nonlinearity and their applications,” IEEE J. Sel. Top. Quantum Electron. 51385–1391 (1999).
[Crossref]

Koenig, S.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Koos, C.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Kraemer, R. G.

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

Kutz, J. N.

J. N. Kutz, X. Fu, and S. Brunton, “Self-tuning fiber lasers: machine learning applied to optical systems,” Advanced Photonics Conf. paper NTu4A.7. (2014).

Kutz, N. J.

Larger, L.

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 (OSA) 5, 756–760 (2018).
[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]

Lau, A. P. T.

T. S. R. Shen and A. P. T. Lau, “Fiber nonlinearity compensation using extreme learning machine for DSP-based coherent communication systems,” OECC816–817 (2011).

Le, S. T.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett. 27387–390 (2015).
[Crossref]

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

Leuthold, J.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Leven, A.

T. A. Eriksson, H. Buelow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Phot. Technol. Lett. 29, 2091–2094 (2017).
[Crossref]

Liem, A.

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

Lima, T. F.

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Rep. 7, 7430(2017).
[Crossref] [PubMed]

Ling, Q.

London, M.

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6, 29080 (2016).
[Crossref] [PubMed]

Lukosevicius, M.

M. Lukosevicius and H. Jaeger, “Reservoir Computing Approaches to Recurrent Neural Network Training,” Computer Science Review 3, 127–149 (2009).
[Crossref]

Mahowald, M.

M. Mahowald and R. Douglas, “A silicon neuron,” Nature 354, 515–518 (1991).
[Crossref]

Maktoobi, S.

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 (OSA) 5, 756–760 (2018).
[Crossref]

Malka, D.

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6, 29080 (2016).
[Crossref] [PubMed]

Massar, S.

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

M. Bauduin, S. Massar, and F. Horlin, “Non-linear satellite channel equalization based on a low complexity echo state network,” Information Science and Systems Conference, 99–104 (2016).

Matzdorf, C.

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

McCarthy, M.

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

McCarthy, M. E.

Meyer, J.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Mhatli, S.

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

Mirasso, C. R.

Mirasso, C.R.

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

Moore, T.

T. A. Engel, N. A. Steinmetz, M. A. Gieselmann, A. Thiele, T. Moore, and K. Boahen, “Selective modulation of cortical state during spatial attention,” Science 354, 1140–1144 (2016).
[Crossref]

Nahmias, M. A.

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Rep. 7, 7430(2017).
[Crossref] [PubMed]

Nakamura, M.

S. Owaki and M. Nakamura, “Equalization of optical nonlinear waveform distortion using neural-network based digital signal processing,” Optoelectronics and Communications Conf. (Photon. Switching) paper WA2-40 (2016).

Nebendahl, B.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Nishimura, M.

T. Okuno, M. Onishi, T. Kashiwada, S. Ishikawa, and M. Nishimura, “Silica-based functional fibers with enhanced nonlinearity and their applications,” IEEE J. Sel. Top. Quantum Electron. 51385–1391 (1999).
[Crossref]

Nolte, S.

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

Oezkul, C.

A. Hideur, T. Chartier, C. Oezkul, and F. Sanchez, “Dynamics and stabilization of a high power side-pumped Yb-doped double-clad fiber laser,” Opt. Commun. 186, 311–317 (2000).
[Crossref]

Okuno, T.

T. Okuno, M. Onishi, T. Kashiwada, S. Ishikawa, and M. Nishimura, “Silica-based functional fibers with enhanced nonlinearity and their applications,” IEEE J. Sel. Top. Quantum Electron. 51385–1391 (1999).
[Crossref]

Onishi, M.

T. Okuno, M. Onishi, T. Kashiwada, S. Ishikawa, and M. Nishimura, “Silica-based functional fibers with enhanced nonlinearity and their applications,” IEEE J. Sel. Top. Quantum Electron. 51385–1391 (1999).
[Crossref]

Owaki, S.

S. Owaki and M. Nakamura, “Equalization of optical nonlinear waveform distortion using neural-network based digital signal processing,” Optoelectronics and Communications Conf. (Photon. Switching) paper WA2-40 (2016).

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.

Pfister, H. D.

C. Hager and H. D. Pfister, “Nonlinear Interference Mitigation via Deep Neural Networks,” Optical Fiber Commun. Conf., paper W3A.4 (2018).
[Crossref]

Prucnal, P. R.

