Abstract

In this work, we propose a scheme of reservoir computing (RC) for processing a Santa-Fe time series prediction task and a signal classification task in parallel, and the performances of the RC have been numerically investigated. For this scheme, a vertical-cavity surface-emitting laser (VCSEL) simultaneously subject to double optical feedback and optical injection is utilized as a nonlinear node, and the parallel information processing of the RC system is implemented based on the dynamical responses of X polarization component (X-PC) and Y polarization component (Y-PC) in the VCSEL. Considering that two different feedback frames (polarization-preserved optical feedback (PP-OF) or polarization-rotated optical feedback (PR-OF)) may be adopted in two feedback loops, four feedback combination cases are numerically analyzed. The simulated results show that the parallel processing ability of the proposed RC system depends on the feedback frames adopted in two loops. After comprehensively evaluating the parallel processing performances of the two tasks under different feedback combinations, the best parallel processing performance can be achieved by adopting PP-OFs in both two feedback loops. Under some optimized operation parameters, this proposed RC system can realize the lowest prediction error of 0.0289 and the lowest signal classification error of 2.78 × 10−5.

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

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2019 (1)

2018 (5)

2017 (1)

2016 (2)

2015 (2)

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]

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] [PubMed]

2014 (2)

2013 (3)

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] [PubMed]

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

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

2012 (4)

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

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

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

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

2011 (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] [PubMed]

S. Y. Xiang, W. Pan, B. Luo, L. Yan, X. Zou, N. Jiang, L. Yang, and H. Zhu, “Unpredictability-enhanced chaotic vertical-cavity surface-emitting lasers with variable-polarization optical feedback,” J. Lightwave Technol. 29(14), 2173–2179 (2011).
[Crossref]

2009 (1)

2007 (2)

2006 (1)

2004 (2)

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

R. Boucekkine, D. D. L. Croix, and O. Licandro, “Modelling vintage structures with DDEs: Principles and applications,” Math. Popul. Stud. 11(3), 151–179 (2004).
[Crossref]

2003 (1)

Z. N. Masoud, A. H. Nayfeh, and A. Al-Mousa, “Delayed position feedback controller for the reduction of payload pendulations of rotary cranes,” J. Vib. Control 9(1), 257–277 (2003).
[Crossref]

2001 (1)

R. J. Henry, Z. N. Masoud, A. H. Nayfeh, and D. T. Mook, “Cargo pendulation reduction on ship-mounted cranes via boom-lu angle actuation,” J. Vib. Control 7(8), 1253–1264 (2001).
[Crossref]

1997 (1)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

Abraham, N. B.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

Al-Mousa, A.

Z. N. Masoud, A. H. Nayfeh, and A. Al-Mousa, “Delayed position feedback controller for the reduction of payload pendulations of rotary cranes,” J. Vib. Control 9(1), 257–277 (2003).
[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(3), 3241–3249 (2012).
[Crossref] [PubMed]

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

Bienstman, P.

Boucekkine, R.

R. Boucekkine, D. D. L. Croix, and O. Licandro, “Modelling vintage structures with DDEs: Principles and applications,” Math. Popul. Stud. 11(3), 151–179 (2004).
[Crossref]

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]

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]

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] [PubMed]

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] [PubMed]

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

Chembo, Y. K.

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

Citrin, D. S.

N. Q. Li, R. M. Nguimdo, A. Locquet, and D. S. Citrin, “Enhancing optical-feedback-induced chaotic dynamics in semiconductor ring lasers via optical injection,” Nonlinear Dyn. 92(2), 315–324 (2018).
[Crossref]

Croix, D. D. L.

R. Boucekkine, D. D. L. Croix, and O. Licandro, “Modelling vintage structures with DDEs: Principles and applications,” Math. Popul. Stud. 11(3), 151–179 (2004).
[Crossref]

D’Haene, M.

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Netw. 20(3), 391–403 (2007).
[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(1), 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(1), 468 (2011).
[Crossref] [PubMed]

Danckaert, J.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Reducing the phase sensitivity of laser-based optical reservoir computing systems,” Opt. Express 24(2), 1238–1252 (2016).
[Crossref] [PubMed]

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] [PubMed]

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

Dejonckheere, A.

Duport, F.

Erneux, T.

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]

Fang, L.

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]

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] [PubMed]

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

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

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

Gatare, I.

Guillet de Chatellus, H.

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] [PubMed]

Haelterman, M.

Henry, R. J.

R. J. Henry, Z. N. Masoud, A. H. Nayfeh, and D. T. Mook, “Cargo pendulation reduction on ship-mounted cranes via boom-lu angle actuation,” J. Vib. Control 7(8), 1253–1264 (2001).
[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.

Hu, C.

Hugon, O.

Jacquin, O.

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]

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

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] [PubMed]

Jayaprasath, E.

Jiang, N.

Jiang, Z.

Kanno, K.

Koyama, F.

Kuriki, Y.

Lacot, E.

Larger, L.

