Abstract

In this paper, an alternative approach for an integrated photonic reservoir computer is presented. The fundamental building block of the reservoir is based on the nonlinear response of a ring resonator, where effects such as two-photon absorption and nonlinear refractive index variation were taken into consideration. In order to investigate the validity of this scheme, the response of a single add/drop micro ring was simulated through a traveling wave numerical model, and the parameters that affect the nonlinearity of the response were identified. Based on these results, a 5×5 matrix of randomly interconnected resonators was utilized in order to classify different high-bit-rate digital patterns. Simulations confirmed that the proposed system could offer a classification error of 0.5% for bit rates up to 160 Gbps and for 8-bit-length digital words.

© 2013 Optical Society of America

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  31. J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, “Silicon microtoroidal resonators with integrated MEMS tunable coupler,” IEEE J. Sel. Top. Quantum Electron. 13, 202–208 (2007).

2013 (1)

2012 (4)

2011 (3)

2008 (3)

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

B. Schrauwen, M. D’Haene, D. Verstraeten, and J. V. Campenhout, “Compact hardware liquid state machines on FPGA for real-time speech recognition,” Neural Netw. 21, 511–523 (2008).
[CrossRef]

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

2007 (2)

H. Simos, C. Mesaritakis, D. Alexandropoulos, and D. Syvridis, “Intraband cross talk properties of add–drop filters based on active microring resonators,” IEEE Photon. Technol. Lett. 19, 1649–1651 (2007).
[CrossRef]

J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, “Silicon microtoroidal resonators with integrated MEMS tunable coupler,” IEEE J. Sel. Top. Quantum Electron. 13, 202–208 (2007).

2006 (1)

C. W. Tee, K. A. Williams, R. V. Penty, and I. H. White, “Fabrication-tolerant active-passive integration scheme for vertically coupled microring resonator,” IEEE J. Sel. Top. Quantum Electron. 12, 108–116 (2006).

2005 (1)

S. Mikroulis, H. Simos, E. Roditi, and D. Syvridis, “Ultrafast all-optical AND logic operation based on FWM in a passive InGaAsP-InP microring resonator,” IEEE Photon. Technol. Lett. 17, 1878–1880 (2005).

2004 (2)

J. Niehusmann, A. Vörckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, “Ultrahigh-quality-factor silicon-on-insulator microring resonator,” Opt. Lett. 29, 2861–2863 (2004).
[CrossRef]

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

2002 (3)

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

M. Hill, E. Edward, E. Frietman, H. de Waardt, H. J. S. Dorren, and G. Khoe, “All fiber-optic neural network using coupled SOA based ring lasers,” IEEE Trans. Neural Netw. 13, 1504–1513 (2002).

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
[CrossRef]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

1996 (1)

J. Kilian and H. Siegelmann, “The dynamic universality of sigmoidal neural networks,” Inform. Comput. 128, 48–56 (1996).

1995 (2)

B. A. Pearlmutter, “Gradient calculations for dynamic recurrent neural networks: a survey,” IEEE Trans. Neural Netw. 6, 1212–1228 (1995).

B. Javidi, J. Li, and Q. Tang, “Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlators,” Appl. Opt. 34, 3950–3962 (1995).
[CrossRef]

1989 (1)

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feed-forward networks are universal approximators,” Neural Netw. 2, 359–366 (1989).
[CrossRef]

1988 (1)

Adams, M. J.

A. Hurtado, K. Schires, I. D. Henning, and M. J. Adams, “Investigation of vertical cavity surface emitting laser dynamics for neuromorphic photonic systems,” AIP Appl. Phys. Lett. 100, 103703 (2012).

Alexandropoulos, D.

H. Simos, C. Mesaritakis, D. Alexandropoulos, and D. Syvridis, “Intraband cross talk properties of add–drop filters based on active microring resonators,” IEEE Photon. Technol. Lett. 19, 1649–1651 (2007).
[CrossRef]

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, 862–871 (2008).
[CrossRef]

Appeltant, L.

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

L. Appeltant, M. C. Soriano, G. V. 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]

Baets, R.

Bienstman, P.

Bolivar, P. H.

Brady, D.

Brunner, D.

Buteneers, P.

P. Buteneers, B. Schrauwen, D. Verstraeten, and D. Stroobandt, “Real-time epileptic seizure detection on intra-cranial rat data using reservoir computing,” Advances in Neuro-Information Processing (Springer, 2013), Vol. 5506, pp. 56–63.