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Rep. 7, 7430(2017).
[Crossref] [PubMed]

Rasmussen, D.

C. Eliasmith, T. C. Stewart, X. Choo, T. Bekolay, T. DeWolf, Y. Tang, and D. Rasmussen, “A Large-Scale Model of the Functioning Brain,” Science 338, 1202–1205 (2012).
[Crossref]

Richter, D.

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

Sanchez, F.

A. Hideur, T. Chartier, C. Oezkul, and F. Sanchez, “Dynamics and stabilization of a high power side-pumped Yb-doped double-clad fiber laser,” Opt. Commun. 186, 311–317 (2000).
[Crossref]

Schmogrow, R.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Schrauwen, B.

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]

Schrauwent, B.

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

Schreiber, T.

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

Secondini, M.

E. Agrell and M. Secondini, “Information-theoretic tools for optical communications engineers,” 2018 IEEE Photonics Conference (IPC) (2018).

Shahmoon, A.

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6, 29080 (2016).
[Crossref] [PubMed]

Shastri, B. J.

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Rep. 7, 7430(2017).
[Crossref] [PubMed]

Shemer, A.

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6, 29080 (2016).
[Crossref] [PubMed]

Shen, T. S. R.

T. S. R. Shen and A. P. T. Lau, “Fiber nonlinearity compensation using extreme learning machine for DSP-based coherent communication systems,” OECC816–817 (2011).

Smerieri, A.

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

Soriano, M. C.

Soriano, M.C.

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]

Sorokina, M.

Sorokina, M. S.

M. S. Sorokina and S. K. Turitsyn, “Regeneration limit of classical Shannon capacity,” Nat. Commun. 5, 3861 (2014).
[Crossref]

Steinmetz, N. A.

T. A. Engel, N. A. Steinmetz, M. A. Gieselmann, A. Thiele, T. Moore, and K. Boahen, “Selective modulation of cortical state during spatial attention,” Science 354, 1140–1144 (2016).
[Crossref]

Stewart, T. C.

C. Eliasmith, T. C. Stewart, X. Choo, T. Bekolay, T. DeWolf, Y. Tang, and D. Rasmussen, “A Large-Scale Model of the Functioning Brain,” Science 338, 1202–1205 (2012).
[Crossref]

Sygletos, S.

Tait, A. N.

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Rep. 7, 7430(2017).
[Crossref] [PubMed]

Tang, Y.

C. Eliasmith, T. C. Stewart, X. Choo, T. Bekolay, T. DeWolf, Y. Tang, and D. Rasmussen, “A Large-Scale Model of the Functioning Brain,” Science 338, 1202–1205 (2012).
[Crossref]

Thiele, A.

T. A. Engel, N. A. Steinmetz, M. A. Gieselmann, A. Thiele, T. Moore, and K. Boahen, “Selective modulation of cortical state during spatial attention,” Science 354, 1140–1144 (2016).
[Crossref]

Tsokanos, A.

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett. 27387–390 (2015).
[Crossref]

Tünnermann, A.

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

Turitsyn, S.

Turitsyn, S. K.

M. S. Sorokina and S. K. Turitsyn, “Regeneration limit of classical Shannon capacity,” Nat. Commun. 5, 3861 (2014).
[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]

Vandoorne, K.

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

Verstraeten, D.

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

Winter, M.

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

Wu, A. X.

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Rep. 7, 7430(2017).
[Crossref] [PubMed]

Zalevsky, Z.

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6, 29080 (2016).
[Crossref] [PubMed]

Zhou, E.

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Rep. 7, 7430(2017).
[Crossref] [PubMed]

Adv. Opt. Photon. (1)

Advances in Neural Information Processing Systems (1)

H. Jaeger, “Adaptive nonlinear system identification with echo state networks,” Advances in Neural Information Processing Systems 15, 593–600 (2003).

Appl. Opt. (1)

Computer Science Review (1)

M. Lukosevicius and H. Jaeger, “Reservoir Computing Approaches to Recurrent Neural Network Training,” Computer Science Review 3, 127–149 (2009).
[Crossref]

Fiber Lasers XV: Technology and Systems (1)

M. Heck, V. Bock, R. G. Kraemer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,” Fiber Lasers XV: Technology and Systems 10512, 105–121 (2018).

