Abstract

Stochastic resonance is theoretically investigated in an optical bistable system, which consists of a unidirectional ring cavity and a photorefractive two-wave mixer. It is found that the output properties of stochastic resonance are mainly determined by the applied noise, the crystal length and the applied electric field. The influences of these parameters on the stochastic resonance are also numerically analyzed via cross-correlation, which offers general guidelines for the optimization of recovering noise-hidden signals. A cross-correlation gain of 4 is obtained by optimizing these parameters. This provides a general method for reconstructing signals in nonlinear communications systems.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Chen, P. K. Varshney, S. M. Kay, J. H. Michels, “Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors,” IEEE Trans. Signal Processing 55(7), 3172–3184 (2007).
    [CrossRef]
  2. R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–16 (1982).
    [CrossRef]
  3. C. Nicolis, “Stochastic aspects of climatic transitions—response to a periodic forcing,” Tellus 34(1), 1–9 (1982).
    [CrossRef]
  4. S. Fauve, F. Heslot, “Stochastic resonance in a bistable system,” Phys. Lett. A 97(1–2), 5–7 (1983).
    [CrossRef]
  5. S. M. Bezrukov, I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature 385(6614), 319–321 (1997).
    [CrossRef] [PubMed]
  6. J. K. Douglass, L. Wilkens, E. Pantazelou, F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
    [CrossRef] [PubMed]
  7. A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen, K. Lindenberg, “Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 3958–3969 (1996).
    [CrossRef] [PubMed]
  8. R. L. Badzey, P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005).
    [CrossRef] [PubMed]
  9. H. B. Chan, C. Stambaugh, “Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator,” Phys. Rev. B 73(22), 224301 (2006).
    [CrossRef]
  10. D. V. Dylov, J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nature 4, 323–328 (1993).
  11. F. Vaudelle, J. Gazengel, G. Rivoire, X. Godivier, F. Chapeau-Blondeau, “Stochastic resonance and noise-enhanced transmission of spatial signals in optics: the case of scattering,” J. Opt. Soc. Am. B 15(11), 2674–2680 (1998).
    [CrossRef]
  12. B. M. Jost, B. E. A. Saleh, “Signal-to-noise ratio improvement by stochastic resonance in a unidirectional photorefractive ring resonator,” Opt. Lett. 21(4), 287–289 (1996).
    [CrossRef] [PubMed]
  13. S. Weiss, B. Fischer, “Photorefractive saturable absorptive and dispersive optical bistability,” Opt. Commun. 70(6), 515–521 (1989).
    [CrossRef]
  14. R. Daisy, B. Fischer, “Optical bistability in a nonlinear - linear interface with two-wave mixing,” Opt. Lett. 17(12), 847–849 (1992).
    [CrossRef] [PubMed]
  15. R. Bartussek, P. Hänggi, P. Jung, “Stochastic resonance in optical bistable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(5), 3930–3939 (1994).
    [CrossRef] [PubMed]
  16. L. Zhang, L. Cao, D. J. Wu, “Effect of correlated noises in an optical bistable system,” Phys. Rev. A 77(1), 015801 (2008).
    [CrossRef]
  17. M. Misono, T. Kohmoto, Y. Fukuda, M. Kunitomo, “Stochastic resonance in an optical bistable system driven by colored noise,” Opt. Commun. 152(4), 255–258 (1998).
    [CrossRef]
  18. J. E. Ford, J. Ma, Y. Fainman, S. H. Lee, “Multiplex holography in strontium barium niobate with applied field,” J. Opt. Soc. Am. B 9(7), 1183–1192 (1992).
  19. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).
  20. S. K. Kwong, M. C. Golomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22(8), 1508–1523 (1986).
    [CrossRef]
  21. R. Bonifacio, L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18(3), 1129–1144 (1978).
    [CrossRef]
  22. P. Yeh, “Theory of unidirectional photorefractive ring oscillators,” J. Opt. Soc. Am. B 2(12), 1924–1928 (1985).
    [CrossRef]
  23. J. Ma, D. Zeng, H. Chen, “Spatial-temporal cross-correlation analysis: a new measure and a case study in infectious disease informatics,” in IEEE International Conference on Intelligence and Security Informatics (2006).
    [CrossRef]
  24. V. S. Anishchenko, M. A. Safonova, L. O. Chua, “Stochastic resonance in the nonautonomous Chua's circuit,” J. Circuits Syst. Comput. 3(2), 553–578 (1993).
    [CrossRef]
  25. B. Xu, Z. P. Jiang, X. Wu, and D. W. Repperger, “Theoretical analysis of image processing using parameter-tuning stochastic resonance technique,” in IEEE American Control Conference ACC'07 (2007), pp. 1747–1752.
    [CrossRef]

