Abstract

An integrated photonic reservoir computing (RC) based on hierarchical time-multiplexing structure is proposed by numerical simulations. A micro-ring array (MRA) is employed as a typical time delay implementation of RC. At the output port of the MRA, a secondary time-multiplexing is achieved by multi-mode interference (MMI) splitter and delay line array. This hierarchical time-multiplexing structure can ensure a large reservoir size with fast processing speed. Simulation results indicate that the proposed RC system yields better performance than previously reported ones. The achieved normalized mean square error between the system output and target sequence are 0.5% and 2.7% for signal classification and chaotic time series prediction, respectively, while the sample rate is as high as 1.3Gbps.

© 2014 Optical Society of America

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2014 (2)

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

T. Baba, H. C. Nguiyen, N. Yazawa, Y. Terada, S. Hashimoto, and T. Watanabe, “Slow-light Mach-Zehnder modulators based on Si photonic crystals,” Sci. Technol. Adv. Mater. 15(2), 024602 (2014).
[Crossref]

2013 (3)

2012 (4)

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]

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

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

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 (8)

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1528–1533 (2011).
[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]

A. Rodan and P. Tino, “Minimum complexity echo state network,” IEEE Trans. Neural Netw. 22(1), 131–144 (2011).
[Crossref] [PubMed]

L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express 19(12), 11841–11851 (2011).
[Crossref] [PubMed]

F. Shinobu, N. Ishikura, Y. Arita, T. Tamanuki, and T. Baba, “Continuously tunable slow-light device consisting of heater-controlled silicon microring array,” Opt. Express 19(14), 13557–13564 (2011).
[Crossref] [PubMed]

F. Shinobu, N. Ishikura, Y. Arita, T. Tamanuki, and T. Baba, “Continuously tunable slow-light device consisting of heater-controlled silicon microring array,” Opt. Express 19(14), 13557–13564 (2011).
[Crossref] [PubMed]

M. P. Nezhad, O. Bondarenko, M. Khajavikhan, A. Simic, and Y. Fainman, “Etch-free low loss silicon waveguides using hydrogen silsesquioxane oxidation masks,” Opt. Express 19(20), 18827–18832 (2011).
[Crossref] [PubMed]

2010 (2)

F. Wyffels and B. Schrauwen, “A comparative study of reservoir computing strategies for monthly time series prediction,” Neurocomputing 73(10-12), 1958–1964 (2010).
[Crossref]

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1 V peak-to-peak driven 10-Gbps slow-light silicon Mach–Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[Crossref]

2009 (1)

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3(3), 127–149 (2009).
[Crossref]

2008 (2)

E. A. Antonelo, B. Schrauwen, and D. Stroobandt, “Event detection and localization for small mobile robots using reservoir computing,” Neural Netw. 21(6), 862–871 (2008).
[Crossref] [PubMed]

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

2007 (2)

H. P. Uranus and H. J. W. M. Hoekstra, “Modeling of loss-induced superluminal an negative group velocity in two-port ring-resonator circuits,” J. Lightwave Technol. 25(9), 2376–2384 (2007).
[Crossref]

M. D. Skowronski and J. G. Harris, “Automatic speech recognition using a predictive echo state network classifier,” Neural Netw. 20(3), 414–423 (2007).
[Crossref] [PubMed]

2006 (1)

S. J. Koester, J. D. Schaob, G. Dehlinger, and J. O. Chu, “Germanium-on-SOI infrared detectors for integrated photonic applications,” IEEE J. Sel. Top. Quantum Electron. 10, 1109 (2006).

2004 (3)

2003 (1)

L. J. Cao, “Support vector machines experts for time series forecasting,” Neurocomputing 51, 321–339 (2003).
[Crossref]

1989 (1)

U. Hübner, N. B. Abraham, and C. O. Weiss, “Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser,” Phys. Rev. A 40(11), 6354–6365 (1989).
[Crossref] [PubMed]

Abraham, N. B.

U. Hübner, N. B. Abraham, and C. O. Weiss, “Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser,” Phys. Rev. A 40(11), 6354–6365 (1989).
[Crossref] [PubMed]

Akiyama, S.

