Abstract

Optical excitable devices that mimic neuronal behavior can be building-blocks of novel, brain-inspired information processing systems. A relevant issue is to understand how such systems represent, via correlated spikes, the information of a weak external input. Semiconductor lasers with optical feedback operating in the low frequency fluctuations regime have been shown to display optical spikes with intrinsic temporal correlations similar to those of biological neurons. Here we investigate how the spiking laser output represents a weak periodic input that is implemented via direct modulation of the laser pump current. We focus on understanding the influence of the modulation frequency. Experimental sequences of inter-spike-intervals (ISIs) are recorded and analyzed by using the ordinal symbolic methodology that identifies and characterizes serial correlations in datasets. The change in the statistics of the various symbols with the modulation frequency is empirically shown to be related to specific changes in the ISI distribution, which arise due to different phase-locking regimes. A good qualitative agreement is also found between simulations of the Lang and Kobayashi model and observations. This methodology is an efficient way to detect subtle changes in noisy correlated ISI sequences and may be applied to investigate other optical excitable devices.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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2014 (5)

2013 (4)

M. Turconi, B. Garbin, M. Feyereisen, M. Giudici, and S. Barland, “Control of excitable pulses in an injection-locked semiconductor laser,” Phys. Rev. E 88, 022923 (2013).
[Crossref]

K. Hicke, X. Porte, and I. Fischer, “Characterizing the deterministic nature of individual power dropouts in semiconductor lasers subject to delayed feedback,” Phys. Rev. E 88, 052904 (2013).
[Crossref]

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. Top. Quantum Electron. 19, 1800212 (2013).
[Crossref]

D. Nikolić, P. Fries, and W. Singer, “Gamma oscillations: precise temporal coordination without a metronome,” Trends Cogn. Sci. 17, 54 (2013).
[Crossref]

2012 (2)

T. Schwalger, J. Tiana-Alsina, M. C. Torrent, J. García-Ojalvo, and B. Lindner, “Interspike-interval correlations induced by two-state switching in an excitable system,” Europhys. Lett. 99, 10004 (2012).
[Crossref]

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. 100, 103703 (2012).
[Crossref]

2011 (3)

W. Coomans, L. Gelens, L. Mashal, 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]

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47, 252–261 (2011).
[Crossref]

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

2010 (3)

J. P. Toomey, D. M. Kane, M. W. Lee, and K. A. Shore, “Nonlinear dynamics of semiconductor lasers with feedback and modulation,” Opt. Express 18, 16955–16972 (2010).
[Crossref] [PubMed]

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, “Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 82, 013189 (2010).
[Crossref]

J. Zamora-Munt, C. Masoller, and J. García-Ojalvo, “Transient low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 81, 033820 (2010).
[Crossref]

2006 (1)

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang–Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[Crossref]

2005 (2)

Y. Hong and K. A. Shore, “Statistical measures of the power dropout ratio in semiconductor lasers subject to optical feedback,” Opt. Lett. 30, 3332 (2005).
[Crossref]

A. B. Neiman and D. F. Russell, “Models of stochastic biperiodic oscillations and extended serial correlations in electroreceptors of paddlefish,” Phys. Rev. E 71, 061915 (2005).
[Crossref]

2004 (2)

J. F. Martínez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Experimental deterministic coherent resonance,” Phys. Rev. Lett. 93, 144101 (2004).
[Crossref]

B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392, 321–424 (2004).
[Crossref]

2003 (3)

J. M. Buldú, D. R. Chialvo, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, “Ghost resonance in a semiconductor laser with optical feedback,” Europhys. Lett. 64, 178 (2003).
[Crossref]

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Mégret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers”, J. Opt. Soc. Am. B 20, 37 (2003).
[Crossref]

W.-S. Lam, N. Parvez, and R. Roy, “Effect of spontaneous emission noise and modulation on semiconductor lasers near threshold with optical feedback,” Int. J. Mod. Phys. B 17, 4123–4138 (2003).
[Crossref]

2002 (3)

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[Crossref] [PubMed]

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88, 174102 (2002).
[Crossref] [PubMed]

J. M. Buldú, J. García-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[Crossref]

2001 (2)

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

J. M. Mendez, R. Laje, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[Crossref]

2000 (1)

D. W. Sukow and D. J. Gauthier, “Entraining power-dropout events in an external-cavity semiconductor laser using weak modulation of the injection current,” IEEE J. Quantum Electron. 36, 175 (2000).
[Crossref]

