Abstract

We propose an equivalent circuit model for photonic spike processing laser neurons with an embedded saturable absorber—a simulation model for photonic excitable lasers (SIMPEL). We show that by mapping the laser neuron rate equations into a circuit model, SPICE analysis can be used as an efficient and accurate engine for numerical calculations, capable of generalization to a variety of different types of laser neurons with saturable absorber found in literature. The development of this model parallels the Hodgkin–Huxley model of neuron biophysics, a circuit framework which brought efficiency, modularity, and generalizability to the study of neural dynamics. We employ the model to study various signal-processing effects such as excitability with excitatory and inhibitory pulses, binary all-or-nothing response, and bistable dynamics.

© 2015 Optical Society of America

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2014 (5)

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

S. Ostojic, “Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons,” Nat. Neurosci. 17, 594–600 (2014).
[Crossref] [PubMed]

F. Selmi, R. Braive, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, “Relative refractory period in an excitable semiconductor laser,” Phys. Rev. Lett. 112, 183902 (2014).
[Crossref] [PubMed]

A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast and weight: an integrated network for scalable photonic spike processing,” J. Lightw. Technol. 32, 3427–3439 (2014).
[Crossref]

B. J. Shastri, A. N. Tait, M. A. Nahmias, and P. R. Prucnal, “Photonic spike processing: ultrafast laser neurons and an integrated photonic network,” IEEE Photon. Soc. Newslett. 28, 4–11 (2014).

2013 (7)

M. A. Nahmias, B. J. Shastri, A. N. Tait, and P. R. Prucnal, “A leaky integrate-and-fire laser neuron for ultrafast cognitive computing,” IEEE J. Sel. Topics Quantum Electron. 19, 1800212 (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, 1364 (2013).
[Crossref]

J. Hasler and H. B. Marr, “Finding a roadmap to achieve large neuromorphic hardware systems,” Front. Neurosci. 7, 118 (2013).
[Crossref] [PubMed]

A. N. Tait, B. J. Shastri, M. P. Fok, M. A. Nahmias, and P. R. Prucnal, “DREAM The: an integrated photonic thresholder,” J. Lightw. Technol. 31, 1263–1272 (2013).
[Crossref]

B. Romeira, J. Javaloyes, C. N. Ironside, J. M. L. Figueiredo, S. Balle, and O. Piro, “Excitability and optical pulse generation in semiconductor lasers driven by resonant tunneling diode photo-detectors,” Opt. Express 21, 20931–20940 (2013).
[Crossref] [PubMed]

K. Alexander, T. V. Vaerenbergh, M. Fiers, P. Mechet, J. Dambre, and P. Bienstman, “Excitability in optically injected microdisk lasers with phase controlled excitatory and inhibitory response,” Opt. Express 21, 26182–26191 (2013).
[Crossref] [PubMed]

T. V. Vaerenbergh, K. Alexander, J. Dambre, and P. Bienstman, “Excitation transfer between optically injected microdisk lasers,” Opt. Express 21, 28922–28932 (2013).
[Crossref]

2012 (3)

D. Woods and T. J. Naughton, “Optical computing: Photonic neural networks,” Nature Phys. 8, 257–259 (2012).
[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, 244101 (2012).
[Crossref] [PubMed]

A. Hurtado, K. Schires, I. D. Henning, and M. J. Adams, “Investigation of vertical cavity surface emitting laser dynamics for neuromorphic photonic systems,” Appl. Phys. Lett. 1000, 1037032012 .
[Crossref]

2011 (7)

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] [PubMed]

D. S. Modha, R. Ananthanarayanan, S. K. Esser, A. Ndirango, A. J. Sherbondy, and R. Singh, “Cognitive computing,” Commun. ACM 54, 62–71 (2011).
[Crossref]

W. Coomans, L. Gelens, S. Beri, J. Danckaert, and G. Van der Sande, “Solitary and coupled semiconductor ring lasers as optical spiking neurons,” Phys. Rev. E 84, 036209 (2011).
[Crossref]

K. S. Kravtsov, M. P. Fok, P. R. Prucnal, and D. Rosenbluth, “Ultrafast all-optical implementation of a leaky integrate-and-fire neuron,” Opt. Express 19, 2133–2147 (2011).
[Crossref] [PubMed]