2008 (1)

L. Zhang, L. Cao, D. J. Wu, “Effect of correlated noises in an optical bistable system,” Phys. Rev. A 77(1), 015801 (2008).
[CrossRef]

2007 (1)

H. Chen, P. K. Varshney, S. M. Kay, J. H. Michels, “Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors,” IEEE Trans. Signal Processing 55(7), 3172–3184 (2007).
[CrossRef]

2006 (1)

H. B. Chan, C. Stambaugh, “Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator,” Phys. Rev. B 73(22), 224301 (2006).
[CrossRef]

2005 (1)

R. L. Badzey, P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005).
[CrossRef] [PubMed]

1998 (2)

F. Vaudelle, J. Gazengel, G. Rivoire, X. Godivier, F. Chapeau-Blondeau, “Stochastic resonance and noise-enhanced transmission of spatial signals in optics: the case of scattering,” J. Opt. Soc. Am. B 15(11), 2674–2680 (1998).
[CrossRef]

M. Misono, T. Kohmoto, Y. Fukuda, M. Kunitomo, “Stochastic resonance in an optical bistable system driven by colored noise,” Opt. Commun. 152(4), 255–258 (1998).
[CrossRef]

1997 (1)

S. M. Bezrukov, I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature 385(6614), 319–321 (1997).
[CrossRef] [PubMed]

1996 (2)

A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen, K. Lindenberg, “Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 3958–3969 (1996).
[CrossRef] [PubMed]

B. M. Jost, B. E. A. Saleh, “Signal-to-noise ratio improvement by stochastic resonance in a unidirectional photorefractive ring resonator,” Opt. Lett. 21(4), 287–289 (1996).
[CrossRef] [PubMed]

1994 (1)

R. Bartussek, P. Hänggi, P. Jung, “Stochastic resonance in optical bistable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(5), 3930–3939 (1994).
[CrossRef] [PubMed]

1993 (3)

V. S. Anishchenko, M. A. Safonova, L. O. Chua, “Stochastic resonance in the nonautonomous Chua's circuit,” J. Circuits Syst. Comput. 3(2), 553–578 (1993).
[CrossRef]

D. V. Dylov, J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nature 4, 323–328 (1993).

J. K. Douglass, L. Wilkens, E. Pantazelou, F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[CrossRef] [PubMed]

1992 (2)

R. Daisy, B. Fischer, “Optical bistability in a nonlinear - linear interface with two-wave mixing,” Opt. Lett. 17(12), 847–849 (1992).
[CrossRef] [PubMed]

J. E. Ford, J. Ma, Y. Fainman, S. H. Lee, “Multiplex holography in strontium barium niobate with applied field,” J. Opt. Soc. Am. B 9(7), 1183–1192 (1992).

1989 (1)

S. Weiss, B. Fischer, “Photorefractive saturable absorptive and dispersive optical bistability,” Opt. Commun. 70(6), 515–521 (1989).
[CrossRef]

1986 (1)

S. K. Kwong, M. C. Golomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22(8), 1508–1523 (1986).
[CrossRef]

1985 (1)

1984 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).

1983 (1)

S. Fauve, F. Heslot, “Stochastic resonance in a bistable system,” Phys. Lett. A 97(1–2), 5–7 (1983).
[CrossRef]

1982 (2)

R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–16 (1982).
[CrossRef]

C. Nicolis, “Stochastic aspects of climatic transitions—response to a periodic forcing,” Tellus 34(1), 1–9 (1982).
[CrossRef]

1978 (1)

R. Bonifacio, L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18(3), 1129–1144 (1978).
[CrossRef]

Anishchenko, V. S.