1999 (1)

J. Mulet and C. R. Mirasso, “Numerical statistics of power dropouts based on the Lang-Kobayashi model,” Phys. Rev. E 59, 5400 (1999).
[Crossref]

1998 (1)

1997 (2)

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414 (1997).
[Crossref]

D. W. Sukow, J. R. Gardner, and D. J. Gauthier, “Statistics of power-dropout events in semiconductor lasers with time-delayed optical feedback,” Phys. Rev. A. 56, R3370 (1997).
[Crossref]

1995 (1)

Y. Liu, N. Kikuchi, and J. Ohtsubo, “Controlling dynamical behavior of a semiconductor laser with external optical feedback,” Phys. Rev. E 51, R2697–R2700 (1995).
[Crossref]

1990 (1)

J. C. Alexander, E. J. Doedel, and H. G. Othmer, “On the resonance structure in a forced excitable system,” SIAM J. Appl. Math. 50, 1373–1418 (1990).
[Crossref]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347 (1980).
[Crossref]

Abraham, N. B.

Ackemann, T.

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. 100, 103703 (2012).
[Crossref]

Alexander, J. C.

J. C. Alexander, E. J. Doedel, and H. G. Othmer, “On the resonance structure in a forced excitable system,” SIAM J. Appl. Math. 50, 1373–1418 (1990).
[Crossref]

Aliaga, J.

J. M. Mendez, R. Laje, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[Crossref]

Aragoneses, A.

A. Aragoneses, T. Sorrentino, S. Perrone, D. J. Gauthier, M. C. Torrent, and C. Masoller, “Experimental and numerical study of the symbolic dynamics of a modulated external-cavity semiconductor laser,” Opt. Express 22, 4705–4713 (2014).
[Crossref] [PubMed]

A. Aragoneses, S. Perrone, T. Sorrentino, M. C. Torrent, and C. Masoller, “Unveiling the complex organization of recurrent patterns in spiking dynamical systems,” Sci. Rep. 4, 4696 (2014).
[Crossref] [PubMed]

Balle, S.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[Crossref] [PubMed]

Bandt, C.

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88, 174102 (2002).
[Crossref] [PubMed]

Barbay, S.

F. Selmi, R. Braive, G. Breaudoin, 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]

Barland, S.

M. Turconi, B. Garbin, M. Feyereisen, M. Giudici, and S. Barland, “Control of excitable pulses in an injection-locked semiconductor laser,” Phys. Rev. E 88, 022923 (2013).
[Crossref]

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang–Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[Crossref]

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[Crossref] [PubMed]

Beri, S.

W. Coomans, L. Gelens, L. Mashal, 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]

Blondel, M.

Braive, R.

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

Breaudoin, G.

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

Buldú, J. M.

J. M. Buldú, D. R. Chialvo, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, “Ghost resonance in a semiconductor laser with optical feedback,” Europhys. Lett. 64, 178 (2003).
[Crossref]

J. M. Buldú, J. García-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[Crossref]

Cavalcante, H. L. D. de S.

J. F. Martínez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Experimental deterministic coherent resonance,” Phys. Rev. Lett. 93, 144101 (2004).
[Crossref]

Chialvo, D. R.

J. M. Buldú, D. R. Chialvo, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, “Ghost resonance in a semiconductor laser with optical feedback,” Europhys. Lett. 64, 178 (2003).
[Crossref]

Coomans, W.

W. Coomans, L. Gelens, L. Mashal, 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]

Danckaert, J.

W. Coomans, L. Gelens, L. Mashal, 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]

Delorme, A.

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

Doedel, E. J.

J. C. Alexander, E. J. Doedel, and H. G. Othmer, “On the resonance structure in a forced excitable system,” SIAM J. Appl. Math. 50, 1373–1418 (1990).
[Crossref]

Feyereisen, M.

M. Turconi, B. Garbin, M. Feyereisen, M. Giudici, and S. Barland, “Control of excitable pulses in an injection-locked semiconductor laser,” Phys. Rev. E 88, 022923 (2013).
[Crossref]

Fischer, I.

K. Hicke, X. Porte, and I. Fischer, “Characterizing the deterministic nature of individual power dropouts in semiconductor lasers subject to delayed feedback,” Phys. Rev. E 88, 052904 (2013).
[Crossref]

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47, 252–261 (2011).
[Crossref]

Fries, P.

