Abstract

In this paper, we demonstrate for the first time an ultrafast fully functional photonic spiking neuron. Our experimental setup constitutes a complete all-optical implementation of a leaky integrate-and-fire neuron, a computational primitive that provides a basis for general purpose analog optical computation. Unlike purely analog computational models, spiking operation eliminates noise accumulation and results in robust and efficient processing. Operating at gigahertz speed, which corresponds to at least 108 speed-up compared with biological neurons, the demonstrated neuron provides all functionality required by the spiking neuron model. The two demonstrated prototypes and a demonstrated feedback operation mode prove the feasibility and stability of our approach and show the obtained performance characteristics.

© 2011 Optical Society of America

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References

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    [PubMed]
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  3. S. Tariq, M. K. Habib, and H. A. Helmy, “Opto-electronic neuron-type operation via stimulated Raman scattering in optical fiber,” J. Lightwave Technol. 15, 938–947 (1997).
  4. E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).
  5. G. Moagar-Poladian, “Reconfigurable optical neuron based on photoelectret materials,” Appl. Opt. 39, 782–787 (2000).
  6. M. T. Hill, E. E. E. Frietman, H. de Waardt, G.-d. Khoe, and H. J. S. Dorren, “All fiber-optic neural network using coupled SOA based ring lasers,” IEEE Trans. Neural Netw. 13, 1504–1513 (2002).
  7. G. Moagar-Poladian and M. Bulinski, “Optical reconfigurable neuron by using the transverse Pockels effect,” J. Optoelectron. Adv. Mater. 4, 929–936 (2002).
  8. R. J. Vogelstein, U. Mallik, J. T. Vogelstein, and G. Cauwenberghs, “Dynamically reconfigurable silicon array of spiking neurons with conductance-based synapses,” IEEE Trans. Neural Netw. 18, 253–265 (2007).
    [PubMed]
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    [PubMed]
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  22. T. Aida and P. Davis, “Storage of optical pulse data sequences in loop memory using multistable oscillations,” Electron. Lett 27, 1544–1546 (1991).
  23. M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).
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  25. J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

2010 (1)

S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Excitability in optical systems close to Z2-symmetry,” Phys. Lett. A 374, 739–743 (2010).

2009 (1)

2008 (1)

2007 (5)

2006 (1)

G. Indiveri, E. Chicca, and R. Douglas, “A VLSI array of low-power spiking neurons and bistable synapses with spike-timing dependent plasticity,” IEEE Trans. Neural Netw. 17, 211–221 (2006).
[PubMed]

2005 (1)

2002 (2)

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

G. Moagar-Poladian and M. Bulinski, “Optical reconfigurable neuron by using the transverse Pockels effect,” J. Optoelectron. Adv. Mater. 4, 929–936 (2002).

2000 (2)

G. Moagar-Poladian, “Reconfigurable optical neuron based on photoelectret materials,” Appl. Opt. 39, 782–787 (2000).

E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).

1998 (1)

R. Sarpeshkar, “Analog versus digital: Extrapolating from electronics to neurobiology,” Neural Comput. 10, 1601–1638 (1998).
[PubMed]

1997 (1)

S. Tariq, M. K. Habib, and H. A. Helmy, “Opto-electronic neuron-type operation via stimulated Raman scattering in optical fiber,” J. Lightwave Technol. 15, 938–947 (1997).

1995 (1)

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

1994 (2)

C. R. Doerr, W. S. Wong, H. A. Haus, and E. P. Ippen, “Additive-pulse mode-locking/limiting storage ring,” Opt. Lett. 19, 1747–1749 (1994).
[PubMed]

A. V. Grigor’yants and I. N. Dyuzhikov, “Formation of a neuron-like pulsed response in a semiconductor resonator cavity with competing optical nonlinearities,” Kvant. Elektron. 21, 511–512 (1994). [Sov. J. Quantum Electron. 24, 469–470 (1994)].

1993 (2)

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).

1991 (1)

T. Aida and P. Davis, “Storage of optical pulse data sequences in loop memory using multistable oscillations,” Electron. Lett 27, 1544–1546 (1991).

1990 (1)

Agrawal, G. P.

Aida, T.

T. Aida and P. Davis, “Storage of optical pulse data sequences in loop memory using multistable oscillations,” Electron. Lett 27, 1544–1546 (1991).

Beri, S.

S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Excitability in optical systems close to Z2-symmetry,” Phys. Lett. A 374, 739–743 (2010).

Blum, M. W.

E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).

Bubnov, M. M.

Bulinski, M.

G. Moagar-Poladian and M. Bulinski, “Optical reconfigurable neuron by using the transverse Pockels effect,” J. Optoelectron. Adv. Mater. 4, 929–936 (2002).

Cauwenberghs, G.

R. J. Vogelstein, U. Mallik, J. T. Vogelstein, and G. Cauwenberghs, “Dynamically reconfigurable silicon array of spiking neurons with conductance-based synapses,” IEEE Trans. Neural Netw. 18, 253–265 (2007).
[PubMed]

Chicca, E.