V. S. Anishchenko, M. A. Safonova, L. O. Chua, “Stochastic resonance in the nonautonomous Chua's circuit,” J. Circuits Syst. Comput. 3(2), 553–578 (1993).
[CrossRef]

Badzey, R. L.

R. L. Badzey, P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005).
[CrossRef] [PubMed]

Bartussek, R.

R. Bartussek, P. Hänggi, P. Jung, “Stochastic resonance in optical bistable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(5), 3930–3939 (1994).
[CrossRef] [PubMed]

Benzi, R.

R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–16 (1982).
[CrossRef]

Bezrukov, S. M.

S. M. Bezrukov, I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature 385(6614), 319–321 (1997).
[CrossRef] [PubMed]

Bonifacio, R.

R. Bonifacio, L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18(3), 1129–1144 (1978).
[CrossRef]

Bulsara, A. R.

A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen, K. Lindenberg, “Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 3958–3969 (1996).
[CrossRef] [PubMed]

Cao, L.

L. Zhang, L. Cao, D. J. Wu, “Effect of correlated noises in an optical bistable system,” Phys. Rev. A 77(1), 015801 (2008).
[CrossRef]

Chan, H. B.

H. B. Chan, C. Stambaugh, “Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator,” Phys. Rev. B 73(22), 224301 (2006).
[CrossRef]

Chapeau-Blondeau, F.

Chen, H.

H. Chen, P. K. Varshney, S. M. Kay, J. H. Michels, “Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors,” IEEE Trans. Signal Processing 55(7), 3172–3184 (2007).
[CrossRef]

J. Ma, D. Zeng, H. Chen, “Spatial-temporal cross-correlation analysis: a new measure and a case study in infectious disease informatics,” in IEEE International Conference on Intelligence and Security Informatics (2006).
[CrossRef]

Chua, L. O.

V. S. Anishchenko, M. A. Safonova, L. O. Chua, “Stochastic resonance in the nonautonomous Chua's circuit,” J. Circuits Syst. Comput. 3(2), 553–578 (1993).
[CrossRef]

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).

Daisy, R.

Doering, C. R.

A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen, K. Lindenberg, “Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 3958–3969 (1996).
[CrossRef] [PubMed]

Douglass, J. K.

J. K. Douglass, L. Wilkens, E. Pantazelou, F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[CrossRef] [PubMed]

Dylov, D. V.

D. V. Dylov, J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nature 4, 323–328 (1993).

Elston, T. C.

A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen, K. Lindenberg, “Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 3958–3969 (1996).
[CrossRef] [PubMed]

Fainman, Y.

J. E. Ford, J. Ma, Y. Fainman, S. H. Lee, “Multiplex holography in strontium barium niobate with applied field,” J. Opt. Soc. Am. B 9(7), 1183–1192 (1992).

Fauve, S.

S. Fauve, F. Heslot, “Stochastic resonance in a bistable system,” Phys. Lett. A 97(1–2), 5–7 (1983).
[CrossRef]

Fischer, B.

R. Daisy, B. Fischer, “Optical bistability in a nonlinear - linear interface with two-wave mixing,” Opt. Lett. 17(12), 847–849 (1992).
[CrossRef] [PubMed]

S. Weiss, B. Fischer, “Photorefractive saturable absorptive and dispersive optical bistability,” Opt. Commun. 70(6), 515–521 (1989).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).

Fleischer, J. W.

D. V. Dylov, J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nature 4, 323–328 (1993).

Ford, J. E.

J. E. Ford, J. Ma, Y. Fainman, S. H. Lee, “Multiplex holography in strontium barium niobate with applied field,” J. Opt. Soc. Am. B 9(7), 1183–1192 (1992).

Fukuda, Y.

M. Misono, T. Kohmoto, Y. Fukuda, M. Kunitomo, “Stochastic resonance in an optical bistable system driven by colored noise,” Opt. Commun. 152(4), 255–258 (1998).
[CrossRef]

Gazengel, J.

Godivier, X.

Golomb, M. C.

S. K. Kwong, M. C. Golomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22(8), 1508–1523 (1986).
[CrossRef]

Hänggi, P.

R. Bartussek, P. Hänggi, P. Jung, “Stochastic resonance in optical bistable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(5), 3930–3939 (1994).
[CrossRef] [PubMed]

Heslot, F.