Caluwaerts, K.

Cameron, C. J. F.

S. A. Marhon, C. J. F. Cameron, and S. C. Kremer, “Recurrent neural networks” in Handbook on Neural Information Processing (Springer, 2013), Vol. 49, pp. 29–65.

Campenhout, J. V.

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

B. Schrauwen, M. D’Haene, D. Verstraeten, and J. V. Campenhout, “Compact hardware liquid state machines on FPGA for real-time speech recognition,” Neural Netw. 21, 511–523 (2008).
[CrossRef]

B. Schrauwen, J. Defour, D. Verstraeten, and J. V. Campenhout, “The introduction of time-scales in reservoir computing, applied to isolated digits recognition,” Artificial Neural Networks—ICANN (Springer, 2007), Vol. 4668, pp. 471–479.

Chu, S. T.

A. Pasquazi, M. Peccianti, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Stable, dual mode, high repetition rate mode-locked laser based on a microring resonator,” Opt. Express 20, 27355–27363 (2012).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Citrin, D. S.

D’Haene, M.

B. Schrauwen, M. D’Haene, D. Verstraeten, and J. V. Campenhout, “Compact hardware liquid state machines on FPGA for real-time speech recognition,” Neural Netw. 21, 511–523 (2008).
[CrossRef]

Dambre, J.

M. Fiers, T. V. Vaerenbergh, K. Caluwaerts, D. V. Ginste, B. Schrauwen, J. Dambre, and P. Bienstman, “Time-domain and frequency-domain modeling of nonlinear optical components at the circuit-level using a node-based approach,” J. Opt. Soc. Am. B 29, 896–900 (2012).
[CrossRef]

L. Appeltant, M. C. Soriano, G. V. 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]

T. V. Vaerenbergh, M. Fiers, K. Vandoorne, B. Schneider, J. Dambre, and P. Bienstman, “Towards a photonic spiking neuron: excitability in a silicon-on-insulator microring,” International Symposium on Nonlinear Theory and its Applications, Palma, Mallorca, 2012, pp. 767–770.

Danckaert, J.

L. Appeltant, M. C. Soriano, G. V. 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]

de Waardt, H.

M. Hill, E. Edward, E. Frietman, H. de Waardt, H. J. S. Dorren, and G. Khoe, “All fiber-optic neural network using coupled SOA based ring lasers,” IEEE Trans. Neural Netw. 13, 1504–1513 (2002).

Defour, J.

B. Schrauwen, J. Defour, D. Verstraeten, and J. V. Campenhout, “The introduction of time-scales in reservoir computing, applied to isolated digits recognition,” Artificial Neural Networks—ICANN (Springer, 2007), Vol. 4668, pp. 471–479.

der Sande, G. V.

L. Appeltant, M. C. Soriano, G. V. 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]

Dierckx, W.

Dorren, H. J. S.

M. Hill, E. Edward, E. Frietman, H. de Waardt, H. J. S. Dorren, and G. Khoe, “All fiber-optic neural network using coupled SOA based ring lasers,” IEEE Trans. Neural Netw. 13, 1504–1513 (2002).

Edward, E.

M. Hill, E. Edward, E. Frietman, H. de Waardt, H. J. S. Dorren, and G. Khoe, “All fiber-optic neural network using coupled SOA based ring lasers,” IEEE Trans. Neural Netw. 13, 1504–1513 (2002).

Fiers, M.

M. Fiers, T. V. Vaerenbergh, K. Caluwaerts, D. V. Ginste, B. Schrauwen, J. Dambre, and P. Bienstman, “Time-domain and frequency-domain modeling of nonlinear optical components at the circuit-level using a node-based approach,” J. Opt. Soc. Am. B 29, 896–900 (2012).
[CrossRef]

T. V. Vaerenbergh, M. Fiers, K. Vandoorne, B. Schneider, J. Dambre, and P. Bienstman, “Towards a photonic spiking neuron: excitability in a silicon-on-insulator microring,” International Symposium on Nonlinear Theory and its Applications, Palma, Mallorca, 2012, pp. 767–770.

Fischer, I.

Fok, M. P.

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Frietman, E.

M. Hill, E. Edward, E. Frietman, H. de Waardt, H. J. S. Dorren, and G. Khoe, “All fiber-optic neural network using coupled SOA based ring lasers,” IEEE Trans. Neural Netw. 13, 1504–1513 (2002).