S. Srinivasan, A. W. Fang, D. Liang, J. Peters, B. Kaye, and J. E. Bowers, “Design of phase-shifted hybrid silicon distributed feedback lasers,” Opt. Express 19, 9255–9261 (2011).
[Crossref] [PubMed]

S. Barbay, R. Kuszelewicz, and A. M. Yacomotti, “Excitability in a semiconductor laser with saturable absorber,” Opt. Lett. 36, 4476–4478 (2011).
[Crossref] [PubMed]

B. J. Shastri, C. Chen, K. D. Choquette, and D. V. Plant, “Circuit modeling of carrier–photon dynamics in composite-resonator vertical-cavity lasers,” IEEE J. Quantum Electron. 47, 1537–1546 (2011).
[Crossref]

2010 (3)

C. Savin, P. Joshi, and J. Triesch, “Independent component analysis in spiking neurons,” PLoS Comput. Biol. 6, e1000757 (2010).
[Crossref] [PubMed]

A. Kumar, S. Rotter, and A. Aertsen, “Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding,” Nat. Rev. Neurosci. 11, 615–627 (2010).
[Crossref] [PubMed]

B. Szatmary and E. M. Izhikevich, “Spike-timing theory of working memory,” PLoS Comput. Biol. 6, e1000879 (2010).
[Crossref] [PubMed]

2008 (3)

2007 (2)

2006 (3)

A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14, 9203–9210 (2006).
[Crossref] [PubMed]

E. M. Izhikevich, “Polychronization: computation with spikes,” Neural Comput. 18, 245–282 (2006).
[Crossref]

F. Koyama, “Recent advances of VCSEL photonics,” J. Lightw. Technol. 24, 4502–4513 (2006).
[Crossref]

2004 (3)

D. Louderback, G. Pickrell, H. C. Lin, M. A. Fish, J. J. Hindi, and P. Guilfoyle, “VCSELs with monolithic coupling to internal horizontal waveguides using integrated diffraction gratings,” Electron. Lett. 40, 1064–1065 (2004).
[Crossref]

E. M. Izhikevich, “Which model to use for cortical spiking neurons?” IEEE Trans. Neural Netw. 15, 1063–1070 (2004).
[Crossref] [PubMed]

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

2003 (1)

E. M. Izhikevich, “Simple model of spiking neurons,” IEEE Trans. Neural Netw. 14, 1569–1572 (2003).
[Crossref]

2002 (2)

W. Maass, T. Natschlaeger, 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] [PubMed]

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Sel. Topics Quantum Electron. 38, 949–955 (2002).
[Crossref]

2001 (1)

S. Thorpe, A. Delorme, and R. Van Rullen, “Spike-based strategies for rapid processing,” Neural Netw. 14, 715–725 (2001).
[Crossref] [PubMed]

2000 (1)

L. F. Abbott and S. B. Nelson, “Synaptic plasticity: taming the beast,” Nat. Neurosci. 3, 1178–1183 (2000).
[Crossref] [PubMed]

1999 (4)

M. Diesmann, M. O. Gewaltig, and A. Aertsen, “Stable propagation of synchronous spiking in cortical neural networks,” Nature 402, 529–533 (1999).
[Crossref] [PubMed]

J. L. A. Dubbeldam, B. Krauskopf, and D. Lenstra, “Excitability and coherence resonance in lasers with saturable absorber,” Phys. Rev. E 60, 6580–6588 (1999).
[Crossref]

A. Borst and F. E. Theunissen, “Information theory and neural coding,” Nat. Neurosci. 2, 947–957 (1999).
[Crossref] [PubMed]

G. E. Giudice, D. V. Kuksenkov, H. Temkin, and K. L. Lear, “Differential carrier lifetime in oxide-confined vertical cavity lasers obtained from electrical impedance measurements,” Appl. Phys. Lett. 74, 899–901 (1999).
[Crossref]

1998 (1)

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

1997 (1)

P. V. Mena, S.-M. Kang, and T. A. DeTemple, “Rate-equation based laser model with a single solution regime,” J. Lightw. Technol. 15, 717–730 (1997).
[Crossref]

1996 (1)

1995 (2)