S. Fauve, F. Heslot, “Stochastic resonance in a bistable system,” Phys. Lett. A 97(1–2), 5–7 (1983).
[CrossRef]

Jost, B. M.

Jung, P.

R. Bartussek, P. Hänggi, P. Jung, “Stochastic resonance in optical bistable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(5), 3930–3939 (1994).
[CrossRef] [PubMed]

Kay, S. M.

H. Chen, P. K. Varshney, S. M. Kay, J. H. Michels, “Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors,” IEEE Trans. Signal Processing 55(7), 3172–3184 (2007).
[CrossRef]

Kohmoto, T.

M. Misono, T. Kohmoto, Y. Fukuda, M. Kunitomo, “Stochastic resonance in an optical bistable system driven by colored noise,” Opt. Commun. 152(4), 255–258 (1998).
[CrossRef]

Kunitomo, M.

M. Misono, T. Kohmoto, Y. Fukuda, M. Kunitomo, “Stochastic resonance in an optical bistable system driven by colored noise,” Opt. Commun. 152(4), 255–258 (1998).
[CrossRef]

Kwong, S. K.

S. K. Kwong, M. C. Golomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22(8), 1508–1523 (1986).
[CrossRef]

Lee, S. H.

J. E. Ford, J. Ma, Y. Fainman, S. H. Lee, “Multiplex holography in strontium barium niobate with applied field,” J. Opt. Soc. Am. B 9(7), 1183–1192 (1992).

Lindenberg, K.

A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen, K. Lindenberg, “Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 3958–3969 (1996).
[CrossRef] [PubMed]

Lowen, S. B.

A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen, K. Lindenberg, “Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 3958–3969 (1996).
[CrossRef] [PubMed]

Lugiato, L. A.

R. Bonifacio, L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18(3), 1129–1144 (1978).
[CrossRef]

Ma, J.

J. E. Ford, J. Ma, Y. Fainman, S. H. Lee, “Multiplex holography in strontium barium niobate with applied field,” J. Opt. Soc. Am. B 9(7), 1183–1192 (1992).

J. Ma, D. Zeng, H. Chen, “Spatial-temporal cross-correlation analysis: a new measure and a case study in infectious disease informatics,” in IEEE International Conference on Intelligence and Security Informatics (2006).
[CrossRef]

Michels, J. H.

H. Chen, P. K. Varshney, S. M. Kay, J. H. Michels, “Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors,” IEEE Trans. Signal Processing 55(7), 3172–3184 (2007).
[CrossRef]

Misono, M.

M. Misono, T. Kohmoto, Y. Fukuda, M. Kunitomo, “Stochastic resonance in an optical bistable system driven by colored noise,” Opt. Commun. 152(4), 255–258 (1998).
[CrossRef]

Mohanty, P.

R. L. Badzey, P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005).
[CrossRef] [PubMed]

Moss, F.

J. K. Douglass, L. Wilkens, E. Pantazelou, F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[CrossRef] [PubMed]

Nicolis, C.

C. Nicolis, “Stochastic aspects of climatic transitions—response to a periodic forcing,” Tellus 34(1), 1–9 (1982).
[CrossRef]

Pantazelou, E.

J. K. Douglass, L. Wilkens, E. Pantazelou, F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[CrossRef] [PubMed]

Parisi, G.

R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–16 (1982).
[CrossRef]

Rivoire, G.

Safonova, M. A.

V. S. Anishchenko, M. A. Safonova, L. O. Chua, “Stochastic resonance in the nonautonomous Chua's circuit,” J. Circuits Syst. Comput. 3(2), 553–578 (1993).
[CrossRef]

Saleh, B. E. A.

Stambaugh, C.

H. B. Chan, C. Stambaugh, “Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator,” Phys. Rev. B 73(22), 224301 (2006).
[CrossRef]

Sutera, A.

R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–16 (1982).
[CrossRef]

Varshney, P. K.

H. Chen, P. K. Varshney, S. M. Kay, J. H. Michels, “Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors,” IEEE Trans. Signal Processing 55(7), 3172–3184 (2007).
[CrossRef]

Vaudelle, F.

Vodyanoy, I.

S. M. Bezrukov, I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature 385(6614), 319–321 (1997).
[CrossRef] [PubMed]

Vulpiani, A.

