Abstract

Via Santa Fe time series prediction and nonlinear channel equalization tasks, the performances of a reservoir computing (RC) system based on an optical feedback semiconductor laser (SL) under electrical information injection are numerically investigated. The simulated results show that the feedback delay time and strength seriously affect the performances of this RC system. By adopting a current-related optimized feedback delay time and strength, the RC can achieve a good performance for an SL biased within a wide region of 1.1–3.5 times its threshold. The prediction errors are smaller than 0.01 when implementing the Santa Fe tests, and the symbol error rates (SERs) are very low on the order of 10−5 for accomplishing nonlinear channel equalization tests under a signal-to-noise ratio (SNR) of 32 dB. Moreover, under a given RC performance level, the information processing rate of the RC can be improved by increasing the SL current.

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

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2019 (1)

Y. S. Hou, G. Q. Xia, E. Jayaprasath, D. Z. Yue, W. Y. Yang, and Z. M. Wu, “Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers,” Opt. Commun. 433, 215–220 (2019).
[Crossref]

2018 (5)

2017 (2)

2016 (3)

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
[Crossref]

M. Tezuka, K. Kanno, and M. Bunsen, “Reservoir computing with a slowly modulated mask signal for preprocessing using a mutually coupled optoelectronic system,” Jpn. J. Appl. Phys. 55(8S3), 08RE06 (2016).
[Crossref]

J. Nakayama, K. Kanno, and A. Uchida, “Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal,” Opt. Express 24(8), 8679–8692 (2016).
[Crossref]

2015 (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]

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4(1), 3629 (2015).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van 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(12), 3301–3307 (2015).
[Crossref]

N. Q. Li, L. Zunino, A. Locquet, B. Kim, D. Choi, W. Pan, and D. S. Citrin, “Multiscale ordinal symbolic analysis of the Lang-Kobayashi model for external-cavity semiconductor lasers: a test of theory,” IEEE J. Quantum Electron. 51(8), 1–6 (2015).
[Crossref]

2014 (2)

2013 (3)

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref]

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

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

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

2007 (2)

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]

G. Q. Xia, S. C. Chan, and J. M. Liu, “Multistability in a semiconductor laser with optoelectronic feedback,” Opt. Express 15(2), 572–576 (2007).
[Crossref]

2004 (1)

H. Jaeger and H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304(5667), 78–80 (2004).
[Crossref]

2003 (1)

F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. 39(4), 562–568 (2003).
[Crossref]

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]

1997 (1)

J. M. Liu, H. F. Chen, X. J. Meng, and T. B. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photonics Technol. Lett. 9(10), 1325–1327 (1997).
[Crossref]

1993 (1)

H. F. Liu and W. F. Ngai, “Nonlinear dynamics of a directly modulated 1.55 μm InGaAsP distributed feedback semiconductor laser,” IEEE J. Quantum Electron. 29(6), 1668–1675 (1993).
[Crossref]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Akrout, A.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
[Crossref]

Appeltant, L.

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4(1), 3629 (2015).
[Crossref]

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

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref]

Bienstman, P.

Brunner, D.

D. Brunner, B. Penkovsky, B. A. Marquez, M. Jacquot, I. Fischer, and L. Larger, “Tutorial: Photonic neural networks in delay systems,” J. Appl. Phys. 124(15), 152004 (2018).
[Crossref]

G. Van der Sande, D. Brunner, and M. C. Soriano, “Advances in photonic reservoir computing,” Nanophotonics 6(3), 561–576 (2017).
[Crossref]

J. Bueno, D. Brunner, M. C. Soriano, and I. Fischer, “Conditions for reservoir computing performance using semiconductor lasers with delayed optical feedback,” Opt. Express 25(3), 2401–2412 (2017).
[Crossref]

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

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref]

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

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

Bueno, J.

Bunsen, M.

M. Tezuka, K. Kanno, and M. Bunsen, “Reservoir computing with a slowly modulated mask signal for preprocessing using a mutually coupled optoelectronic system,” Jpn. J. Appl. Phys. 55(8S3), 08RE06 (2016).
[Crossref]

Chan, S. C.