G. Indiveri, E. Chicca, and R. Douglas, “A VLSI array of low-power spiking neurons and bistable synapses with spike-timing dependent plasticity,” IEEE Trans. Neural Netw. 17, 211–221 (2006).
[PubMed]

Danckaert, J.

S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Excitability in optical systems close to Z2-symmetry,” Phys. Lett. A 374, 739–743 (2010).

Davis, P.

T. Aida and P. Davis, “Storage of optical pulse data sequences in loop memory using multistable oscillations,” Electron. Lett 27, 1544–1546 (1991).

de Waardt, H.

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

E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).

Dianov, E. M.

Doerr, C. R.

Dorren, H. J. S.

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

Douglas, R.

G. Indiveri, E. Chicca, and R. Douglas, “A VLSI array of low-power spiking neurons and bistable synapses with spike-timing dependent plasticity,” IEEE Trans. Neural Netw. 17, 211–221 (2006).
[PubMed]

Dyuzhikov, I. N.

A. V. Grigor’yants and I. N. Dyuzhikov, “Formation of a neuron-like pulsed response in a semiconductor resonator cavity with competing optical nonlinearities,” Kvant. Elektron. 21, 511–512 (1994). [Sov. J. Quantum Electron. 24, 469–470 (1994)].

Farhat, N. H.

Fok, M. P.

Frietman, E. E. E.

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

Gelens, L.

S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Excitability in optical systems close to Z2-symmetry,” Phys. Lett. A 374, 739–743 (2010).

Glesk, I.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).

Grigor’yants, A. V.

A. V. Grigor’yants and I. N. Dyuzhikov, “Formation of a neuron-like pulsed response in a semiconductor resonator cavity with competing optical nonlinearities,” Kvant. Elektron. 21, 511–512 (1994). [Sov. J. Quantum Electron. 24, 469–470 (1994)].

Habib, M. K.

S. Tariq, M. K. Habib, and H. A. Helmy, “Opto-electronic neuron-type operation via stimulated Raman scattering in optical fiber,” J. Lightwave Technol. 15, 938–947 (1997).

Hall, K. L.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

Haus, H. A.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

C. R. Doerr, W. S. Wong, H. A. Haus, and E. P. Ippen, “Additive-pulse mode-locking/limiting storage ring,” Opt. Lett. 19, 1747–1749 (1994).
[PubMed]

Helmy, H. A.

S. Tariq, M. K. Habib, and H. A. Helmy, “Opto-electronic neuron-type operation via stimulated Raman scattering in optical fiber,” J. Lightwave Technol. 15, 938–947 (1997).

Hill, M. T.

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

E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).

Hoppenbrouwers, J. J. L.

E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).

Indiveri, G.

G. Indiveri, E. Chicca, and R. Douglas, “A VLSI array of low-power spiking neurons and bistable synapses with spike-timing dependent plasticity,” IEEE Trans. Neural Netw. 17, 211–221 (2006).
[PubMed]

Ippen, E. P.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

C. R. Doerr, W. S. Wong, H. A. Haus, and E. P. Ippen, “Additive-pulse mode-locking/limiting storage ring,” Opt. Lett. 19, 1747–1749 (1994).
[PubMed]

Jenkins, B. K.

Kane, M.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).

Khoe, G.-d.

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

Kimura, Y.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).

Koch, C.

C. Koch, Biophysics of Computation (Oxford University Press, 1999).

Kravtsov, K.

Kubota, H.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).

LePage, S. M.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

Mallik, U.

R. J. Vogelstein, U. Mallik, J. T. Vogelstein, and G. Cauwenberghs, “Dynamically reconfigurable silicon array of spiking neurons with conductance-based synapses,” IEEE Trans. Neural Netw. 18, 253–265 (2007).
[PubMed]

Mashall, L.

S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Excitability in optical systems close to Z2-symmetry,” Phys. Lett. A 374, 739–743 (2010).

Mashinsky, V. M.

Mezosi, G.

S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Excitability in optical systems close to Z2-symmetry,” Phys. Lett. A 374, 739–743 (2010).

Moagar-Poladian, G.

G. Moagar-Poladian and M. Bulinski, “Optical reconfigurable neuron by using the transverse Pockels effect,” J. Optoelectron. Adv. Mater. 4, 929–936 (2002).

G. Moagar-Poladian, “Reconfigurable optical neuron based on photoelectret materials,” Appl. Opt. 39, 782–787 (2000).

Moores, J. D.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

Mos, E. C.

E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).

Nakazawa, M.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).

Nešic, D.

Pashaie, R.

Premaratne, M.

Prucnal, P. R.

Rauschenbach, K. A.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

Romariz, A. R. S.

Rosenbluth, D.

Sarpeshkar, R.

R. Sarpeshkar, “Analog versus digital: Extrapolating from electronics to neurobiology,” Neural Comput. 10, 1601–1638 (1998).
[PubMed]

Schleipen, J. J. H. B.

E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).

Sokoloff, J. P.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).

Sorel, M.