D. Nikolić, P. Fries, and W. Singer, “Gamma oscillations: precise temporal coordination without a metronome,” Trends Cogn. Sci. 17, 54 (2013).
[Crossref]

Garbin, B.

M. Turconi, B. Garbin, M. Feyereisen, M. Giudici, and S. Barland, “Control of excitable pulses in an injection-locked semiconductor laser,” Phys. Rev. E 88, 022923 (2013).
[Crossref]

Garcia-Ojalvo, J.

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, “Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 82, 013189 (2010).
[Crossref]

García-Ojalvo, J.

T. Schwalger, J. Tiana-Alsina, M. C. Torrent, J. García-Ojalvo, and B. Lindner, “Interspike-interval correlations induced by two-state switching in an excitable system,” Europhys. Lett. 99, 10004 (2012).
[Crossref]

J. Zamora-Munt, C. Masoller, and J. García-Ojalvo, “Transient low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 81, 033820 (2010).
[Crossref]

B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392, 321–424 (2004).
[Crossref]

J. M. Buldú, D. R. Chialvo, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, “Ghost resonance in a semiconductor laser with optical feedback,” Europhys. Lett. 64, 178 (2003).
[Crossref]

J. M. Buldú, J. García-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[Crossref]

Gardner, J. R.

D. W. Sukow, J. R. Gardner, and D. J. Gauthier, “Statistics of power-dropout events in semiconductor lasers with time-delayed optical feedback,” Phys. Rev. A. 56, R3370 (1997).
[Crossref]

Gauthier, D. J.

A. Aragoneses, T. Sorrentino, S. Perrone, D. J. Gauthier, M. C. Torrent, and C. Masoller, “Experimental and numerical study of the symbolic dynamics of a modulated external-cavity semiconductor laser,” Opt. Express 22, 4705–4713 (2014).
[Crossref] [PubMed]

D. W. Sukow and D. J. Gauthier, “Entraining power-dropout events in an external-cavity semiconductor laser using weak modulation of the injection current,” IEEE J. Quantum Electron. 36, 175 (2000).
[Crossref]

D. W. Sukow, J. R. Gardner, and D. J. Gauthier, “Statistics of power-dropout events in semiconductor lasers with time-delayed optical feedback,” Phys. Rev. A. 56, R3370 (1997).
[Crossref]

Gelens, L.

W. Coomans, L. Gelens, L. Mashal, 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]

Giacomelli, G.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang–Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[Crossref]

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414 (1997).
[Crossref]

Giudici, M.

M. Turconi, B. Garbin, M. Feyereisen, M. Giudici, and S. Barland, “Control of excitable pulses in an injection-locked semiconductor laser,” Phys. Rev. E 88, 022923 (2013).
[Crossref]

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[Crossref] [PubMed]

J. M. Mendez, R. Laje, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[Crossref]

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414 (1997).
[Crossref]

Green, C.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414 (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,” Appl. Phys. Lett. 100, 103703 (2012).
[Crossref]

Hicke, K.

K. Hicke, X. Porte, and I. Fischer, “Characterizing the deterministic nature of individual power dropouts in semiconductor lasers subject to delayed feedback,” Phys. Rev. E 88, 052904 (2013).
[Crossref]

Hong, Y.

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. 100, 103703 (2012).
[Crossref]

Izhikevich, E.

E. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (The MIT Press, 2007).

Kane, D. M.

Kikuchi, N.

Y. Liu, N. Kikuchi, and J. Ohtsubo, “Controlling dynamical behavior of a semiconductor laser with external optical feedback,” Phys. Rev. E 51, R2697–R2700 (1995).
[Crossref]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347 (1980).
[Crossref]

Kuszelewicz, R.

F. Selmi, R. Braive, G. Breaudoin, 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]

Laje, R.

J. M. Mendez, R. Laje, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[Crossref]

Lam, W.-S.

W.-S. Lam, N. Parvez, and R. Roy, “Effect of spontaneous emission noise and modulation on semiconductor lasers near threshold with optical feedback,” Int. J. Mod. Phys. B 17, 4123–4138 (2003).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347 (1980).
[Crossref]

Lee, M. W.

Lindner, B.