R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–16 (1982).
[CrossRef]

Weiss, S.

S. Weiss, B. Fischer, “Photorefractive saturable absorptive and dispersive optical bistability,” Opt. Commun. 70(6), 515–521 (1989).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).

Wilkens, L.

J. K. Douglass, L. Wilkens, E. Pantazelou, F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[CrossRef] [PubMed]

Wu, D. J.

L. Zhang, L. Cao, D. J. Wu, “Effect of correlated noises in an optical bistable system,” Phys. Rev. A 77(1), 015801 (2008).
[CrossRef]

Yariv, A.

S. K. Kwong, M. C. Golomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22(8), 1508–1523 (1986).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).

Yeh, P.

Zeng, D.

J. Ma, D. Zeng, H. Chen, “Spatial-temporal cross-correlation analysis: a new measure and a case study in infectious disease informatics,” in IEEE International Conference on Intelligence and Security Informatics (2006).
[CrossRef]

Zhang, L.

L. Zhang, L. Cao, D. J. Wu, “Effect of correlated noises in an optical bistable system,” Phys. Rev. A 77(1), 015801 (2008).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).

S. K. Kwong, M. C. Golomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22(8), 1508–1523 (1986).
[CrossRef]

IEEE Trans. Signal Processing (1)

H. Chen, P. K. Varshney, S. M. Kay, J. H. Michels, “Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors,” IEEE Trans. Signal Processing 55(7), 3172–3184 (2007).
[CrossRef]

J. Circuits Syst. Comput. (1)

V. S. Anishchenko, M. A. Safonova, L. O. Chua, “Stochastic resonance in the nonautonomous Chua's circuit,” J. Circuits Syst. Comput. 3(2), 553–578 (1993).
[CrossRef]

J. Opt. Soc. Am. B (3)

Nature (4)

S. M. Bezrukov, I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature 385(6614), 319–321 (1997).
[CrossRef] [PubMed]

J. K. Douglass, L. Wilkens, E. Pantazelou, F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[CrossRef] [PubMed]

R. L. Badzey, P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005).
[CrossRef] [PubMed]

D. V. Dylov, J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nature 4, 323–328 (1993).

Opt. Commun. (2)

S. Weiss, B. Fischer, “Photorefractive saturable absorptive and dispersive optical bistability,” Opt. Commun. 70(6), 515–521 (1989).
[CrossRef]

M. Misono, T. Kohmoto, Y. Fukuda, M. Kunitomo, “Stochastic resonance in an optical bistable system driven by colored noise,” Opt. Commun. 152(4), 255–258 (1998).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (1)

S. Fauve, F. Heslot, “Stochastic resonance in a bistable system,” Phys. Lett. A 97(1–2), 5–7 (1983).
[CrossRef]

Phys. Rev. A (2)

L. Zhang, L. Cao, D. J. Wu, “Effect of correlated noises in an optical bistable system,” Phys. Rev. A 77(1), 015801 (2008).
[CrossRef]

R. Bonifacio, L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18(3), 1129–1144 (1978).
[CrossRef]

Phys. Rev. B (1)

H. B. Chan, C. Stambaugh, “Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator,” Phys. Rev. B 73(22), 224301 (2006).
[CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. (1)

R. Bartussek, P. Hänggi, P. Jung, “Stochastic resonance in optical bistable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(5), 3930–3939 (1994).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen, K. Lindenberg, “Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 3958–3969 (1996).
[CrossRef] [PubMed]

Tellus (2)

R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–16 (1982).
[CrossRef]

C. Nicolis, “Stochastic aspects of climatic transitions—response to a periodic forcing,” Tellus 34(1), 1–9 (1982).
[CrossRef]

Other (2)

J. Ma, D. Zeng, H. Chen, “Spatial-temporal cross-correlation analysis: a new measure and a case study in infectious disease informatics,” in IEEE International Conference on Intelligence and Security Informatics (2006).
[CrossRef]

B. Xu, Z. P. Jiang, X. Wu, and D. W. Repperger, “Theoretical analysis of image processing using parameter-tuning stochastic resonance technique,” in IEEE American Control Conference ACC'07 (2007), pp. 1747–1752.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Principle diagram of the unidirectional photorefractive ring cavity with an injected signal. C, crystal; BS, beam splitters; M1,2, mirrors.