Ginste, D. V.

Gutierrez, J. M.

Haas, H.

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

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Henning, I. D.

A. Hurtado, K. Schires, I. D. Henning, and M. J. Adams, “Investigation of vertical cavity surface emitting laser dynamics for neuromorphic photonic systems,” AIP Appl. Phys. Lett. 100, 103703 (2012).

Henschel, W.

Hill, M.

M. Hill, E. Edward, E. Frietman, H. de Waardt, H. J. S. Dorren, and G. Khoe, “All fiber-optic neural network using coupled SOA based ring lasers,” IEEE Trans. Neural Netw. 13, 1504–1513 (2002).

Hornik, K.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feed-forward networks are universal approximators,” Neural Netw. 2, 359–366 (1989).
[CrossRef]

Hurtado, A.

A. Hurtado, K. Schires, I. D. Henning, and M. J. Adams, “Investigation of vertical cavity surface emitting laser dynamics for neuromorphic photonic systems,” AIP Appl. Phys. Lett. 100, 103703 (2012).

Jaeger, H.

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

Javidi, B.

Joshi, P.

P. Joshi and W. Maass, “Movement generation and control with generic neural microcircuits,” in Proceedings of BIO-AUDIT (Springer, 2004), pp. 16–31.

Khoe, G.

M. Hill, E. Edward, E. Frietman, H. de Waardt, H. J. S. Dorren, and G. Khoe, “All fiber-optic neural network using coupled SOA based ring lasers,” IEEE Trans. Neural Netw. 13, 1504–1513 (2002).

Kilian, J.

J. Kilian and H. Siegelmann, “The dynamic universality of sigmoidal neural networks,” Inform. Comput. 128, 48–56 (1996).

Kravtsov, K.

Kremer, S. C.

S. A. Marhon, C. J. F. Cameron, and S. C. Kremer, “Recurrent neural networks” in Handbook on Neural Information Processing (Springer, 2013), Vol. 49, pp. 29–65.

Kurz, H.

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Larger, L.

Lee, M.-C. M.

J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, “Silicon microtoroidal resonators with integrated MEMS tunable coupler,” IEEE J. Sel. Top. Quantum Electron. 13, 202–208 (2007).

Leuenberger, D.

J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, “Silicon microtoroidal resonators with integrated MEMS tunable coupler,” IEEE J. Sel. Top. Quantum Electron. 13, 202–208 (2007).

Li, J.

Little, B. E.

A. Pasquazi, M. Peccianti, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Stable, dual mode, high repetition rate mode-locked laser based on a microring resonator,” Opt. Express 20, 27355–27363 (2012).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Maass, W.

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

P. Joshi and W. Maass, “Movement generation and control with generic neural microcircuits,” in Proceedings of BIO-AUDIT (Springer, 2004), pp. 16–31.

Marhon, S. A.

S. A. Marhon, C. J. F. Cameron, and S. C. Kremer, “Recurrent neural networks” in Handbook on Neural Information Processing (Springer, 2013), Vol. 49, pp. 29–65.

Markram, H.

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

Massar, S.

L. Appeltant, M. C. Soriano, G. V. 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]

Mesaritakis, C.

H. Simos, C. Mesaritakis, D. Alexandropoulos, and D. Syvridis, “Intraband cross talk properties of add–drop filters based on active microring resonators,” IEEE Photon. Technol. Lett. 19, 1649–1651 (2007).
[CrossRef]

Mikroulis, S.

S. Mikroulis, H. Simos, E. Roditi, and D. Syvridis, “Ultrafast all-optical AND logic operation based on FWM in a passive InGaAsP-InP microring resonator,” IEEE Photon. Technol. Lett. 17, 1878–1880 (2005).

Mirasso, C. R.

Morandotti, R.

Moss, D. J.

Natschlager, T.

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

Niehusmann, J.

Ortín, S.

Pasquazi, A.

Pearlmutter, B. A.

B. A. Pearlmutter, “Gradient calculations for dynamic recurrent neural networks: a survey,” IEEE Trans. Neural Netw. 6, 1212–1228 (1995).

Peccianti, M.

Penty, R. V.

C. W. Tee, K. A. Williams, R. V. Penty, and I. H. White, “Fabrication-tolerant active-passive integration scheme for vertically coupled microring resonator,” IEEE J. Sel. Top. Quantum Electron. 12, 108–116 (2006).