T. Schwalger, J. Tiana-Alsina, M. C. Torrent, J. García-Ojalvo, and B. Lindner, “Interspike-interval correlations induced by two-state switching in an excitable system,” Europhys. Lett. 99, 10004 (2012).
[Crossref]

B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392, 321–424 (2004).
[Crossref]

Liu, Y.

Y. Takiguchi, Y. Liu, and J. Ohtsubo, “Low-frequency fluctuation induced by injection-current modulation in semiconductor lasers with optical feedback,” Opt. Lett. 23, 1369–1371 (1998).
[Crossref]

Y. Liu, N. Kikuchi, and J. Ohtsubo, “Controlling dynamical behavior of a semiconductor laser with external optical feedback,” Phys. Rev. E 51, R2697–R2700 (1995).
[Crossref]

Marin, F.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang–Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[Crossref]

Marino, F.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[Crossref] [PubMed]

Martínez Avila, J. F.

J. F. Martínez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Experimental deterministic coherent resonance,” Phys. Rev. Lett. 93, 144101 (2004).
[Crossref]

Mashal, L.

W. Coomans, L. Gelens, L. Mashal, 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]

Masoller, C.

A. Aragoneses, S. Perrone, T. Sorrentino, M. C. Torrent, and C. Masoller, “Unveiling the complex organization of recurrent patterns in spiking dynamical systems,” Sci. Rep. 4, 4696 (2014).
[Crossref] [PubMed]

A. Aragoneses, T. Sorrentino, S. Perrone, D. J. Gauthier, M. C. Torrent, and C. Masoller, “Experimental and numerical study of the symbolic dynamics of a modulated external-cavity semiconductor laser,” Opt. Express 22, 4705–4713 (2014).
[Crossref] [PubMed]

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, “Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 82, 013189 (2010).
[Crossref]

J. Zamora-Munt, C. Masoller, and J. García-Ojalvo, “Transient low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 81, 033820 (2010).
[Crossref]

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Mégret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers”, J. Opt. Soc. Am. B 20, 37 (2003).
[Crossref]

Mégret, P.

Mendez, J. M.

J. M. Mendez, R. Laje, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[Crossref]

Mindlin, G. B.

J. M. Mendez, R. Laje, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[Crossref]

Mirasso, C. R.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47, 252–261 (2011).
[Crossref]

J. M. Buldú, D. R. Chialvo, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, “Ghost resonance in a semiconductor laser with optical feedback,” Europhys. Lett. 64, 178 (2003).
[Crossref]

J. M. Buldú, J. García-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[Crossref]

J. Mulet and C. R. Mirasso, “Numerical statistics of power dropouts based on the Lang-Kobayashi model,” Phys. Rev. E 59, 5400 (1999).
[Crossref]

Mulet, J.

J. Mulet and C. R. Mirasso, “Numerical statistics of power dropouts based on the Lang-Kobayashi model,” Phys. Rev. E 59, 5400 (1999).
[Crossref]

Nahmias, M. A.

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. Top. Quantum Electron. 19, 1800212 (2013).
[Crossref]

Neiman, A.

B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392, 321–424 (2004).
[Crossref]

Neiman, A. B.

A. B. Neiman and D. F. Russell, “Models of stochastic biperiodic oscillations and extended serial correlations in electroreceptors of paddlefish,” Phys. Rev. E 71, 061915 (2005).
[Crossref]

Nespolo, U.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414 (1997).
[Crossref]

Nikolic, D.

D. Nikolić, P. Fries, and W. Singer, “Gamma oscillations: precise temporal coordination without a metronome,” Trends Cogn. Sci. 17, 54 (2013).
[Crossref]

Ohtsubo, J.

Y. Takiguchi, Y. Liu, and J. Ohtsubo, “Low-frequency fluctuation induced by injection-current modulation in semiconductor lasers with optical feedback,” Opt. Lett. 23, 1369–1371 (1998).
[Crossref]

Y. Liu, N. Kikuchi, and J. Ohtsubo, “Controlling dynamical behavior of a semiconductor laser with external optical feedback,” Phys. Rev. E 51, R2697–R2700 (1995).
[Crossref]

Othmer, H. G.

J. C. Alexander, E. J. Doedel, and H. G. Othmer, “On the resonance structure in a forced excitable system,” SIAM J. Appl. Math. 50, 1373–1418 (1990).
[Crossref]

Parvez, N.