Fig. 2
Fig. 2

Schematic diagram of the stochastic resonance system.

Fig. 3
Fig. 3

Photorefractive optical bistability. Normalized output intensity X versus normalized input intensity Y for (a): E0 = 0 kV/cm, leff = 1 mm (red), 3 mm (green) and 5 mm (blue) ; (b) leff = 2 mm, E0 = 0 kV/cm (red), 2 kV/cm (green) and 4 kV/cm (blue), respectively.

Fig. 4
Fig. 4

Potential V is plotted versus the input and output light intensity Y and X.

Fig. 5
Fig. 5

Transmission property of the optical stochastic resonance system. (a)-(d) Input signals Y with the white Gaussian noise intensity D = 0, D = 0.4, D = 1.2 and D = 2.0, respectively; (a′)-(d′) are the output signals X corresponding to the input signals. Insets: detail showing the signals at t = 5 s. In simulations, E0 = 2 kV/cm, leff = 2 mm.

Fig. 6
Fig. 6

Cross-correlation coefficients (a) and the cross-correlation gain (b) as a function of the noise intensity D. The black curves are under the particular conditions of fixed noise distribution. In simulations, E0 = 2 kV/cm, leff = 2 mm.

Fig. 7
Fig. 7

The cross-correlation coefficients versus (a) the interaction length leff with E0 = 2 kV/cm and (b) the applied electric field E0 with leff = 2 mm,(Y0 = 0.05, D = 1.2), respectively. Insets: cross-correlation gain. and fixed noise intensity.

Fig. 8
Fig. 8

The complex coupling coefficient (a) and the value of﹣Γ′/ Γ (b) versus the applied electric field E0, respectively.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

d A 1 dz =γ A 1 A 2 A 2 I 0 α 2 A 1 , d A 2 dz = γ A 1 A 1 A 2 I 0 α 2 A 2 ,
γ= ω r eff n 0 3 4c E q ( E 0 +i E D ) [ E 0 Ω τ 0 ( E D + E μ )]+i[ E D + E q +Ω τ 0 E 0 ] ,
d I 1 dz =Γ I 1 I 2 I 0 α I 1 , d I 2 dz =Γ I 1 I 2 I 0 α I 2 d φ 1 dz = Γ I 2 I 1 + I 2 , d φ 2 dz = Γ I 1 I 1 + I 2 .
I 1 (z)= I 1 (0) 1+m 1+mexp(Γz) exp(αz) I 2 (z)= I 2 (0) 1+m m+exp(Γz) exp(αz) Δ φ 1 (z)= Γ Γ ln( 1+m m+exp(Γz) ) , Δ φ 2 (z)= Γ Γ ln( 1+m m+exp(Γz) )
A 2 (0)= T 1/2 A in + R 1/2 A 2 (l)exp(i δ 0 ),
A out = T 1/2 A 2 (l),
I in = A in A in = T 1 [ I 2 (0)+R I 2 (l)2 R I 2 (0) I 2 (l) cos( δ 0 +Δ φ 2 ) ],
I out =T I 2 (l),
Y=[ m(X)+RX2 m(X)RX cos( δ 0 +Δ φ 2 ) ].
m(X)= 1 2 [ aX1+ (aX1) 2 +4 aX /b ],
dX dt =B(Y,X)= dV(X) dX ,
B(Y,X)=Y[ m(X)+RX2 m(X)RX cos( δ 0 +Δ φ 2 ) ],
V(X)= 0 X B(X) dX.
Y(t)= Y 0 (t)+DN(t),
Y 0 (t)= y 0 exp[2 (t/ t g ) 2 ],
C Y 0 X = Y 0 |X = ( Y 0 Y 0 )( X X ) [ ( Y 0 Y 0 ) 2 ( X X ) 2 ] 1/2 ,
C Y 0 Y = Y 0 |Y = ( Y 0 Y 0 )( Y Y ) [ ( Y 0 Y 0 ) 2 ( Y Y ) 2 ] 1/2 .
C g = C Y 0 X / C Y 0 Y = Y 0 |X / Y 0 |Y .

Metrics