Noise-assisted transmission of binary information: Theory and experiment

Sylvain Barbay; Giovanni Giacomelli; Francesco Marin

doi:10.1103/PhysRevE.63.051110

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Noise-assisted transmission of binary information: Theory and experiment

Sylvain Barbay¹, Giovanni Giacomelli^1,2,*, and Francesco Marin^2,3

¹Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy
²Istituto Nazionale di Fisica della Materia, unità di Firenze, Firenze, Italy
³Dipartimento di Fisica, Università di Firenze, and Laboratorio Europeo di Spettroscopia Nonlineare, Largo E. Fermi 2, 50125 Firenze, Italy

^*Email address: gianni@ino.it

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Phys. Rev. E 63, 051110 – Published 23 April, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.051110

Abstract

We study the response of a bistable vertical cavity surface emitting laser to an aperiodic binary signal, by adding a variable amount of noise. The resulting behavior is an example of aperiodic stochastic resonance, and in this work we give a detailed comparison between analytical and numerical results and accurate experimental measurements. We characterize the phenomenon by using different appropriate indicators, which also allow us to quantify the binary information transmission. We show that the quality of the transmission is enhanced by a suitable amount of noise, and we give a physical picture of the phenomenon.

References (24)

R. Benzi, A. Sutera, and A. Vulpiani, J. Phys. A 14, 453 (1981); R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, Tellus 34, 10 (1982).
C. Nicolis and G. Nicolis, Tellus 33, 225 (1981).
B. McNamara, K. Wiesenfeld, and R. Roy, Phys. Rev. Lett. 60, 2626 (1988).
See, e.g., L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998), and references therein.
G. Giacomelli, F. Marin, and I. Rabbiosi, Phys. Rev. Lett. 82, 675 (1999).
S. Barbay, G. Giacomelli, and F. Marin, Phys. Rev. E 61, 157 (2000).
A. Neiman and L. Schimansky-Geier, Phys. Rev. Lett. 72, 2988 (1994).
J.J. Collins, C.C. Chow, and T.T. Imhoff, Phys. Rev. E 52, R3321 (1995); Nature (London) 376, 236 (1995).
J.J. Collins, C.C. Chow, A.C. Capela, and T.T. Imhoff, Phys. Rev. E 54, 5575 (1996).
A. Neiman, L. Schimansky-Geier, F. Moss, B. Shulgin, and J.J. Collins, Phys. Rev. E 60, 284 (1999).
F. Chapeau-Blondeau, Phys. Rev. E 55, 2016 (1997).
P. Cordo et al., Nature (London) 383, 769 (1996); ibid.J.J. Collins, T.T. Imhoff, and P. Grigg, 383, 770 (1996); J. Neurophysiol. 76, 642 (1996); E. Simonotto et al., Phys. Rev. Lett. 78, 1186 (1997); A. Fulinski, Chaos 8, 549 (1998), and references therein.
S. Barbay, G. Giacomelli, and F. Marin, Phys. Rev. Lett. 85, 4652 (2000).
S. Barbay, G. Giacomelli, and F. Marin, Opt. Lett. 25, 1095 (2000); Un procedimento ed un dispositivo di trasmissione ottica di informazioni codificate, Italian patent, February 15, 2000.
J. van’t Hoff, in Etudes de Dynamiques Chimiques (Muller, Amsterdam, 1884).
S. Arrhenius, Z. Phys. Chem. (Leipzig) 4, 226 (1889).
H. Kramers, Physica (Utrecht) 7, 284 (1940).
M. San Miguel, Q. Feng, and J.V. Moloney, Phys. Rev. A 52, 1728 (1995); J. Martin-Regalado, F. Prati, M. San Miguel, and N.B. Abra-ham, IEEE J. Quantum Electron. 33, 765 (1997).
M.B. Willemsen, M.U.F. Khalid, M.P. van Exter, and J.P. Woerdman, Phys. Rev. Lett. 82, 4815 (1999).
J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux (unpublished).
G. Giacomelli and F. Marin, Quantum Semiclassic. Opt. 10, 469 (1998).
R.L. Honeycutt, Phys. Rev. A 45, 600 (1992).
We assume that $\int_{a}^{b} δ (x - x_{0} {) f (x) d x = f (x}_{0})$ if $x_{0} \in [a, b]$ (extrema included).
P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).

[c1] R. Benzi, A. Sutera, and A. Vulpiani, J. Phys. A 14, 453 (1981); R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, Tellus 34, 10 (1982).

[c2] C. Nicolis and G. Nicolis, Tellus 33, 225 (1981).

[c3] B. McNamara, K. Wiesenfeld, and R. Roy, Phys. Rev. Lett. 60, 2626 (1988).

[c4] See, e.g., L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998), and references therein.

[c5] G. Giacomelli, F. Marin, and I. Rabbiosi, Phys. Rev. Lett. 82, 675 (1999).

[c6] S. Barbay, G. Giacomelli, and F. Marin, Phys. Rev. E 61, 157 (2000).

[c7] A. Neiman and L. Schimansky-Geier, Phys. Rev. Lett. 72, 2988 (1994).

[c8] J.J. Collins, C.C. Chow, and T.T. Imhoff, Phys. Rev. E 52, R3321 (1995); Nature (London) 376, 236 (1995).

[c9] J.J. Collins, C.C. Chow, A.C. Capela, and T.T. Imhoff, Phys. Rev. E 54, 5575 (1996).

[c10] A. Neiman, L. Schimansky-Geier, F. Moss, B. Shulgin, and J.J. Collins, Phys. Rev. E 60, 284 (1999).

[c11] F. Chapeau-Blondeau, Phys. Rev. E 55, 2016 (1997).

[c12] P. Cordo et al., Nature (London) 383, 769 (1996); ibid.J.J. Collins, T.T. Imhoff, and P. Grigg, 383, 770 (1996); J. Neurophysiol. 76, 642 (1996); E. Simonotto et al., Phys. Rev. Lett. 78, 1186 (1997); A. Fulinski, Chaos 8, 549 (1998), and references therein.

[c13] S. Barbay, G. Giacomelli, and F. Marin, Phys. Rev. Lett. 85, 4652 (2000).

[c14] S. Barbay, G. Giacomelli, and F. Marin, Opt. Lett. 25, 1095 (2000); Un procedimento ed un dispositivo di trasmissione ottica di informazioni codificate, Italian patent, February 15, 2000.

[c15] J. van’t Hoff, in Etudes de Dynamiques Chimiques (Muller, Amsterdam, 1884).

[c16] S. Arrhenius, Z. Phys. Chem. (Leipzig) 4, 226 (1889).

[c17] H. Kramers, Physica (Utrecht) 7, 284 (1940).

[c18] M. San Miguel, Q. Feng, and J.V. Moloney, Phys. Rev. A 52, 1728 (1995); J. Martin-Regalado, F. Prati, M. San Miguel, and N.B. Abra-ham, IEEE J. Quantum Electron. 33, 765 (1997).

[c19] M.B. Willemsen, M.U.F. Khalid, M.P. van Exter, and J.P. Woerdman, Phys. Rev. Lett. 82, 4815 (1999).

[c20] J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux (unpublished).

[c21] G. Giacomelli and F. Marin, Quantum Semiclassic. Opt. 10, 469 (1998).

[c22] R.L. Honeycutt, Phys. Rev. A 45, 600 (1992).

[c23] We assume that $\int_{a}^{b} δ (x - x_{0} {) f (x) d x = f (x}_{0})$ if $x_{0} \in [a, b]$ (extrema included).

[c24] P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).

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Noise-assisted transmission of binary information: Theory and experiment

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