W.-S. Lam, N. Parvez, and R. Roy, “Effect of spontaneous emission noise and modulation on semiconductor lasers near threshold with optical feedback,” Int. J. Mod. Phys. B 17, 4123–4138 (2003).
[Crossref]

Perrone, S.

A. Aragoneses, S. Perrone, T. Sorrentino, M. C. Torrent, and C. Masoller, “Unveiling the complex organization of recurrent patterns in spiking dynamical systems,” Sci. Rep. 4, 4696 (2014).
[Crossref] [PubMed]

A. Aragoneses, T. Sorrentino, S. Perrone, D. J. Gauthier, M. C. Torrent, and C. Masoller, “Experimental and numerical study of the symbolic dynamics of a modulated external-cavity semiconductor laser,” Opt. Express 22, 4705–4713 (2014).
[Crossref] [PubMed]

Pompe, B.

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88, 174102 (2002).
[Crossref] [PubMed]

Porte, X.

K. Hicke, X. Porte, and I. Fischer, “Characterizing the deterministic nature of individual power dropouts in semiconductor lasers subject to delayed feedback,” Phys. Rev. E 88, 052904 (2013).
[Crossref]

Prucnal, P. R.

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. Top. Quantum Electron. 19, 1800212 (2013).
[Crossref]

Rios Leite, J. R.

J. F. Martínez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Experimental deterministic coherent resonance,” Phys. Rev. Lett. 93, 144101 (2004).
[Crossref]

Rogister, F.

Rosso, O. A.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47, 252–261 (2011).
[Crossref]

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, “Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 82, 013189 (2010).
[Crossref]

Roy, R.

W.-S. Lam, N. Parvez, and R. Roy, “Effect of spontaneous emission noise and modulation on semiconductor lasers near threshold with optical feedback,” Int. J. Mod. Phys. B 17, 4123–4138 (2003).
[Crossref]

Russell, D. F.

A. B. Neiman and D. F. Russell, “Models of stochastic biperiodic oscillations and extended serial correlations in electroreceptors of paddlefish,” Phys. Rev. E 71, 061915 (2005).
[Crossref]

Sagnes, I.

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

Schimansky-Geier, L.

B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392, 321–424 (2004).
[Crossref]

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,” Appl. Phys. Lett. 100, 103703 (2012).
[Crossref]

Schwalger, T.

T. Schwalger, J. Tiana-Alsina, M. C. Torrent, J. García-Ojalvo, and B. Lindner, “Interspike-interval correlations induced by two-state switching in an excitable system,” Europhys. Lett. 99, 10004 (2012).
[Crossref]

Sciamanna, M.

Selmi, F.

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

Shastri, B. J.

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. Top. Quantum Electron. 19, 1800212 (2013).
[Crossref]

Shore, K. A.

Singer, W.

D. Nikolić, P. Fries, and W. Singer, “Gamma oscillations: precise temporal coordination without a metronome,” Trends Cogn. Sci. 17, 54 (2013).
[Crossref]

Soriano, M. C.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47, 252–261 (2011).
[Crossref]

Sorrentino, T.

A. Aragoneses, T. Sorrentino, S. Perrone, D. J. Gauthier, M. C. Torrent, and C. Masoller, “Experimental and numerical study of the symbolic dynamics of a modulated external-cavity semiconductor laser,” Opt. Express 22, 4705–4713 (2014).
[Crossref] [PubMed]

A. Aragoneses, S. Perrone, T. Sorrentino, M. C. Torrent, and C. Masoller, “Unveiling the complex organization of recurrent patterns in spiking dynamical systems,” Sci. Rep. 4, 4696 (2014).
[Crossref] [PubMed]

Sukow, D. W.

D. W. Sukow and D. J. Gauthier, “Entraining power-dropout events in an external-cavity semiconductor laser using weak modulation of the injection current,” IEEE J. Quantum Electron. 36, 175 (2000).
[Crossref]

D. W. Sukow, J. R. Gardner, and D. J. Gauthier, “Statistics of power-dropout events in semiconductor lasers with time-delayed optical feedback,” Phys. Rev. A. 56, R3370 (1997).
[Crossref]

Tait, A. N.

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. Top. Quantum Electron. 19, 1800212 (2013).
[Crossref]

Takiguchi, Y.

Thorpe, S.

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

Tiana-Alsina, J.