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1 V peak-to-peak driven 10-Gbps slow-light silicon Mach–Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[Crossref]

Alloatti, L.

Antonelo, E. A.

E. A. Antonelo, B. Schrauwen, and D. Stroobandt, “Event detection and localization for small mobile robots using reservoir computing,” Neural Netw. 21(6), 862–871 (2008).
[Crossref] [PubMed]

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

Arita, Y.

Baba, T.

T. Baba, H. C. Nguiyen, N. Yazawa, Y. Terada, S. Hashimoto, and T. Watanabe, “Slow-light Mach-Zehnder modulators based on Si photonic crystals,” Sci. Technol. Adv. Mater. 15(2), 024602 (2014).
[Crossref]

F. Shinobu, N. Ishikura, Y. Arita, T. Tamanuki, and T. Baba, “Continuously tunable slow-light device consisting of heater-controlled silicon microring array,” Opt. Express 19(14), 13557–13564 (2011).
[Crossref] [PubMed]

F. Shinobu, N. Ishikura, Y. Arita, T. Tamanuki, and T. Baba, “Continuously tunable slow-light device consisting of heater-controlled silicon microring array,” Opt. Express 19(14), 13557–13564 (2011).
[Crossref] [PubMed]

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1 V peak-to-peak driven 10-Gbps slow-light silicon Mach–Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[Crossref]

Baets, R.

Barklund, A.

Beausoleil, R. G.

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1528–1533 (2011).
[Crossref]

Bienstman, P.

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

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

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

Bogaerts, W.

Bondarenko, O.

Bowers, J. E.

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1528–1533 (2011).
[Crossref]

Boyraz, O.

Brunner, D.

Cao, L. J.

L. J. Cao, “Support vector machines experts for time series forecasting,” Neurocomputing 51, 321–339 (2003).
[Crossref]

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]

Chu, J. O.

S. J. Koester, J. D. Schaob, G. Dehlinger, and J. O. Chu, “Germanium-on-SOI infrared detectors for integrated photonic applications,” IEEE J. Sel. Top. Quantum Electron. 10, 1109 (2006).

Dambre, J.

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

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

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

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 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]

Dehlinger, G.

S. J. Koester, J. D. Schaob, G. Dehlinger, and J. O. Chu, “Germanium-on-SOI infrared detectors for integrated photonic applications,” IEEE J. Sel. Top. Quantum Electron. 10, 1109 (2006).

Dierckx, W.

Dinu, R.

Dumon, P.

Duport, F.

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

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

Fainman, Y.

Fedeli, J.

Fiers, M.

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

Fiorentino, M.

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1528–1533 (2011).
[Crossref]

Fischer, I.

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

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

Fournier, M.

Freude, W.

Friis, H.

H. Friis, “Noise figure of radio receivers,” Proc. IRE32, 419–422, (1944)

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.

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

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

Harris, J. G.

M. D. Skowronski and J. G. Harris, “Automatic speech recognition using a predictive echo state network classifier,” Neural Netw. 20(3), 414–423 (2007).
[Crossref] [PubMed]

Hashimoto, S.

T. Baba, H. C. Nguiyen, N. Yazawa, Y. Terada, S. Hashimoto, and T. Watanabe, “Slow-light Mach-Zehnder modulators based on Si photonic crystals,” Sci. Technol. Adv. Mater. 15(2), 024602 (2014).
[Crossref]

Hatori, N.

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1 V peak-to-peak driven 10-Gbps slow-light silicon Mach–Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[Crossref]

Hillerkuss, D.

Hoekstra, H. J. W. M.

Hübner, U.

U. Hübner, N. B. Abraham, and C. O. Weiss, “Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser,” Phys. Rev. A 40(11), 6354–6365 (1989).
[Crossref] [PubMed]

Indukuri, T.

Ishikura, N.

Jacquot, M.

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.

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3(3), 127–149 (2009).
[Crossref]

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

Jalali, B.

Khajavikhan, M.

Koester, S. J.

S. J. Koester, J. D. Schaob, G. Dehlinger, and J. O. Chu, “Germanium-on-SOI infrared detectors for integrated photonic applications,” IEEE J. Sel. Top. Quantum Electron. 10, 1109 (2006).

Koos, C.