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]

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] [PubMed]

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

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

Li, N. Q.

N. Q. Li, R. M. Nguimdo, A. Locquet, and D. S. Citrin, “Enhancing optical-feedback-induced chaotic dynamics in semiconductor ring lasers via optical injection,” Nonlinear Dyn. 92(2), 315–324 (2018).
[Crossref]

Licandro, O.

R. Boucekkine, D. D. L. Croix, and O. Licandro, “Modelling vintage structures with DDEs: Principles and applications,” Math. Popul. Stud. 11(3), 151–179 (2004).
[Crossref]

Locquet, A.

N. Q. Li, R. M. Nguimdo, A. Locquet, and D. S. Citrin, “Enhancing optical-feedback-induced chaotic dynamics in semiconductor ring lasers via optical injection,” Nonlinear Dyn. 92(2), 315–324 (2018).
[Crossref]

I. Gatare, M. Sciamanna, A. Locquet, and K. Panajotov, “Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers,” Opt. Lett. 32(12), 1629–1631 (2007).
[Crossref] [PubMed]

Luo, B.

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]

Martinenghi, R.

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

Martin-Regalado, J.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

Masoud, Z. N.

Z. N. Masoud, A. H. Nayfeh, and A. Al-Mousa, “Delayed position feedback controller for the reduction of payload pendulations of rotary cranes,” J. Vib. Control 9(1), 257–277 (2003).
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R. J. Henry, Z. N. Masoud, A. H. Nayfeh, and D. T. Mook, “Cargo pendulation reduction on ship-mounted cranes via boom-lu angle actuation,” J. Vib. Control 7(8), 1253–1264 (2001).
[Crossref]

Massar, S.

Mirasso, C. R.

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

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

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

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

Mook, D. T.

R. J. Henry, Z. N. Masoud, A. H. Nayfeh, and D. T. Mook, “Cargo pendulation reduction on ship-mounted cranes via boom-lu angle actuation,” J. Vib. Control 7(8), 1253–1264 (2001).
[Crossref]

Nakayama, J.

Nayfeh, A. H.

Z. N. Masoud, A. H. Nayfeh, and A. Al-Mousa, “Delayed position feedback controller for the reduction of payload pendulations of rotary cranes,” J. Vib. Control 9(1), 257–277 (2003).
[Crossref]

R. J. Henry, Z. N. Masoud, A. H. Nayfeh, and D. T. Mook, “Cargo pendulation reduction on ship-mounted cranes via boom-lu angle actuation,” J. Vib. Control 7(8), 1253–1264 (2001).
[Crossref]

Nguimdo, R. M.

Ortín, S.

Oudar, J. L.

Pan, W.

Panajotov, K.

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] [PubMed]

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.

Prati, F.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
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Rontani, D.

Rybalko, S.

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

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J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

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

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

Sciamanna, M.

Smerieri, A.

Soriano, M. C.

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

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

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

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

Takano, K.

Uchida, A.

Van der Sande, G.

Vandoorne, K.

Vatin, J.

Verschaffelt, G.

Verstraeten, D.

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

Vinckier, Q.

Wang, D.

Wu, J. G.

Wu, Z.

Wu, Z. M.

Xia, G.

Xia, G. Q.

Xiang, S. Y.

Yan, L.

Yang, L.

Yang, W.

Zhu, H.

Zou, X.

IEEE J. Quantum Electron. (1)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[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 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] [PubMed]

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]

J. Lightwave Technol. (2)

J. Vib. Control (2)

R. J. Henry, Z. N. Masoud, A. H. Nayfeh, and D. T. Mook, “Cargo pendulation reduction on ship-mounted cranes via boom-lu angle actuation,” J. Vib. Control 7(8), 1253–1264 (2001).
[Crossref]

Z. N. Masoud, A. H. Nayfeh, and A. Al-Mousa, “Delayed position feedback controller for the reduction of payload pendulations of rotary cranes,” J. Vib. Control 9(1), 257–277 (2003).
[Crossref]

Math. Popul. Stud. (1)

R. Boucekkine, D. D. L. Croix, and O. Licandro, “Modelling vintage structures with DDEs: Principles and applications,” Math. Popul. Stud. 11(3), 151–179 (2004).
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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] [PubMed]

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

Neural Netw. (1)

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Netw. 20(3), 391–403 (2007).
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Nonlinear Dyn. (1)

N. Q. Li, R. M. Nguimdo, A. Locquet, and D. S. Citrin, “Enhancing optical-feedback-induced chaotic dynamics in semiconductor ring lasers via optical injection,” Nonlinear Dyn. 92(2), 315–324 (2018).
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Opt. Express (10)

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
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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).
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F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and S. Massar, “All-optical reservoir computing,” Opt. Express 20(20), 22783–22795 (2012).
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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] [PubMed]