Chen, H. F.

J. M. Liu, H. F. Chen, X. J. Meng, and T. B. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photonics Technol. Lett. 9(10), 1325–1327 (1997).
[Crossref]

Choi, D.

N. Q. Li, L. Zunino, A. Locquet, B. Kim, D. Choi, W. Pan, and D. S. Citrin, “Multiscale ordinal symbolic analysis of the Lang-Kobayashi model for external-cavity semiconductor lasers: a test of theory,” IEEE J. Quantum Electron. 51(8), 1–6 (2015).
[Crossref]

Citrin, D. S.

N. Q. Li, L. Zunino, A. Locquet, B. Kim, D. Choi, W. Pan, and D. S. Citrin, “Multiscale ordinal symbolic analysis of the Lang-Kobayashi model for external-cavity semiconductor lasers: a test of theory,” IEEE J. Quantum Electron. 51(8), 1–6 (2015).
[Crossref]

Cui, K. Y.

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]

Dambre, J.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref]

Danckaert, J.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van 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(12), 3301–3307 (2015).
[Crossref]

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4(1), 3629 (2015).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Fast photonic information processing using semiconductor lasers with delayed optical feedback: Role of phase dynamics,” Opt. Express 22(7), 8672–8686 (2014).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref]

Dou, W. B.

Duport, F.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
[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]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref]

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

Escalona-Morán, M. A.

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

Feng, X.

Fischer, I.

D. Brunner, B. Penkovsky, B. A. Marquez, M. Jacquot, I. Fischer, and L. Larger, “Tutorial: Photonic neural networks in delay systems,” J. Appl. Phys. 124(15), 152004 (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(3), 2401–2412 (2017).
[Crossref]

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4(1), 3629 (2015).
[Crossref]

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

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref]

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

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

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref]

Gershenfeld, N. A.

A. S. Weigend and N. A. Gershenfeld, “Time series prediction: forecasting the future and understanding the past,” http://www-psych.stanford.edu/∼andreas/Time-Series/SantaFe.html (1993).

Gutierrez, J. M.

Haas, H.

H. Jaeger and H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304(5667), 78–80 (2004).
[Crossref]

Haelterman, M.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
[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]

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

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref]

Hicke, K.

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

Hou, Y. S.

Y. S. Hou, G. Q. Xia, E. Jayaprasath, D. Z. Yue, W. Y. Yang, and Z. M. Wu, “Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers,” Opt. Commun. 433, 215–220 (2019).
[Crossref]

Y. S. Hou, G. Q. Xia, W. Y. Yang, D. Wang, E. Jayaprasath, Z. F. Jiang, C. X. Hu, and Z. M. Wu, “Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection,” Opt. Express 26(8), 10211–10219 (2018).
[Crossref]

Hu, C. X.

Huang, Y. D.

Jacquot, M.

D. Brunner, B. Penkovsky, B. A. Marquez, M. Jacquot, I. Fischer, and L. Larger, “Tutorial: Photonic neural networks in delay systems,” J. Appl. Phys. 124(15), 152004 (2018).
[Crossref]

Jaeger, H.

H. Jaeger and H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304(5667), 78–80 (2004).
[Crossref]

H. Jaeger, “The ‘echo state’ approach to analysing and training recurrent neural networks,” Technical Report GMD Report 148, German National Research Center for Information Technology (2001).

Jayaprasath, E.

Y. S. Hou, G. Q. Xia, E. Jayaprasath, D. Z. Yue, W. Y. Yang, and Z. M. Wu, “Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers,” Opt. Commun. 433, 215–220 (2019).
[Crossref]

Y. S. Hou, G. Q. Xia, W. Y. Yang, D. Wang, E. Jayaprasath, Z. F. Jiang, C. X. Hu, and Z. M. Wu, “Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection,” Opt. Express 26(8), 10211–10219 (2018).
[Crossref]

Jiang, Z. F.

Kanno, K.