D. G. H. Nugent, R. G. S. Plumb, M. Fisher, and D. A. O. Davies, “Self-pulsations in vertical-cavity surface emitting lasers,” Electron. Lett. 31, 43–44 (1995).
[Crossref]

S. A. Javro and S. M. Kang, “Transforming Tucker’s linearized laser rate equations to a form that has a single solution regime,” J. Lightw. Technol. 13, 1899–1904 (1995).
[Crossref]

1993 (1)

T. A. DeTemple and C. M. Herzinger, “On the semiconductor laser logarithmic gain-current density relation,” IEEE J. Quantum Electron. 29, 1246–1252 (1993).
[Crossref]

1991 (1)

M. Mahowald and R. Douglas, “A silicon neuron,” Nature 354, 515–518 (1991).
[Crossref] [PubMed]

1990 (1)

P. Williams, P. Charles, I. Griffith, L. Considine, and A. Carter, “High performance buried ridge DFB lasers monolithically integrated with butt coupled strip loaded passive waveguides for OEIC,” Electron. Lett. 26, 142–143 (1990).
[Crossref]

1983 (1)

R. S. Tucker and D. J. Pope, “Circuit modeling of the effect of diffusion on damping in a narrow-stripe semiconductor laser,” IEEE J. Quantum Electron. 19, 1179–1183 (1983).
[Crossref]

1979 (1)

D. J. Channin, “Effect of gain saturation on injection laser switching,” J. Appl. Phys. 50, 3858–3860 (1979).
[Crossref]

1952 (1)

A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J. Physiol. 117, 500–544 (1952).
[Crossref] [PubMed]

Abbott, L. F.

L. F. Abbott and S. B. Nelson, “Synaptic plasticity: taming the beast,” Nat. Neurosci. 3, 1178–1183 (2000).
[Crossref] [PubMed]

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,” Appl. Phys. Lett. 1000, 1037032012 .
[Crossref]

Aertsen, A.

A. Kumar, S. Rotter, and A. Aertsen, “Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding,” Nat. Rev. Neurosci. 11, 615–627 (2010).
[Crossref] [PubMed]

M. Diesmann, M. O. Gewaltig, and A. Aertsen, “Stable propagation of synchronous spiking in cortical neural networks,” Nature 402, 529–533 (1999).
[Crossref] [PubMed]

Akopyan, F.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

Alexander, K.

Alvarez-Icaza, R.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

Amir, A.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

Ananthanarayanan, R.

D. S. Modha, R. Ananthanarayanan, S. K. Esser, A. Ndirango, A. J. Sherbondy, and R. Singh, “Cognitive computing,” Commun. ACM 54, 62–71 (2011).
[Crossref]

Appeltant, L.

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] [PubMed]

Appuswamy, R.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

Arthur, J. V.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

Baets, R.

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

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Sel. Topics Quantum Electron. 38, 949–955 (2002).
[Crossref]

Balle, S.

Barbay, S.

F. Selmi, R. Braive, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, “Relative refractory period in an excitable semiconductor laser,” Phys. Rev. Lett. 112, 183902 (2014).
[Crossref] [PubMed]

S. Barbay, R. Kuszelewicz, and A. M. Yacomotti, “Excitability in a semiconductor laser with saturable absorber,” Opt. Lett. 36, 4476–4478 (2011).
[Crossref] [PubMed]

Beaudoin, G.

F. Selmi, R. Braive, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, “Relative refractory period in an excitable semiconductor laser,” Phys. Rev. Lett. 112, 183902 (2014).
[Crossref] [PubMed]

Beri, S.

W. Coomans, L. Gelens, S. Beri, J. Danckaert, and G. Van der Sande, “Solitary and coupled semiconductor ring lasers as optical spiking neurons,” Phys. Rev. E 84, 036209 (2011).
[Crossref]

Bienstman, P.

Bogaerts, W.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Sel. Topics Quantum Electron. 38, 949–955 (2002).
[Crossref]

Borst, A.

A. Borst and F. E. Theunissen, “Information theory and neural coding,” Nat. Neurosci. 2, 947–957 (1999).
[Crossref] [PubMed]

Bowers, J. E.

Braive, R.

F. Selmi, R. Braive, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, “Relative refractory period in an excitable semiconductor laser,” Phys. Rev. Lett. 112, 183902 (2014).
[Crossref] [PubMed]

Brezzo, B.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

Brunner, D.