T. Schwalger, J. Tiana-Alsina, M. C. Torrent, J. García-Ojalvo, and B. Lindner, “Interspike-interval correlations induced by two-state switching in an excitable system,” Europhys. Lett. 99, 10004 (2012).
[Crossref]

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, “Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 82, 013189 (2010).
[Crossref]

Toomey, J. P.

Torcini, A.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang–Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[Crossref]

Torrent, M. C.

A. Aragoneses, S. Perrone, T. Sorrentino, M. C. Torrent, and C. Masoller, “Unveiling the complex organization of recurrent patterns in spiking dynamical systems,” Sci. Rep. 4, 4696 (2014).
[Crossref] [PubMed]

A. Aragoneses, T. Sorrentino, S. Perrone, D. J. Gauthier, M. C. Torrent, and C. Masoller, “Experimental and numerical study of the symbolic dynamics of a modulated external-cavity semiconductor laser,” Opt. Express 22, 4705–4713 (2014).
[Crossref] [PubMed]

T. Schwalger, J. Tiana-Alsina, M. C. Torrent, J. García-Ojalvo, and B. Lindner, “Interspike-interval correlations induced by two-state switching in an excitable system,” Europhys. Lett. 99, 10004 (2012).
[Crossref]

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, “Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 82, 013189 (2010).
[Crossref]

J. M. Buldú, D. R. Chialvo, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, “Ghost resonance in a semiconductor laser with optical feedback,” Europhys. Lett. 64, 178 (2003).
[Crossref]

J. M. Buldú, J. García-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[Crossref]

Tredicce, J. R.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414 (1997).
[Crossref]

Turconi, M.

M. Turconi, B. Garbin, M. Feyereisen, M. Giudici, and S. Barland, “Control of excitable pulses in an injection-locked semiconductor laser,” Phys. Rev. E 88, 022923 (2013).
[Crossref]

Van der Sande, G.

W. Coomans, L. Gelens, L. Mashal, 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]

Van Rullen, R.

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

Yacomotti, A. M.

Zamora-Munt, J.

J. Zamora-Munt, C. Masoller, and J. García-Ojalvo, “Transient low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 81, 033820 (2010).
[Crossref]

Zunino, L.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47, 252–261 (2011).
[Crossref]

Appl. Phys. Lett. (1)

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. 100, 103703 (2012).
[Crossref]

Europhys. Lett. (2)

J. M. Buldú, D. R. Chialvo, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, “Ghost resonance in a semiconductor laser with optical feedback,” Europhys. Lett. 64, 178 (2003).
[Crossref]

T. Schwalger, J. Tiana-Alsina, M. C. Torrent, J. García-Ojalvo, and B. Lindner, “Interspike-interval correlations induced by two-state switching in an excitable system,” Europhys. Lett. 99, 10004 (2012).
[Crossref]

IEEE J. Quantum Electron. (3)

D. W. Sukow and D. J. Gauthier, “Entraining power-dropout events in an external-cavity semiconductor laser using weak modulation of the injection current,” IEEE J. Quantum Electron. 36, 175 (2000).
[Crossref]

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47, 252–261 (2011).
[Crossref]

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347 (1980).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

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. Top. Quantum Electron. 19, 1800212 (2013).
[Crossref]

Int. J. Mod. Phys. B (1)

W.-S. Lam, N. Parvez, and R. Roy, “Effect of spontaneous emission noise and modulation on semiconductor lasers near threshold with optical feedback,” Int. J. Mod. Phys. B 17, 4123–4138 (2003).
[Crossref]

J. Opt. Soc. Am. B (1)

Neural Netw. (1)

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

Opt. Express (4)

Opt. Lett. (3)

Phys. Rep. (1)

B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392, 321–424 (2004).
[Crossref]

Phys. Rev. A (3)

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang–Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[Crossref]

J. Zamora-Munt, C. Masoller, and J. García-Ojalvo, “Transient low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 81, 033820 (2010).
[Crossref]

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, “Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback,” Phys. Rev. A 82, 013189 (2010).
[Crossref]

Phys. Rev. A. (1)

D. W. Sukow, J. R. Gardner, and D. J. Gauthier, “Statistics of power-dropout events in semiconductor lasers with time-delayed optical feedback,” Phys. Rev. A. 56, R3370 (1997).
[Crossref]

Phys. Rev. E (9)

J. Mulet and C. R. Mirasso, “Numerical statistics of power dropouts based on the Lang-Kobayashi model,” Phys. Rev. E 59, 5400 (1999).
[Crossref]