J. Nakayama, K. Kanno, and A. Uchida, “Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal,” Opt. Express 24(8), 8679–8692 (2016).
[Crossref]

M. Tezuka, K. Kanno, and M. Bunsen, “Reservoir computing with a slowly modulated mask signal for preprocessing using a mutually coupled optoelectronic system,” Jpn. J. Appl. Phys. 55(8S3), 08RE06 (2016).
[Crossref]

Kim, B.

N. Q. Li, L. Zunino, A. Locquet, B. Kim, D. Choi, W. Pan, and D. S. Citrin, “Multiscale ordinal symbolic analysis of the Lang-Kobayashi model for external-cavity semiconductor lasers: a test of theory,” IEEE J. Quantum Electron. 51(8), 1–6 (2015).
[Crossref]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Kuriki, Y.

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Larger, L.

Li, B. X.

Li, N. Q.

N. Q. Li, L. Zunino, A. Locquet, B. Kim, D. Choi, W. Pan, and D. S. Citrin, “Multiscale ordinal symbolic analysis of the Lang-Kobayashi model for external-cavity semiconductor lasers: a test of theory,” IEEE J. Quantum Electron. 51(8), 1–6 (2015).
[Crossref]

Lin, F. Y.

F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. 39(4), 562–568 (2003).
[Crossref]

Liu, F.

Liu, H. F.

H. F. Liu and W. F. Ngai, “Nonlinear dynamics of a directly modulated 1.55 μm InGaAsP distributed feedback semiconductor laser,” IEEE J. Quantum Electron. 29(6), 1668–1675 (1993).
[Crossref]

Liu, J. M.

G. Q. Xia, S. C. Chan, and J. M. Liu, “Multistability in a semiconductor laser with optoelectronic feedback,” Opt. Express 15(2), 572–576 (2007).
[Crossref]

F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. 39(4), 562–568 (2003).
[Crossref]

J. M. Liu, H. F. Chen, X. J. Meng, and T. B. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photonics Technol. Lett. 9(10), 1325–1327 (1997).
[Crossref]

Locquet, A.

N. Q. Li, L. Zunino, A. Locquet, B. Kim, D. Choi, W. Pan, and D. S. Citrin, “Multiscale ordinal symbolic analysis of the Lang-Kobayashi model for external-cavity semiconductor lasers: a test of theory,” IEEE J. Quantum Electron. 51(8), 1–6 (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]

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]

Marquez, B. A.

D. Brunner, B. Penkovsky, B. A. Marquez, M. Jacquot, I. Fischer, and L. Larger, “Tutorial: Photonic neural networks in delay systems,” J. Appl. Phys. 124(15), 152004 (2018).
[Crossref]

Massar, S.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
[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]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and S. Massar, “All-optical reservoir computing,” Opt. Express 20(20), 22783–22795 (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(1), 468 (2011).
[Crossref]

Meng, X. J.

J. M. Liu, H. F. Chen, X. J. Meng, and T. B. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photonics Technol. Lett. 9(10), 1325–1327 (1997).
[Crossref]

Mirasso, C. R.

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

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref]

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

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

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref]

Nakayama, J.

Natschläger, T.

W. Maass, T. Natschläger, and H. Markram, “Real-time computing without stable States: A new framework for neural computation based on perturbations,” Neural Comput. 14(11), 2531–2560 (2002).
[Crossref]

Ngai, W. F.

H. F. Liu and W. F. Ngai, “Nonlinear dynamics of a directly modulated 1.55 μm InGaAsP distributed feedback semiconductor laser,” IEEE J. Quantum Electron. 29(6), 1668–1675 (1993).
[Crossref]

Nguimdo, R. M.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van 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(12), 3301–3307 (2015).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Fast photonic information processing using semiconductor lasers with delayed optical feedback: Role of phase dynamics,” Opt. Express 22(7), 8672–8686 (2014).
[Crossref]

Ortín, S.

Pan, W.

N. Q. Li, L. Zunino, A. Locquet, B. Kim, D. Choi, W. Pan, and D. S. Citrin, “Multiscale ordinal symbolic analysis of the Lang-Kobayashi model for external-cavity semiconductor lasers: a test of theory,” IEEE J. Quantum Electron. 51(8), 1–6 (2015).
[Crossref]

Paquot, Y.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref]

Parlitz, U.