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]

Bubnov, M. M.

Campenhout, J. V.

Carter, A.

P. Williams, P. Charles, I. Griffith, L. Considine, and A. Carter, “High performance buried ridge DFB lasers monolithically integrated with butt coupled strip loaded passive waveguides for OEIC,” Electron. Lett. 26, 142–143 (1990).
[Crossref]

Cassidy, A. S.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

Chandrappan, J.

J. Zhang, B. Li, J. Chandrappan, Q. X. Zhang, P. V. Ramana, P. Prabhathan, H. S. Lau, D. L. Kwong, and M. V. Matham, “Taper couplers for coupling between laser and silicon waveguide with large allowable tolerance,” Proc. SPIE 6899, 689909 (2008).
[Crossref]

Chang, M. P.

B. J. Shastri, M. A. Nahmias, A. N. Tait, Y. Tian, M. P. Fok, M. P. Chang, B. Wu, and P. R. Prucnal, “Exploring excitability in graphene for spike processing networks,” in “Proc. Numerical Simulation of Optoelectron. Devices (NUSOD),” (Vancouver, BC, Canada, 2013), pp. 83–84.

Channin, D. J.

D. J. Channin, “Effect of gain saturation on injection laser switching,” J. Appl. Phys. 50, 3858–3860 (1979).
[Crossref]

Charles, P.

P. Williams, P. Charles, I. Griffith, L. Considine, and A. Carter, “High performance buried ridge DFB lasers monolithically integrated with butt coupled strip loaded passive waveguides for OEIC,” Electron. Lett. 26, 142–143 (1990).
[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, 244101 (2012).
[Crossref] [PubMed]

Chen, C.

B. J. Shastri, C. Chen, K. D. Choquette, and D. V. Plant, “Circuit modeling of carrier–photon dynamics in composite-resonator vertical-cavity lasers,” IEEE J. Quantum Electron. 47, 1537–1546 (2011).
[Crossref]

Choquette, K. D.

B. J. Shastri, C. Chen, K. D. Choquette, and D. V. Plant, “Circuit modeling of carrier–photon dynamics in composite-resonator vertical-cavity lasers,” IEEE J. Quantum Electron. 47, 1537–1546 (2011).
[Crossref]

Cohen, O.

Coldren, L. A.

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, Wiley Series in Microwave and Optical Engineering (Wiley, New York, NY, USA, 2011).

Considine, L.

P. Williams, P. Charles, I. Griffith, L. Considine, and A. Carter, “High performance buried ridge DFB lasers monolithically integrated with butt coupled strip loaded passive waveguides for OEIC,” Electron. Lett. 26, 142–143 (1990).
[Crossref]

Coomans, W.

W. Coomans, L. Gelens, S. Beri, J. Danckaert, and G. Van der Sande, “Solitary and coupled semiconductor ring lasers as optical spiking neurons,” Phys. Rev. E 84, 036209 (2011).
[Crossref]

Corzine, S. W.

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, Wiley Series in Microwave and Optical Engineering (Wiley, New York, NY, USA, 2011).

Dambre, J.

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] [PubMed]

W. Coomans, L. Gelens, S. Beri, J. Danckaert, and G. Van der Sande, “Solitary and coupled semiconductor ring lasers as optical spiking neurons,” Phys. Rev. E 84, 036209 (2011).
[Crossref]

Davies, D. A. O.

D. G. H. Nugent, R. G. S. Plumb, M. Fisher, and D. A. O. Davies, “Self-pulsations in vertical-cavity surface emitting lasers,” Electron. Lett. 31, 43–44 (1995).
[Crossref]

De Mesel, K.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Sel. Topics Quantum Electron. 38, 949–955 (2002).
[Crossref]

Delorme, A.

S. Thorpe, A. Delorme, and R. Van Rullen, “Spike-based strategies for rapid processing,” Neural Netw. 14, 715–725 (2001).
[Crossref] [PubMed]

DeTemple, T. A.

P. V. Mena, S.-M. Kang, and T. A. DeTemple, “Rate-equation based laser model with a single solution regime,” J. Lightw. Technol. 15, 717–730 (1997).
[Crossref]

T. A. DeTemple and C. M. Herzinger, “On the semiconductor laser logarithmic gain-current density relation,” IEEE J. Quantum Electron. 29, 1246–1252 (1993).
[Crossref]

Dierckx, W.