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).
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A. Dejonckheere, F. Duport, A. Smerieri, L. Fang, J. L. Oudar, M. Haelterman, and S. Massar, “All-optical reservoir computer based on saturation of absorption,” Opt. Express 22(9), 10868–10881 (2014).
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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).
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Y. Hou, G. Xia, W. Yang, D. Wang, E. Jayaprasath, Z. Jiang, C. Hu, and Z. 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).
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R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Reducing the phase sensitivity of laser-based optical reservoir computing systems,” Opt. Express 24(2), 1238–1252 (2016).
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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).
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Opt. Lett. (4)

Optica (1)

Phys. Rev. Lett. (1)

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, and L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108(24), 244101 (2012).
[Crossref] [PubMed]

Sci. Rep. (1)

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

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of a RC system based on a VCSEL subject to double optical feedback and optical injection for processing two independent tasks in parallel. OC: optical circulator; VOA: variable optical attenuator; PC: polarization controller; FC: fiber coupler; PFC: polarization fiber coupler; PBS: polarization beam splitter; PM: phase modulator; SL: semiconductor laser.
Fig. 2
Fig. 2 Mean NMSE of 10 calculations for (a) TASKx and (b) TASKy as a function of the number N of virtual nodes with ∆f1, 2 = 0 GHz, Pinj = 1 and γ = 1. The solid lines with solid marks correspond to the parallel processing of two tasks by the RC system under four feedback combination cases, and the dashed lines with hollow square marks corresponds to a single task processing by the RC system under PP-PP-OF.
Fig. 3
Fig. 3 Performance illustrations of TASKx (the left column) and TASKy (the right column) under PP-PP-OF with N = 500, ∆f1, 2 = 0 GHz, Pinj = 1, and γ = 1. (a) A sample of target chaotic Santa-Fe time series data ӯ(n); (b) Predicted output y(n) of the proposed VCSEL-based RC system; (c) Error (y(n)- ӯ(n)) between the target value and the reservoir output; (d) A set of input data composed of random concatenation of sine and square waves; (e) Target values, where 0 and 1 correspond sine and square waves, respectively; (f) Classification output of the proposed VCSEL-based RC system.
Fig. 4
Fig. 4 Mean NMSE of 10 calculations for (a) TASKx and (b) TASKy as a function of the frequency detuning ∆f under cases of PP-PP-OF (blue lines with square marks), PP-PR-OF (green lines with triangle marks), PR-PP-OF (black lines with cross marks), or PR-PR-OF (red lines with circle marks) with N = 500, Pinj = 1, and γ = 1.
Fig. 5
Fig. 5 Mean NMSE of 10 calculations for processing (a) TASKx and (b) TASKy as a function of the injected power Pinj for the RC under PP-PP-OF with N = 500, ∆f = −12 GHz and γ = 1, where error bars are the statistical results of 10 calculations.
Fig. 6
Fig. 6 Evolution maps of the NMSE values in a Pinjγ parameter space for the RC under PP-PP-OF to implement (a) TASKx and (b) TASKy with N = 500 and ∆f = −12 GHz.

Equations (12)

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d E x dt =κ(1+iα)(N E x - E x +in E y )-( γ a +i γ p ) E x + k inj ε 1 (t)+ η 1 Φ 1x (t)+ η 2 Φ 2x (t)+ F x (t),
d E y dt =κ(1+iα)(N E y - E y -in E x )+( γ a +i γ p ) E y + k inj ε 2 (t)+ η 1 Φ 1y (t)+ η 2 Φ 2y (t)+ F y (t),
dN dt =- γ e [N-μ+N( | E x | 2 + | E y | 2 )+in( E y E x * - E x E y * )],
dn dt =- γ s n- γ e [n( | E x | 2 + | E y | 2 )+iN( E y E x * - E x E y * )],
ε 1,2 (t)= P inj e iπ S 1,2 (t) e i2πΔ f 1,2 t ,
S 1,2 (t)=γ×Mas k 1,2 (t)× U 1,2 (n),
PPPPOF: Φ 1x,1y (t)= E x,y (t- τ 1 ) e -i ω 0 τ 1 , Φ 2x,2y (t)= E x,y (t- τ 2 ) e -i ω 0 τ 2 ,
PPPROF: Φ 1x,1y (t)= E x,y (t- τ 1 ) e -i ω 0 τ 1 , Φ 2x,2y (t)= E y,x (t- τ 2 ) e -i ω 0 τ 2 ,
PRPPOF: Φ 1x,1y (t)= E y,x (t- τ 1 ) e -i ω 0 τ 1 , Φ 2x,2y (t)= E x,y (t- τ 2 ) e -i ω 0 τ 2 ,
PRPROF: Φ 1x,1y (t)= E y,x (t- τ 1 ) e -i ω 0 τ 1 , Φ 2x,2y (t)= E y,x (t- τ 2 ) e -i ω 0 τ 2 ,
F x (t)= β sp 2 ( N+n ξ 1 + N-n ξ 2 ), F y (t)=i β sp 2 ( N+n ξ 1 N-n ξ 2 ),
NMSE= 1 L n=1 L ( y(n) y ¯ (n) ) 2 var( y ) ,

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