S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Excitability in optical systems close to Z2-symmetry,” Phys. Lett. A 374, 739–743 (2010).

Suzuki, K.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).

Takaya, M.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).

Tariq, S.

S. Tariq, M. K. Habib, and H. A. Helmy, “Opto-electronic neuron-type operation via stimulated Raman scattering in optical fiber,” J. Lightwave Technol. 15, 938–947 (1997).

Van der Sande, G.

S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Excitability in optical systems close to Z2-symmetry,” Phys. Lett. A 374, 739–743 (2010).

Verschaffelt, G.

S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Excitability in optical systems close to Z2-symmetry,” Phys. Lett. A 374, 739–743 (2010).

Vogelstein, J. T.

R. J. Vogelstein, U. Mallik, J. T. Vogelstein, and G. Cauwenberghs, “Dynamically reconfigurable silicon array of spiking neurons with conductance-based synapses,” IEEE Trans. Neural Netw. 18, 253–265 (2007).
[PubMed]

Vogelstein, R. J.

R. J. Vogelstein, U. Mallik, J. T. Vogelstein, and G. Cauwenberghs, “Dynamically reconfigurable silicon array of spiking neurons with conductance-based synapses,” IEEE Trans. Neural Netw. 18, 253–265 (2007).
[PubMed]

Wagner, K. H.

Wang, C.-H.

Wong, W. S.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

C. R. Doerr, W. S. Wong, H. A. Haus, and E. P. Ippen, “Additive-pulse mode-locking/limiting storage ring,” Opt. Lett. 19, 1747–1749 (1994).
[PubMed]

Yamada, E.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).

Appl. Opt. (5)

Electron. Lett (2)

T. Aida and P. Davis, “Storage of optical pulse data sequences in loop memory using multistable oscillations,” Electron. Lett 27, 1544–1546 (1991).

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).

IEEE Photon. Technol. Lett. (2)

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).

IEEE Trans. Neural Netw. (4)

E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).

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Figures (10)

Fig. 1
Fig. 1 Schematic drawing of a biological neuron.

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Fig. 2
Fig. 2 Block diagram of the photonic neuron. G — variable attenuator, T — variable delay line, SOA — semiconductor optical amplifier, HD fiber — heavily GeO2-doped fiber, TOAD — terahertz optical asymmetric demultiplexer.

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Fig. 3
Fig. 3 Experimental setup. G — variable attenuator, T — variable delay line, PC — polarization controller, TI — tunable isolator [18], EDFA — erbium-doped fiber amplifier, C — circulator, HD NL fiber — heavily GeO2-doped nonlinear fiber.

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Fig. 4
Fig. 4 Signal propagating through the neuron. (A) — input signal, (B) — signal after the integrator, (C) — result of the first thresholding, (D) — inverted sequence, (E) — neuron output.

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Fig. 5
Fig. 5 Neuron excitation with multiple pulses per integration time. All the graphs show a part of a particular bit period in a sequence with 622 MHz repetition rate. Rows a and b show the model of the input signal and its measured time dependence respectively. c corresponds to the output of the neuron’s integration stage, sampled with three pulses per bit period shown in f. The last row (d) shows a measured thresholder output, equivalent to detection of the smallest pulses in the sequence i.e. detection of the aligned pulse triplets. Part e is a measured eye diagram of the input signal.

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Fig. 6
Fig. 6 Schematic of the symmetric photonic neuron with excitatory and inhibitory inputs. The setup consists of two identical SOA integration stages with corresponding passive input circuits, and the thresholder. G — variable gain/attenuation; T — variable time delay. The inset shows an example of signal propagation through the neuron. Each waveform is measured at the certain point in the setup: a and b are excitatory and inhibitory inputs respectively, c is the output of the second integration stage, and d is the neuron output, i.e. the thresholded version of c.

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Fig. 7
Fig. 7 Measured waveforms at the outputs of the two SOA stages of the neuron shown together with the input data. Column a — only excitatory pulses are sent to the neuron; b — inhibitory pulses only; c — both excitatory and inhibitory pulse streams are provided.

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Fig. 8
Fig. 8 Principle of storing data in a neuron-based loop with positive feedback. Three stages of the process are shown.

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Fig. 9
Fig. 9 Block diagram of the feedback-mode operation of the neuron. Mod — Mach-Zehnder intensity modulator.

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Fig. 10
Fig. 10 Examples of the stored bit patterns in the neural feedback loop. The total round-trip time is equal to 485 bit intervals, so patterns of a length of 5, 97, and 485 bits can be stored in this configuration. The diagram shows one example of a 97 bit-long pattern, two examples of different 5-bit patterns, and, in the last column, a 485-bit pattern. The last one, due to its large length, has also a zoomed-in version of its part.

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Equations (2)

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d V m ( t ) d t = V rest τ m − V m ( t ) τ m − 1 C m V m ( t ) σ ( t )
d N ′ ( t ) d t = N rest ′ τ e − N ′ ( t ) τ e − Γ a E p N ′ ( t ) I ( t )

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