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414 (1997).
[Crossref]

J. M. Buldú, J. García-Ojalvo, C. R. Mirasso, and M. C. Torrent, “Stochastic entrainment of optical power dropouts,” Phys. Rev. E 66, 021106 (2002).
[Crossref]

K. Hicke, X. Porte, and I. Fischer, “Characterizing the deterministic nature of individual power dropouts in semiconductor lasers subject to delayed feedback,” Phys. Rev. E 88, 052904 (2013).
[Crossref]

Y. Liu, N. Kikuchi, and J. Ohtsubo, “Controlling dynamical behavior of a semiconductor laser with external optical feedback,” Phys. Rev. E 51, R2697–R2700 (1995).
[Crossref]

M. Turconi, B. Garbin, M. Feyereisen, M. Giudici, and S. Barland, “Control of excitable pulses in an injection-locked semiconductor laser,” Phys. Rev. E 88, 022923 (2013).
[Crossref]

W. Coomans, L. Gelens, L. Mashal, 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]

J. M. Mendez, R. Laje, M. Giudici, J. Aliaga, and G. B. Mindlin, “Dynamics of periodically forced semiconductor laser with optical feedback,” Phys. Rev. E 63, 066218 (2001).
[Crossref]

A. B. Neiman and D. F. Russell, “Models of stochastic biperiodic oscillations and extended serial correlations in electroreceptors of paddlefish,” Phys. Rev. E 71, 061915 (2005).
[Crossref]

Phys. Rev. Lett. (4)

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[Crossref] [PubMed]

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88, 174102 (2002).
[Crossref] [PubMed]

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[Crossref]

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[Crossref] [PubMed]

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A. Aragoneses, S. Perrone, T. Sorrentino, M. C. Torrent, and C. Masoller, “Unveiling the complex organization of recurrent patterns in spiking dynamical systems,” Sci. Rep. 4, 4696 (2014).
[Crossref] [PubMed]

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[Crossref]

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[Crossref]

Other (2)

B. J. Shastri, M. A. Nahmias, A. N. Tait, B. Wu, and P. R. Prucnal, “SIMPEL: Circuit model for photonic spike processing laser neurons,” http://arxiv.org/abs/1409.7030 [physics.optics] (2014).

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Figures (6)

Fig. 1
Fig. 1

Experimental time series of LFF intensity spikes (left column) and the corresponding inter-spike-interval (ISI) distribution (right column). The modulation amplitude is 1.2% of IDC and the modulation frequency is 7 MHz (a–b); 14 MHz (c–d); 26 MHz (e–f); 31 MHz (g–h); 39 MHz (i–j); 49 MHz (k–l). In the left panels only 30 modulation cycles are shown, but the ISI distributions in the right panels are computed from 40000 ISIs.

Fig. 2
Fig. 2

(a) Mean ISI as a function of the modulation frequency for several modulation amplitudes. (b) Ratio between the mean ISI and the modulation period, <ΔT>/Tmod, versus modulation frequency for several modulation amplitudes.

Fig. 3
Fig. 3

Probability, pn, that an ISI value is within the interval nTmodTmod/2, nTmod + Tmod/2. n values in the legend. The first five probabilities are shown, for the same modulation amplitude as Fig. 1 (1.2%).

Fig. 4
Fig. 4

(a) Probabilities of D = 2 ordinal patterns and the transition probabilities. (b) D = 3 OPs probabilities. (c), (d) Same as (a),(b) but when the OPs and TPs are computed from surrogate (shuffled) IDI sequences.

Fig. 5
Fig. 5

Histograms probabilities and OPs and transition probabilities for D = 2 versus modulation frequency for four different modulation amplitudes. 0.8% of IDC (a,c); 1.2% (b,d); 1.6% (e,g); 2.0% (f,h). Legends as in Figs. 3 and 4(a).

Fig. 6
Fig. 6

First row: OP and transition probabilities for D = 2. (a) Experimental, (b) Numerical. Second row: OP probabilities for D = 3. (c) Experimental, (d) Numerical. Modulation amplitude: 0.8% of IDC. Legends as in Fig. 4.

Equations (2)

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d E d t = 1 2 τ p ( 1 + i α ) ( G 1 ) E + η E ( t τ ) e i ω 0 τ + 2 β sp ξ ,
d N d t = 1 τ N ( μ N G | E | 2 ) ,

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