Pesquera, L.

Prucnal, P. R.

Psaltis, D.

Roditi, E.

S. Mikroulis, H. Simos, E. Roditi, and D. Syvridis, “Ultrafast all-optical AND logic operation based on FWM in a passive InGaAsP-InP microring resonator,” IEEE Photon. Technol. Lett. 17, 1878–1880 (2005).

Rosenbluth, D.

Schires, K.

A. Hurtado, K. Schires, I. D. Henning, and M. J. Adams, “Investigation of vertical cavity surface emitting laser dynamics for neuromorphic photonic systems,” AIP Appl. Phys. Lett. 100, 103703 (2012).

Schneider, B.

T. V. Vaerenbergh, M. Fiers, K. Vandoorne, B. Schneider, J. Dambre, and P. Bienstman, “Towards a photonic spiking neuron: excitability in a silicon-on-insulator microring,” International Symposium on Nonlinear Theory and its Applications, Palma, Mallorca, 2012, pp. 767–770.

Schrauwen, B.

M. Fiers, T. V. Vaerenbergh, K. Caluwaerts, D. V. Ginste, B. Schrauwen, J. Dambre, and P. Bienstman, “Time-domain and frequency-domain modeling of nonlinear optical components at the circuit-level using a node-based approach,” J. Opt. Soc. Am. B 29, 896–900 (2012).
[CrossRef]

L. Appeltant, M. C. Soriano, G. V. 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]

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

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Figures (7)

Fig. 1.
Fig. 1.

(a) Basic schematic of a photonic reservoir computing system followed by a simple perceptron. u(t) corresponds to the time-dependent input and xi(t) to the reservoir outputs, whereas Wi are the trainable weights, finally P14 are the final classification results. (b) Basic schematic of an add/drop MRR, where Ainput corresponds to the system input, and Athrough and Adrop are the two outputs. In our case, no add signal is utilized. (c) Rain-fall topology of the MRR-based reservoir with various feedback loops. First MRR in the matrix is the input, while the last column provides five outputs.

Fig. 2.
Fig. 2.

(a) Through-port transfer function of a single MRR with various input power ranging from 1 μW to 100 mW. (b) Drop-port transfer function for the same input power range.

Fig. 3.
Fig. 3.

Drop output power versus input for various cases. (a) Power response of both ports for the structural parameters used in Fig. 2. (b) Radius investigation for losses=200cm1 k=0.1. (c) Losses investigation for R=45μm, k=0.1. (d) Coupling investigation for R=10μm and α=10cm1.

Fig. 4.
Fig. 4.

(a)–(d) Time series produced from four different reservoir outputs for four discrete digital words (000, 101, 110, 111).

Fig. 5.
Fig. 5.

Optical input for four digital words with P1=10mW. (a) 10 dB extinction ratio noiseless case (0 dB gain). (b) 10 dB extinction ratio 20 dB EDFA gain. (c) 5 dB extinction ratio 20 dB EDFA gain. (d) Total classification error versus the extinction ratio for two cases (black square) correspond to input power of 10 mW (red circles) 100 mW.

Fig. 6.
Fig. 6.

Total classification error for the aforementioned MRR reservoir versus input power and for a constant extinction ratio of 3 dB (black squares) and 10 dB (red circles).

Fig. 7.
Fig. 7.

(a) Time trace of the input bit stream, four different words are used α: “11111010”; β: “10011010”; γ: “10011111”; and δ:“00000000” with an EDFA level of 5 dB. (b) Perceptron output classifiers- Cα, Cβ, Cγ, and Cδ, correspond to the α, β, γ, δ bit patterns, respectively. (c) Same as (a) with 20 dB gain form the EDFA. (d) Corresponding classifiers with errors (in circle).

Tables (1)

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Table 1. MRR Simulation Parameters

Equations (6)

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ϑAϑz=[α2]·A+[β2·Aeff+j·γ]×A+[Nf·σα2+jω·σα·Nfc]·A,
Nft=β2ω·Aeff2·P2Nfτph,
A(0,t)=jkAin(t)+τ·A(2πR,t)·ej2πkR,
A(πR,t)=jk·Aadd(t)+τ·A(πR,t)ejπnkR,
Athr(t)=τ·Ain(t)jk·A(2πR,t)·ej2πnkR,
Adrp(t)=jk·A(πR,t)·ejπnkR.

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