Diesmann, M.

M. Diesmann, M. O. Gewaltig, and A. Aertsen, “Stable propagation of synchronous spiking in cortical neural networks,” Nature 402, 529–533 (1999).
[Crossref] [PubMed]

Douglas, R.

M. Mahowald and R. Douglas, “A silicon neuron,” Nature 354, 515–518 (1991).
[Crossref] [PubMed]

Dubbeldam, J. L. A.

J. L. A. Dubbeldam, B. Krauskopf, and D. Lenstra, “Excitability and coherence resonance in lasers with saturable absorber,” Phys. Rev. E 60, 6580–6588 (1999).
[Crossref]

Esser, S. K.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

D. S. Modha, R. Ananthanarayanan, S. K. Esser, A. Ndirango, A. J. Sherbondy, and R. Singh, “Cognitive computing,” Commun. ACM 54, 62–71 (2011).
[Crossref]

Fang, A. W.

Fiers, M.

Figueiredo, J. M. L.

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]

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] [PubMed]

Fish, M. A.

D. Louderback, G. Pickrell, H. C. Lin, M. A. Fish, J. J. Hindi, and P. Guilfoyle, “VCSELs with monolithic coupling to internal horizontal waveguides using integrated diffraction gratings,” Electron. Lett. 40, 1064–1065 (2004).
[Crossref]

Fisher, M.

D. G. H. Nugent, R. G. S. Plumb, M. Fisher, and D. A. O. Davies, “Self-pulsations in vertical-cavity surface emitting lasers,” Electron. Lett. 31, 43–44 (1995).
[Crossref]

Flickner, M. D.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

Fok, M. P.

A. N. Tait, B. J. Shastri, M. P. Fok, M. A. Nahmias, and P. R. Prucnal, “DREAM The: an integrated photonic thresholder,” J. Lightw. Technol. 31, 1263–1272 (2013).
[Crossref]

K. S. Kravtsov, M. P. Fok, P. R. Prucnal, and D. Rosenbluth, “Ultrafast all-optical implementation of a leaky integrate-and-fire neuron,” Opt. Express 19, 2133–2147 (2011).
[Crossref] [PubMed]

B. J. Shastri, M. A. Nahmias, A. N. Tait, Y. Tian, M. P. Fok, M. P. Chang, B. Wu, and P. R. Prucnal, “Exploring excitability in graphene for spike processing networks,” in “Proc. Numerical Simulation of Optoelectron. Devices (NUSOD),” (Vancouver, BC, Canada, 2013), pp. 83–84.

Gelens, L.

W. Coomans, L. Gelens, S. Beri, J. Danckaert, and G. Van der Sande, “Solitary and coupled semiconductor ring lasers as optical spiking neurons,” Phys. Rev. E 84, 036209 (2011).
[Crossref]

Gewaltig, M. O.

M. Diesmann, M. O. Gewaltig, and A. Aertsen, “Stable propagation of synchronous spiking in cortical neural networks,” Nature 402, 529–533 (1999).
[Crossref] [PubMed]

Giudice, G. E.

G. E. Giudice, D. V. Kuksenkov, H. Temkin, and K. L. Lear, “Differential carrier lifetime in oxide-confined vertical cavity lasers obtained from electrical impedance measurements,” Appl. Phys. Lett. 74, 899–901 (1999).
[Crossref]

Griffith, I.

P. Williams, P. Charles, I. Griffith, L. Considine, and A. Carter, “High performance buried ridge DFB lasers monolithically integrated with butt coupled strip loaded passive waveguides for OEIC,” Electron. Lett. 26, 142–143 (1990).
[Crossref]

Guilfoyle, P.

D. Louderback, G. Pickrell, H. C. Lin, M. A. Fish, J. J. Hindi, and P. Guilfoyle, “VCSELs with monolithic coupling to internal horizontal waveguides using integrated diffraction gratings,” Electron. Lett. 40, 1064–1065 (2004).
[Crossref]

Guo, C.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

Haas, H.

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

Hasler, J.