Korn, D.

Kurahashi, T.

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1 V peak-to-peak driven 10-Gbps slow-light silicon Mach–Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[Crossref]

Larger, L.

Leuthold, J.

Li, J.

Liang, D.

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1528–1533 (2011).
[Crossref]

Lukoševicius, M.

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3(3), 127–149 (2009).
[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]

Massar, S.

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

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

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

Mechet, P.

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

Mesaritakis, C.

Mirasso, C. R.

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

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

Morthier, G.

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

Nezhad, M. P.

Nguiyen, H. C.

T. Baba, H. C. Nguiyen, N. Yazawa, Y. Terada, S. Hashimoto, and T. Watanabe, “Slow-light Mach-Zehnder modulators based on Si photonic crystals,” Sci. Technol. Adv. Mater. 15(2), 024602 (2014).
[Crossref]

Ortín, S.

Palmer, R.

Papataxiarhis, V.

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.

Poon, J. K. S.

Rodan, A.

A. Rodan and P. Tino, “Minimum complexity echo state network,” IEEE Trans. Neural Netw. 22(1), 131–144 (2011).
[Crossref] [PubMed]

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]

Schaob, J. D.

S. J. Koester, J. D. Schaob, G. Dehlinger, and J. O. Chu, “Germanium-on-SOI infrared detectors for integrated photonic applications,” IEEE J. Sel. Top. Quantum Electron. 10, 1109 (2006).

Scheuer, J.

Schneider, B.

Schrauwen, B.

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

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

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

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

F. Wyffels and B. Schrauwen, “A comparative study of reservoir computing strategies for monthly time series prediction,” Neurocomputing 73(10-12), 1958–1964 (2010).
[Crossref]

E. A. Antonelo, B. Schrauwen, and D. Stroobandt, “Event detection and localization for small mobile robots using reservoir computing,” Neural Netw. 21(6), 862–871 (2008).
[Crossref] [PubMed]

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

Shinobu, F.

Simic, A.

Skowronski, M. D.

M. D. Skowronski and J. G. Harris, “Automatic speech recognition using a predictive echo state network classifier,” Neural Netw. 20(3), 414–423 (2007).
[Crossref] [PubMed]

Smerieri, A.

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

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

Soriano, M. C.

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, 1364 (2013).
[Crossref] [PubMed]

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

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

Srinivasan, S.

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1528–1533 (2011).
[Crossref]

Stroobandt, D.

E. A. Antonelo, B. Schrauwen, and D. Stroobandt, “Event detection and localization for small mobile robots using reservoir computing,” Neural Netw. 21(6), 862–871 (2008).
[Crossref] [PubMed]

Syvridis, D.

Tamanuki, T.

Terada, Y.

T. Baba, H. C. Nguiyen, N. Yazawa, Y. Terada, S. Hashimoto, and T. Watanabe, “Slow-light Mach-Zehnder modulators based on Si photonic crystals,” Sci. Technol. Adv. Mater. 15(2), 024602 (2014).
[Crossref]

Tino, P.

A. Rodan and P. Tino, “Minimum complexity echo state network,” IEEE Trans. Neural Netw. 22(1), 131–144 (2011).
[Crossref] [PubMed]

Uranus, H. P.

Usuki, T.

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1 V peak-to-peak driven 10-Gbps slow-light silicon Mach–Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[Crossref]

Van Campenhout, J.

Van der Sande, G.

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

Van Vaerenbergh, T.

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

Vandoorne, K.

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

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

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

Verstraeten, D.

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

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

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

Watanabe, T.

T. Baba, H. C. Nguiyen, N. Yazawa, Y. Terada, S. Hashimoto, and T. Watanabe, “Slow-light Mach-Zehnder modulators based on Si photonic crystals,” Sci. Technol. Adv. Mater. 15(2), 024602 (2014).
[Crossref]

Weiss, C. O.

U. Hübner, N. B. Abraham, and C. O. Weiss, “Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser,” Phys. Rev. A 40(11), 6354–6365 (1989).
[Crossref] [PubMed]

Wieland, J.

Wyffels, F.