R. S. Zimmermann and U. Parlitz, “Observing spatio-temporal dynamics of excitable media using reservoir computing,” Chaos 28(4), 043118 (2018).
[Crossref]

Penkovsky, B.

D. Brunner, B. Penkovsky, B. A. Marquez, M. Jacquot, I. Fischer, and L. Larger, “Tutorial: Photonic neural networks in delay systems,” J. Appl. Phys. 124(15), 152004 (2018).
[Crossref]

Pesquera, L.

Rontani, D.

Schneider, B.

Schrauwen, B.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref]

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]

Sciamanna, M.

Simpson, T. B.

J. M. Liu, H. F. Chen, X. J. Meng, and T. B. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photonics Technol. Lett. 9(10), 1325–1327 (1997).
[Crossref]

Smerieri, A.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
[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]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref]

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

Soriano, M. C.

G. Van der Sande, D. Brunner, and M. C. Soriano, “Advances in photonic reservoir computing,” Nanophotonics 6(3), 561–576 (2017).
[Crossref]

J. Bueno, D. Brunner, M. C. Soriano, and I. Fischer, “Conditions for reservoir computing performance using semiconductor lasers with delayed optical feedback,” Opt. Express 25(3), 2401–2412 (2017).
[Crossref]

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

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref]

K. Hicke, M. A. Escalona-Morán, D. Brunner, M. C. Soriano, I. Fischer, and C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501610 (2013).
[Crossref]

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

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref]

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]

Takano, K.

Tezuka, M.

M. Tezuka, K. Kanno, and M. Bunsen, “Reservoir computing with a slowly modulated mask signal for preprocessing using a mutually coupled optoelectronic system,” Jpn. J. Appl. Phys. 55(8S3), 08RE06 (2016).
[Crossref]

Uchida, A.

Van der Sande, G.

G. Van der Sande, D. Brunner, and M. C. Soriano, “Advances in photonic reservoir computing,” Nanophotonics 6(3), 561–576 (2017).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van 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(12), 3301–3307 (2015).
[Crossref]

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4(1), 3629 (2015).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Fast photonic information processing using semiconductor lasers with delayed optical feedback: Role of phase dynamics,” Opt. Express 22(7), 8672–8686 (2014).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2(1), 468 (2011).
[Crossref]

Vandoorne, K.

Vatin, J.

Verschaffelt, G.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van 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(12), 3301–3307 (2015).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Fast photonic information processing using semiconductor lasers with delayed optical feedback: Role of phase dynamics,” Opt. Express 22(7), 8672–8686 (2014).
[Crossref]

Verstraeten, 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]

Vinckier, Q.

Wang, D.

Wang, Y.

Weigend, A. S.

A. S. Weigend and N. A. Gershenfeld, “Time series prediction: forecasting the future and understanding the past,” http://www-psych.stanford.edu/∼andreas/Time-Series/SantaFe.html (1993).

Wu, Z. M.

Y. S. Hou, G. Q. Xia, E. Jayaprasath, D. Z. Yue, W. Y. Yang, and Z. M. Wu, “Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers,” Opt. Commun. 433, 215–220 (2019).
[Crossref]

Y. S. Hou, G. Q. Xia, W. Y. Yang, D. Wang, E. Jayaprasath, Z. F. Jiang, C. X. Hu, and Z. M. Wu, “Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection,” Opt. Express 26(8), 10211–10219 (2018).
[Crossref]

Xia, G. Q.

Yang, W. Y.

Y. S. Hou, G. Q. Xia, E. Jayaprasath, D. Z. Yue, W. Y. Yang, and Z. M. Wu, “Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers,” Opt. Commun. 433, 215–220 (2019).
[Crossref]

Y. S. Hou, G. Q. Xia, W. Y. Yang, D. Wang, E. Jayaprasath, Z. F. Jiang, C. X. Hu, and Z. M. Wu, “Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection,” Opt. Express 26(8), 10211–10219 (2018).
[Crossref]

Yue, D. Z.