J. Hasler and H. B. Marr, “Finding a roadmap to achieve large neuromorphic hardware systems,” Front. Neurosci. 7, 118 (2013).
[Crossref] [PubMed]

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,” Appl. Phys. Lett. 1000, 1037032012 .
[Crossref]

Herzinger, C. M.

T. A. DeTemple and C. M. Herzinger, “On the semiconductor laser logarithmic gain-current density relation,” IEEE J. Quantum Electron. 29, 1246–1252 (1993).
[Crossref]

Hindi, J. J.

D. Louderback, G. Pickrell, H. C. Lin, M. A. Fish, J. J. Hindi, and P. Guilfoyle, “VCSELs with monolithic coupling to internal horizontal waveguides using integrated diffraction gratings,” Electron. Lett. 40, 1064–1065 (2004).
[Crossref]

Hodgkin, A. L.

A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J. Physiol. 117, 500–544 (1952).
[Crossref] [PubMed]

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,” Appl. Phys. Lett. 1000, 1037032012 .
[Crossref]

Huxley, A. F.

A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J. Physiol. 117, 500–544 (1952).
[Crossref] [PubMed]

Imam, N.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

Ironside, C. N.

Izhikevich, E. M.

B. Szatmary and E. M. Izhikevich, “Spike-timing theory of working memory,” PLoS Comput. Biol. 6, e1000879 (2010).
[Crossref] [PubMed]

E. M. Izhikevich, “Polychronization: computation with spikes,” Neural Comput. 18, 245–282 (2006).
[Crossref]

E. M. Izhikevich, “Which model to use for cortical spiking neurons?” IEEE Trans. Neural Netw. 15, 1063–1070 (2004).
[Crossref] [PubMed]

E. M. Izhikevich, “Simple model of spiking neurons,” IEEE Trans. Neural Netw. 14, 1569–1572 (2003).
[Crossref]

Jackson, B. L.

P. A. Merolla, J. V. Arthur, R. Alvarez-Icaza, A. S. Cassidy, J. Sawada, F. Akopyan, B. L. Jackson, N. Imam, C. Guo, Y. Nakamura, B. Brezzo, I. Vo, S. K. Esser, R. Appuswamy, B. Taba, A. Amir, M. D. Flickner, W. P. Risk, R. Manohar, and D. S. Modha, “A million spiking-neuron integrated circuit with a scalable communication network and interface,” Science 345, 668–673 (2014).
[Crossref] [PubMed]

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, 244101 (2012).
[Crossref] [PubMed]

Jaeger, H.

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

Javaloyes, J.

Javro, S. A.

S. A. Javro and S. M. Kang, “Transforming Tucker’s linearized laser rate equations to a form that has a single solution regime,” J. Lightw. Technol. 13, 1899–1904 (1995).
[Crossref]

Jones, R.

Joshi, P.

C. Savin, P. Joshi, and J. Triesch, “Independent component analysis in spiking neurons,” PLoS Comput. Biol. 6, e1000757 (2010).
[Crossref] [PubMed]

Kang, S. M.

S. A. Javro and S. M. Kang, “Transforming Tucker’s linearized laser rate equations to a form that has a single solution regime,” J. Lightw. Technol. 13, 1899–1904 (1995).
[Crossref]

Kang, S.-M.

P. V. Mena, S.-M. Kang, and T. A. DeTemple, “Rate-equation based laser model with a single solution regime,” J. Lightw. Technol. 15, 717–730 (1997).
[Crossref]

Kaye, B.

Koyama, F.

F. Koyama, “Recent advances of VCSEL photonics,” J. Lightw. Technol. 24, 4502–4513 (2006).
[Crossref]

Krauskopf, B.

J. L. A. Dubbeldam, B. Krauskopf, and D. Lenstra, “Excitability and coherence resonance in lasers with saturable absorber,” Phys. Rev. E 60, 6580–6588 (1999).
[Crossref]

Krauss, T.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Sel. Topics Quantum Electron. 38, 949–955 (2002).
[Crossref]

Kravtsov, K.

Kravtsov, K. S.

Kuksenkov, D. V.

G. E. Giudice, D. V. Kuksenkov, H. Temkin, and K. L. Lear, “Differential carrier lifetime in oxide-confined vertical cavity lasers obtained from electrical impedance measurements,” Appl. Phys. Lett. 74, 899–901 (1999).
[Crossref]

Kumar, A.