F. Wyffels and B. Schrauwen, “A comparative study of reservoir computing strategies for monthly time series prediction,” Neurocomputing 73(10-12), 1958–1964 (2010).
[Crossref]

Xu, Y.

Yamamoto, T.

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1 V peak-to-peak driven 10-Gbps slow-light silicon Mach–Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[Crossref]

Yariv, A.

Yazawa, N.

T. Baba, H. C. Nguiyen, N. Yazawa, Y. Terada, S. Hashimoto, and T. Watanabe, “Slow-light Mach-Zehnder modulators based on Si photonic crystals,” Sci. Technol. Adv. Mater. 15(2), 024602 (2014).
[Crossref]

Yu, H.

Appl. Phys. Express (1)

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1 V peak-to-peak driven 10-Gbps slow-light silicon Mach–Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[Crossref]

Comput. Sci. Rev. (1)

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3(3), 127–149 (2009).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

S. J. Koester, J. D. Schaob, G. Dehlinger, and J. O. Chu, “Germanium-on-SOI infrared detectors for integrated photonic applications,” IEEE J. Sel. Top. Quantum Electron. 10, 1109 (2006).

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1528–1533 (2011).
[Crossref]

IEEE Trans. Neural Netw. (2)

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, and P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22(9), 1469–1481 (2011).
[Crossref] [PubMed]

A. Rodan and P. Tino, “Minimum complexity echo state network,” IEEE Trans. Neural Netw. 22(1), 131–144 (2011).
[Crossref] [PubMed]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Nat Commun (3)

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

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

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

Neural Netw. (2)

M. D. Skowronski and J. G. Harris, “Automatic speech recognition using a predictive echo state network classifier,” Neural Netw. 20(3), 414–423 (2007).
[Crossref] [PubMed]

E. A. Antonelo, B. Schrauwen, and D. Stroobandt, “Event detection and localization for small mobile robots using reservoir computing,” Neural Netw. 21(6), 862–871 (2008).
[Crossref] [PubMed]

Neurocomputing (2)

F. Wyffels and B. Schrauwen, “A comparative study of reservoir computing strategies for monthly time series prediction,” Neurocomputing 73(10-12), 1958–1964 (2010).
[Crossref]

L. J. Cao, “Support vector machines experts for time series forecasting,” Neurocomputing 51, 321–339 (2003).
[Crossref]

Opt. Express (9)

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]

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

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

O. Boyraz, T. Indukuri, and B. Jalali, “Self-phase-modulation induced spectral broadening in silicon waveguides,” Opt. Express 12(5), 829–834 (2004).
[Crossref] [PubMed]

F. Shinobu, N. Ishikura, Y. Arita, T. Tamanuki, and T. Baba, “Continuously tunable slow-light device consisting of heater-controlled silicon microring array,” Opt. Express 19(14), 13557–13564 (2011).
[Crossref] [PubMed]

L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express 19(12), 11841–11851 (2011).
[Crossref] [PubMed]

M. P. Nezhad, O. Bondarenko, M. Khajavikhan, A. Simic, and Y. Fainman, “Etch-free low loss silicon waveguides using hydrogen silsesquioxane oxidation masks,” Opt. Express 19(20), 18827–18832 (2011).
[Crossref] [PubMed]

F. Shinobu, N. Ishikura, Y. Arita, T. Tamanuki, and T. Baba, “Continuously tunable slow-light device consisting of heater-controlled silicon microring array,” Opt. Express 19(14), 13557–13564 (2011).
[Crossref] [PubMed]

Phys. Rev. A (1)

U. Hübner, N. B. Abraham, and C. O. Weiss, “Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser,” Phys. Rev. A 40(11), 6354–6365 (1989).
[Crossref] [PubMed]

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, 287 (2012).
[Crossref] [PubMed]

Sci. Technol. Adv. Mater. (1)

T. Baba, H. C. Nguiyen, N. Yazawa, Y. Terada, S. Hashimoto, and T. Watanabe, “Slow-light Mach-Zehnder modulators based on Si photonic crystals,” Sci. Technol. Adv. Mater. 15(2), 024602 (2014).
[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] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic of the proposed optical reservoir computing system. PM is a phase modulator to load the signal on optical pulse. MR1~5 is the cascaded micro-ring cavities. (b) Schematic of the masking process. u(t) is the input time dependent signal and w(i) is the random input mask. (c) Schematic of the processing of the MRA (dark green) and the secondary time-multiplexing (light green). m(t) is the time-domain transfer coefficient defined in Fig. 2. Superposition between the adjacent pulses is done within the MRA. Secondary time-multiplexing is made within each pulse interval at different output ports.