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

T. Okuno, M. Onishi, T. Kashiwada, S. Ishikawa, and M. Nishimura, “Silica-based functional fibers with enhanced nonlinearity and their applications,” IEEE J. Sel. Top. Quantum Electron. 51385–1391 (1999).
[Crossref]

IEEE Phot. Technol. Lett. (1)

T. A. Eriksson, H. Buelow, and A. Leven, “Applying neural networks in optical communication systems: possible pitfalls,” IEEE Phot. Technol. Lett. 29, 2091–2094 (2017).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. A. Jarajreh, E. Giacoumidis, I. Aldaya, S. T. Le, A. Tsokanos, Z. Ghassemlooy, and N. J. Doran, “Artificial neural network nonlinear equalizer for coherent optical OFDM,” IEEE Photon. Technol. Lett. 27387–390 (2015).
[Crossref]

IEEE Trans. Neural Netw. (1)

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

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

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

M. S. Sorokina and S. K. Turitsyn, “Regeneration limit of classical Shannon capacity,” Nat. Commun. 5, 3861 (2014).
[Crossref]

Nature (1)

M. Mahowald and R. Douglas, “A silicon neuron,” Nature 354, 515–518 (1991).
[Crossref]

Opt. Commun. (1)

A. Hideur, T. Chartier, C. Oezkul, and F. Sanchez, “Dynamics and stabilization of a high power side-pumped Yb-doped double-clad fiber laser,” Opt. Commun. 186, 311–317 (2000).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

E. Giacoumidis, S. T. Le, M. Ghanbarisabagh, M. McCarthy, I. Aldaya, S. Mhatli, M. A. Jarajreh, P. A. Haigh, N. J. Doran, A. D. Ellis, and B. J. Eggleton, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” Opt. Lett. P40, 5113–5116 (2015).
[Crossref]

M. Sorokina, S. Sygletos, and S. Turitsyn, “Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM,” Opt. Lett. 40, 3117–3120 (2015).
[Crossref] [PubMed]

Optica (OSA) (1)

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 (OSA) 5, 756–760 (2018).
[Crossref]

Sci. Rep. (5)

A. Argyris, J. Bueno, and I. Fischer, “Photonic machine learning implementation for signal recovery in optical communications,” Sci. Rep. 8 (1), 8487 (2018).
[Crossref]

E. Cohen, D. Malka, A. Shemer, A. Shahmoon, Z. Zalevsky, and M. London, “Neural networks within multi-core optic fibers,” Sci. Rep. 6, 29080 (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]

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]

A. N. Tait, T. F. Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Rep. 7, 7430(2017).
[Crossref] [PubMed]

Science (2)

C. Eliasmith, T. C. Stewart, X. Choo, T. Bekolay, T. DeWolf, Y. Tang, and D. Rasmussen, “A Large-Scale Model of the Functioning Brain,” Science 338, 1202–1205 (2012).
[Crossref]

T. A. Engel, N. A. Steinmetz, M. A. Gieselmann, A. Thiele, T. Moore, and K. Boahen, “Selective modulation of cortical state during spatial attention,” Science 354, 1140–1144 (2016).
[Crossref]

Other (11)

C. Hager and H. D. Pfister, “Nonlinear Interference Mitigation via Deep Neural Networks,” Optical Fiber Commun. Conf., paper W3A.4 (2018).
[Crossref]

T. S. R. Shen and A. P. T. Lau, “Fiber nonlinearity compensation using extreme learning machine for DSP-based coherent communication systems,” OECC816–817 (2011).

S. Owaki and M. Nakamura, “Equalization of optical nonlinear waveform distortion using neural-network based digital signal processing,” Optoelectronics and Communications Conf. (Photon. Switching) paper WA2-40 (2016).

M. Bauduin, S. Massar, and F. Horlin, “Non-linear satellite channel equalization based on a low complexity echo state network,” Information Science and Systems Conference, 99–104 (2016).

https://www.technologyreview.com/s/404874/smart-fibers/

J. N. Kutz, X. Fu, and S. Brunton, “Self-tuning fiber lasers: machine learning applied to optical systems,” Advanced Photonics Conf. paper NTu4A.7. (2014).

http://www.optonicus.com/infoco/

https://fiber-optic-catalog.ofsoptics.com/item/optical-fibers/highly-nonlinear-fiber-optical-fibers1/hnlf-pm-highly-non-linear-fiber-modules

C. L. Guintrand, “Stimulated Brillouin scattering threshold variations due to bend-induced birefringence in a non-polarization-maintaining fiber amplifier,” CLEO JW2A-23 (2014).