A. Kumar, S. Rotter, and A. Aertsen, “Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding,” Nat. Rev. Neurosci. 11, 615–627 (2010).
[Crossref] [PubMed]

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Kuszelewicz, R.

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Tait, A. N.

B. J. Shastri, A. N. Tait, M. A. Nahmias, and P. R. Prucnal, “Photonic spike processing: ultrafast laser neurons and an integrated photonic network,” IEEE Photon. Soc. Newslett. 28, 4–11 (2014).

A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast and weight: an integrated network for scalable photonic spike processing,” J. Lightw. Technol. 32, 3427–3439 (2014).
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A. N. Tait, B. J. Shastri, M. P. Fok, M. A. Nahmias, and P. R. Prucnal, “DREAM The: an integrated photonic thresholder,” J. Lightw. Technol. 31, 1263–1272 (2013).
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B. J. Shastri, M. A. Nahmias, A. N. Tait, Y. Tian, B. Wu, and P. R. Prucnal, “Graphene excitable laser for photonic spike processing,” in “Proc. IEEE Photon. Conf. (IPC),” (Seattle, WA, USA, 2013), pp. 1–2.

B. J. Shastri, M. A. Nahmias, A. N. Tait, Y. Tian, M. P. Fok, M. P. Chang, B. Wu, and P. R. Prucnal, “Exploring excitability in graphene for spike processing networks,” in “Proc. Numerical Simulation of Optoelectron. Devices (NUSOD),” (Vancouver, BC, Canada, 2013), pp. 83–84.

A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast-and-weight interconnects for integrated distributed processing systems,” in “Proc. IEEE Opt. Interconnects Conf. (OI),” (Coronado Bay, CA, USA, 2014), pp. 108–109.

M. A. Nahmias, A. N. Tait, B. J. Shastri, and P. R. Prucnal, “O-BAR: A scalable, optical neuromorphic communication protocol,” in “Proc. IEEE Opt. Interconnects Conf. (OI),” (Coronado Bay, CA, USA, 2014).

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A. N. Tait, M. A. Nahmias, Y. Tian, B. J. Shastri, and P. R. Prucnal, “Photonic neuromorphic signal processing and computing,” in “Nanophotonic Information Physics,”, M. Naruse, ed. (Springer Berlin Heidelberg, 2014), Nano-Optics and Nanophotonics, pp. 183–222.
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B. J. Shastri, M. A. Nahmias, A. N. Tait, Y. Tian, B. Wu, and P. R. Prucnal, “Graphene excitable laser for photonic spike processing,” in “Proc. IEEE Photon. Conf. (IPC),” (Seattle, WA, USA, 2013), pp. 1–2.

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Figures (7)

Fig. 1
Fig. 1 Schematic of a biological neuron and a two-section excitable laser that share key dynamical properties. In the LIF neuron model, weighted and delayed input signals are spatially summed at the dendritic tree into an input current, which travel to the soma and perturb the internal state variable, the voltage. The soma performs integration and then applies a threshold to make a spike or no-spike decision. After a spike is released, the voltage is reset. The resulting spike is sent to other neurons in the network. The excitable laser is composed of a gain section, SA, and mirrors for cavity feedback. The inputs selectively perturb the gain optically or electrically. The gain medium acts as a temporal integrator while the SA acts as a threshold detector; it extracts most of the stored energy from the gain medium into the optical mode. These dynamics emulate excitability, one of the most critical properties of a spiking neuron.
Fig. 2
Fig. 2 Circuit-level implementation to model the laser neuron.
Fig. 3
Fig. 3 (a) Cross section of a VCSEL-SA excitable laser. The single cavity mode interacts with two independent sets of quantum wells (blue). Metal contacts (orange) inject current into gain and SA sections from below and above, respectively. Insulating regions confine current to the mode center (yellow). (b) Cross section of a DFB-SA excitable laser. A refractive index grating etched in the waveguide core (dark grey) creates a high-finesse, single mode cavity whose mode interacts with both gain and SA MQW active regions (blue). Metal contacts (orange) inject current into gain and SA sections, which are electrically isolated by a H+ implanted layer (yellow).
Fig. 4
Fig. 4 Circuit setup to simulate the laser neuron equivalent circuit model.
Fig. 5
Fig. 5 Simulation of the excitable VCSEL neuron exhibiting neural spiking behavior by selectively modulating the gain through both excitatory (gain enhancement) and inhibitory (gain depletion) pulses. First row: input perturbations to the gain. Second row: output and sech2 fitting curve. Third row: gain region and SA region carrier concentrations.
Fig. 6
Fig. 6 (a) Laser neuron circuit setup to investigating bistable dynamics. Note that the dc biasing conditions have been left out for the sake of brevity. (b) Simulation of the excitable VCSEL neuron system exhibiting bistability with connection delays of 4 ns. Top row: input perturbations to the gain. Second row: output power. Third row: gain region carrier concentration. Fourth row: SA region carrier concentration.
Fig. 7
Fig. 7 Characteristics of the excitable laser neurons biased just below threshold (LIF VCSEL-SA: Ia = 2.7 mA and Is = 0 mA; LIF DFB-SA: Ia = 16.45 mA and Is = 0 mA) to a single impulse. (a) Energy transfer function. (b) Decision latency as a function of the input pulse energy.