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Fig. 2
Fig. 2 Wave shape on time-domain of the input pulse and the output after MRA. m(t) is the defined transfer coefficient.

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Fig. 3
Fig. 3 Sketch of micro-ring cavity model; subset: sketch of the interface of the shallow-ridge waveguide.

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Fig. 4
Fig. 4 Illustration of the secondary time-multiplexing. (a) Output intensity of the MRA after a single pulse input. (b) and (c) Output intensity of two different ports A and B. The output shape of each port is similar to (a) with deviations of a time delay of 11ps (port A) or 21ps (port B) and split intensity. Each port includes three channels (A1~A3 for port A and B1~B3 for port B). The value of each channels is represented by the notch.

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Fig. 5
Fig. 5 Illustration and performance of signal classification task. (a) A set of input data, which is a random concatenation of square and sine waves. (b) The target output, one for square waves and zero for sine wave. (c) The output of the proposed optical RC system. (d) Relation between the error rate and SNR with constant node number of 480. (e) Relation between error rate and node number N with constant SNR of 20dB.

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Fig. 6
Fig. 6 Illustration and performance of chaotic prediction task. (a) A sample of target chaotic time-series data. (b) The prediction output of the proposed optical RC system. (c) Relation between error rate and SNR at constant node number of 120. (d) Relation between error rate and N at constant SNR of 20dB.

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Tables (3)

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Table 1 Simulation parameters

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Table 2 Parameters of Devices for Practical Implement

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Table 3 Comparison of different RC implements

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Equations (24)

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x out RA (t)= Σ i=0 q m t 0 +iθ ⋅exp[j⋅( ϕ i + x t−iθ )]
X RA out (t)= | x out RA (t) | 2 = [ Σ i=0 q m t 0 +iθ ⋅cos( x t-iθ − x t +Δ ϕ i ) ] 2 + [ Σ i=0 q m t 0 +iθ ⋅sin( x t-iθ − x t +Δ ϕ i ) ] 2
X j out (t)= | x out j (t) | 2 = [ Σ i=0 q m t j +iθ ⋅cos( x t-iθ − x t +Δ ϕ i,j ) ] 2 + [ Σ i=0 q m t j +iθ ⋅sin( x t-iθ − x t +Δ ϕ i,j ) ] 2 (j=1,2,3...)
MSE= 1 L ∑ n=1 L (y(n)− y ^ (n)) 2
NMSE= 1 L ∑ n=1 L (y(n)− y ^ (n)) 2 /var(y)
E 4 =τ E 3 ⋅exp(iϕ)
E 3 =r⋅ E 4 +it⋅ E 1
E 2 =r⋅ E 1 +it⋅ E 4
E 2 E 1 =−exp(iϕ) τ−r⋅exp(−iϕ) 1−rτ⋅exp(iϕ)
Tr= | E 2 E 1 | 2 = τ 2 −2rτcos(ϕ)+ r 2 1−2rτcos(ϕ)+ r 2 τ 2
τ=dγ
ϕ= d n eff λ
1/Q=1/ Q e +1/ Q 0
Q 0 = ω n eff γc
Q e = ω n eff d |r | 2 c
γ TPA = β A eff P
P c = P in |F | 2
|F | 2 = c L n eff ω ⋅ 4/ Q e (1/ Q e +1/ Q 0 ) 2
N s =2( I d + I c )⋅ΔB⋅e⋅r
N t =4 k B T⋅ΔB
NF=N F 1 + N F 2 −1 G 1
NF= S in / N in S out / N out = S in /( k B T⋅ΔB) G⋅ S in /(G⋅ k B T⋅ΔB+ N a ) =1+ N a G⋅ k B T⋅ΔB
N a =( NF−1 )⋅G⋅ k B T⋅ΔB
SN R output = S out N out = G S in G N in + N a =167=22dB

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