Y. S. Hou, G. Q. Xia, E. Jayaprasath, D. Z. Yue, W. Y. Yang, and Z. M. Wu, “Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers,” Opt. Commun. 433, 215–220 (2019).
[Crossref]

Zhang, H.

Zimmermann, R. S.

R. S. Zimmermann and U. Parlitz, “Observing spatio-temporal dynamics of excitable media using reservoir computing,” Chaos 28(4), 043118 (2018).
[Crossref]

Zunino, L.

N. Q. Li, L. Zunino, A. Locquet, B. Kim, D. Choi, W. Pan, and D. S. Citrin, “Multiscale ordinal symbolic analysis of the Lang-Kobayashi model for external-cavity semiconductor lasers: a test of theory,” IEEE J. Quantum Electron. 51(8), 1–6 (2015).
[Crossref]

Chaos (1)

R. S. Zimmermann and U. Parlitz, “Observing spatio-temporal dynamics of excitable media using reservoir computing,” Chaos 28(4), 043118 (2018).
[Crossref]

IEEE J. Quantum Electron. (4)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

H. F. Liu and W. F. Ngai, “Nonlinear dynamics of a directly modulated 1.55 μm InGaAsP distributed feedback semiconductor laser,” IEEE J. Quantum Electron. 29(6), 1668–1675 (1993).
[Crossref]

F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. 39(4), 562–568 (2003).
[Crossref]

N. Q. Li, L. Zunino, A. Locquet, B. Kim, D. Choi, W. Pan, and D. S. Citrin, “Multiscale ordinal symbolic analysis of the Lang-Kobayashi model for external-cavity semiconductor lasers: a test of theory,” IEEE J. Quantum Electron. 51(8), 1–6 (2015).
[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(4), 1501610 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (1)

J. M. Liu, H. F. Chen, X. J. Meng, and T. B. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photonics Technol. Lett. 9(10), 1325–1327 (1997).
[Crossref]

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

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van 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(12), 3301–3307 (2015).
[Crossref]

J. Appl. Phys. (1)

D. Brunner, B. Penkovsky, B. A. Marquez, M. Jacquot, I. Fischer, and L. Larger, “Tutorial: Photonic neural networks in delay systems,” J. Appl. Phys. 124(15), 152004 (2018).
[Crossref]

Jpn. J. Appl. Phys. (1)

M. Tezuka, K. Kanno, and M. Bunsen, “Reservoir computing with a slowly modulated mask signal for preprocessing using a mutually coupled optoelectronic system,” Jpn. J. Appl. Phys. 55(8S3), 08RE06 (2016).
[Crossref]

Nanophotonics (1)

G. Van der Sande, D. Brunner, and M. C. Soriano, “Advances in photonic reservoir computing,” Nanophotonics 6(3), 561–576 (2017).
[Crossref]

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

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4(1), 1364 (2013).
[Crossref]

Neural Comput. (1)

W. Maass, T. Natschläger, and H. Markram, “Real-time computing without stable States: A new framework for neural computation based on perturbations,” Neural Comput. 14(11), 2531–2560 (2002).
[Crossref]

Neural Networks (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]

Opt. Commun. (1)

Y. S. Hou, G. Q. Xia, E. Jayaprasath, D. Z. Yue, W. Y. Yang, and Z. M. Wu, “Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers,” Opt. Commun. 433, 215–220 (2019).
[Crossref]

Opt. Express (10)

J. Bueno, D. Brunner, M. C. Soriano, and I. Fischer, “Conditions for reservoir computing performance using semiconductor lasers with delayed optical feedback,” Opt. Express 25(3), 2401–2412 (2017).
[Crossref]

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

Y. S. Hou, G. Q. Xia, W. Y. Yang, D. Wang, E. Jayaprasath, Z. F. Jiang, C. X. Hu, and Z. M. Wu, “Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection,” Opt. Express 26(8), 10211–10219 (2018).
[Crossref]

J. Nakayama, K. Kanno, and A. Uchida, “Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal,” Opt. Express 24(8), 8679–8692 (2016).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Fast photonic information processing using semiconductor lasers with delayed optical feedback: Role of phase dynamics,” Opt. Express 22(7), 8672–8686 (2014).
[Crossref]