Tables (1)

Tables Icon

Table 1 Typical VCSEL-SA and DFB-SA Excitable Laser Parameters [7, 40, 5560]

Equations (28)

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d V m ( t ) d t Activation = V L τ m Active pumping V m ( t ) τ m Leakage + 1 C m I a p p ( t ) External input ;
if V m ( t ) > V thresh then release a pulse and set V m ( t ) V reset .
d G ( t ) d t Activation = γ G A Active pumping γ G G ( t ) Leakage + θ ( t ) External input
if G ( t ) > G thresh then release a pulse and set G ( t ) G reset .
d n a d t = η i , a i a q V a current injection n a τ a carrier recomb . Γ a g ( n a ) N p h V a stimulated-emission
d n s d t = η i , s i s q V s current injection n s τ s carrier recomb . Γ s g ( n s ) N p h V s stimulated-emission
d N ph d t = N p h τ p h Photon decay + Γ a g ( n a ) N p h + Γ s g ( n s ) N p h stimulated-emission + V a β B r n a 2 recombination
N ph P out = λ τ ph η c Γ s h c ϑ
n a = n eq , a exp ( q v a n k T )
n s = n eq , s exp ( q v s n k T )
P out = ( v m + δ ) 2
q n eq , χ n k T exp ( q v χ n k T ) d v χ d t = η i , χ i χ q V χ n eq , χ τ χ [ exp ( q v χ n k T ) 1 ] n eq , χ τ χ Γ χ g ( n χ ) V χ ϑ ( v m + δ ) 2 .
i χ = i χ T 1 + i χ T 2 + G χ
i χ T 1 = i χ D 1 + i χ C 1
i χ T 2 = i χ D 2 + i χ C 2
i χ D 1 = q n eq , χ V χ 2 η i , χ τ χ [ exp ( q v χ n k T ) 1 ]
i χ D 2 = q n eq , χ V χ 2 η i , χ τ χ [ exp ( q v χ n k T ) 1 + 2 q τ χ n k T exp ( q v χ n k T ) q v χ d t ]
i χ C 1 = q n eq , χ V χ 2 η i , χ τ χ
i χ C 2 = i χ C 1
G χ = ϑ q Γ χ η i , χ g ( Θ χ i χ T 1 ) ( v m + δ ) 2
n χ = Θ χ i χ T 1 and Θ χ 2 η i , χ τ χ q V χ .
2 ( v m + δ ) d v m d t = ( v m + δ ) 2 τ ph + { Γ a g ( n a ) + Γ s g ( n s ) } ( v m + δ ) 2 + V a β B r n a 2 ϑ
C ph d v m d t + v m R ph = G r , a + G r , s + B
G r , a = τ ph Γ a g ( Θ a I a T 1 ) ( v m + δ ) δ
G r , s = τ ph Γ s g ( Θ s I s T 1 ) ( v m + δ )
B = η c Γ a h c V a β B r λ ( v m + δ ) ( Θ a i a T 1 ) 2
C ph = 2 τ ph and R ph = 1 Ω .
P out = E pf = ( v m + δ ) 2 .

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