E. Agrell and M. Secondini, “Information-theoretic tools for optical communications engineers,” 2018 IEEE Photonics Conference (IPC) (2018).

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER,” International Conference on Transparent Optical Networks (2012).

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Figures (3)

Fig. 1
Fig. 1 The proposed reservoir setup. (a) Reservoir computing basics; (b) Transfer functions: ideal tanh-function (green squares) and approximations by sin-function (blue circles), analytical approximation (violet squares) and FESNA-generated (red diamonds). (c) 1D-processing setup with parameters: 1W pump power (ξ = 1), nonlinear fiber parameters |ξ|2γL = 2.2π, attenuation coefficient A = −22.5dB. A 3dB coupler is assumed. (d) 2D-processing setup with parameters: pump (ξ = 1 + 1i), nonlinear fiber parameters |ξ|2/2γL = 2.2π, attenuation coefficients (A1 = −18.5dB, A2 = −6dB).
Fig. 2
Fig. 2 FESNA for prediction tasks. The test signal is taken from a standard Mackey-Glass test, where we could perform prediction for a signal with 100 GHz bandwidth. For comparison, we plot (and as there is no significant difference visually, we show the mean square error (MSE)) the predicted signal obtained with tanh-function (blue, solid, the mean squared error of test-regime MSE = 4.8 × 10−9), with sin-function (green, squares, MSE = 8 × 10−7), FESNA-generated function (red, diamonds, MSE = 6 × 10−7). Panel (a) depicts one-step ahead prediction (i.e. for test-regime the previous target signal data points are used to generate further one-step ahead prediction) and panel (b) depicts feedback forcing or generation, (i.e. for test-regime the predicted data points are used to generate further predictions). One can see that, in the considered interval, both cases result in highly accurate performance comparable to that of ideal RC; bandwidth of (c) input signal and (d) output signal after FESNA.
Fig. 3
Fig. 3 Fiber reservoir computing for 16-,64-, and 256-QAM signal processing. (a) Q2-factor for a signal with varied input power for a transmission distance of 100 km, processed with a linear equalizer (LE, which compensates dispersion and phase shift), digital back-propagation (DBP, with 16 samples per symbol and 50 steps per span), and fiber reservoir computing (FESNA, with four and 16 samples per symbol) with reservoir size 27 and training on 1000 symbols. Performance of ideal (sigmoid-based) RC is shown for comparison. (b) Q2-improvement due to FESNA-processing over linear equalization. The reservoir and signal parameters are the same as in Fig. 2 with a sampling rate of 16. (c) The corresponding BER. (d) 16-, (e) 64-, and (f) 256-QAM modulated signal after linear equalization (blue) and FESNA processing (red) for 10 dBm input power.

Equations (10)

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

x n = f ( W x n 1 + W in u n )
x n + 1 ( 1 ) = W x n + W in u n + 1
x n + 1 ( 2 ) = A x n + 1 ( 1 ) + ξ
x n + 1 ( 3 ) = x n + 1 ( 2 ) e i γ L | x n + 1 ( 2 ) | 2
x n + 1 ( 3 ) = x n + 1 ( 2 ) e i γ L | x n + 1 ( 2 ) | , 𝔍 x n + 1 ( 3 ) sin ( 𝔍 x n + 1 ( 2 ) ) ,
x n + 1 ( 1 ) = W x n + W in u n + 1
x n + 1 ( 3 ) CW = x n + 1 ( 2 ) / 2 + ξ ; x n + 1 ( 3 ) CCW = i x n + 1 ( 2 ) / 2 + ξ
x n + 1 ( 4 ) CW / CCW = x n + 1 ( 3 ) CW / CCW e i γ L | x n + 1 ( 3 ) CW / CCW | 2 ,
x n + 1 = f ( x ) = A 2 / 2 ( x n + 1 ( 4 ) CW + i x n + 1 ( 4 ) CCW )
d y d t = α y ( t τ ) 1 + y β ( t τ ) γ y ( t )