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

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

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

H. Zhang, X. Feng, B. X. Li, Y. Wang, K. Y. Cui, F. Liu, W. B. Dou, and Y. D. Huang, “Integrated photonic reservoir computing based on hierarchical time-multiplexing structure,” Opt. Express 22(25), 31356–31370 (2014).
[Crossref]

G. Q. Xia, S. C. Chan, and J. M. Liu, “Multistability in a semiconductor laser with optoelectronic feedback,” Opt. Express 15(2), 572–576 (2007).
[Crossref]

Opt. Lett. (1)

Optica (1)

Sci. Rep. (3)

L. Appeltant, G. Van der Sande, J. Danckaert, and I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4(1), 3629 (2015).
[Crossref]

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2(1), 287 (2012).
[Crossref]

Science (1)

H. Jaeger and H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304(5667), 78–80 (2004).
[Crossref]

Other (3)

A. S. Weigend and N. A. Gershenfeld, “Time series prediction: forecasting the future and understanding the past,” http://www-psych.stanford.edu/∼andreas/Time-Series/SantaFe.html (1993).

A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).

H. Jaeger, “The ‘echo state’ approach to analysing and training recurrent neural networks,” Technical Report GMD Report 148, German National Research Center for Information Technology (2001).

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of reservoir computing based on an optical feedback semiconductor laser under electrical information injection. SL: semiconductor laser; OC: optical circulator; VA: variable attenuator.
Fig. 2.
Fig. 2. Relaxation oscillation frequency fro and relaxation oscillation characteristic time Tro of the free-running SL as a function of the normalized bias current jb.
Fig. 3.
Fig. 3. (a) Bifurcation diagram as a function of feedback strength k for jb = 2.0 and τ = 1.5 ns; (b) Feedback strength at the bifurcate point (kBP) as a function of the normalized bias current jb under θ = H0 Tro, where H0 takes 0.1, 0.2, 0.3, 0.4 and 0.5.
Fig. 4.
Fig. 4. NMSEs as a function of feedback strength k, where (a) jb = 1.5, (b) jb = 2.5, and (c) jb = 3.0.
Fig. 5.
Fig. 5. (a) NMSEs as a function of jb, where the blue line is for the case of θ = 0.2Tro and k = 0.5kBP and the red line is for the case of θ = 0.2 ns and k = 0.15ns-1; (b) Delay time (blue line) and information processing rate (red line) under θ = 0.2Tro as a function of jb.
Fig. 6.
Fig. 6. SERs of nonlinear channel equalization task with θ = 0.2Tro. (a) SERs as a function of k under SNR = 24 dB; (b) SERs as a function of jb under k = 0.5kBP and SNR = 24 dB; (c) SERs as a function of SNR under k = 0.5kBP.

Equations (6)

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N M S E = 1 L n = 1 L ( y o u t ( n ) y d ( n ) ) 2 / v a r ( y d ) ,
d E ( t ) d t = 1 2 ( 1 + i α ) [ G N ( N ( t ) N 0 ) 1 + ε | E ( t ) | 2 1 τ p ] E ( t ) + k E ( t τ ) e i ω 0 τ + F ( t ) ,
d N ( t ) d t = j b ( 1 + γ j m ( t ) ) J t h N ( t ) τ s G N ( N ( t ) N 0 ) 1 + ε | E ( t ) | 2 | E ( t ) | 2 ,
f r o = G N J t h ( j b 1 ) / ( 2 π ) .
q ( n ) = 0.08 d ( n + 2 ) 0.12 d ( n + 1 ) + d ( n ) + 0.18 d ( n 1 ) 0.1 d ( n 2 ) + 0.091 d ( n 3 ) 0.05 d ( n 4 ) + 0.04 d ( n 5 ) + 0.03 d ( n 6 ) + 0.01 d ( n 7 ) .
u ( n ) = q ( n ) + 0.036 q 2 ( n ) 0.011 q 3 ( n ) + ξ e ( n ) ,

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