Abstract

The nonlinear effect of noise-enhanced signal transmission by means of stochastic resonance in optics is studied. We investigate this effect for the novel case of spatial signals or images. With a theoretical model involving a threshold nonlinearity we describe a mechanism whereby the transmission of an image can be improved by the addition of noise. We argue that such a nonlinear mechanism can operate in different types of light scattering. With a stimulated Raman scattering experiment we verify the existence of a stochastic resonance effect in the transmission of a laser image; we show that maximal efficacy is obtained with the assistance of a speckle of sufficient intensity. The results extend the scope of stochastic resonance and can serve as a basis for further development of the effect in optics.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Wiesenfeld and F. Moss, “Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs,” Nature (London) 373, 33–36 (1995).
    [CrossRef]
  2. A. R. Bulsara and L. Gammaitoni, “Tuning in to noise,” Phys. Today 49(3), 39–45 (1996).
    [CrossRef]
  3. R. Benzi, A. Sutera, and A. Vulpiani, “The mechanism of stochastic resonance,” J. Phys. A 14, L453–L458 (1981).
    [CrossRef]
  4. P. Debye, Polar Molecules (Dover, New York, 1929).
  5. M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, “Stochastic resonance in perspective,” Nuovo Cimento D 17, 661–683 (1995).
    [CrossRef]
  6. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
    [CrossRef]
  7. B. McNamara and K. Wiesenfeld, “Theory of stochastic resonance,” Phys. Rev. A 39, 4854–4869 (1989).
    [CrossRef] [PubMed]
  8. L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, and S. Santucci, “Stochastic resonance in bistable systems,” Phys. Rev. Lett. 62, 349–352 (1989).
    [CrossRef] [PubMed]
  9. M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
    [CrossRef]
  10. J. J. Collins, C. C. Chow, and T. T. Imhoff, “Aperiodic stochastic resonance in excitable systems,” Phys. Rev. E 52, R3321–R3324 (1995).
    [CrossRef]
  11. F. Chapeau-Blondeau, “Noise-enhanced capacity via stochastic resonance in an asymmetric binary channel,” Phys. Rev. E 55, 2016–2019 (1997).
    [CrossRef]
  12. F. Chapeau-Blondeau and X. Godivier, “Theory of stochastic resonance in signal transmission by static nonlinear systems,” Phys. Rev. E 55, 1478–1495 (1997).
    [CrossRef]
  13. L. Gammaitoni, “Stochastic resonance and the dithering effect in threshold physical systems,” Phys. Rev. E 52, 4691–4698 (1995).
    [CrossRef]
  14. P. Jung, “Threshold devices: fractal noise and neural talk,” Phys. Rev. E 50, 2513–2522 (1994).
    [CrossRef]
  15. X. Godivier, J. Rojas-Varela, and F. Chapeau-Blondeau, “Noise-assisted signal transmission via stochastic resonance in a diode nonlinearity,” Electron. Lett. 33, 1666–1668 (1997).
    [CrossRef]
  16. F. Chapeau-Blondeau and X. Godivier, “Stochastic resonance in nonlinear transmission of spike signals: an exact model and an application to the neuron,” Int. J. Bifurcation Chaos 6, 2069–2076 (1996).
    [CrossRef]
  17. E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
    [CrossRef]
  18. G. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).
  19. S. M. Bezrukov and I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature (London) 385, 319–321 (1997).
    [CrossRef]
  20. W. Kaiser and M. Maier, “Stimulated Rayleigh, Brillouin and Raman spectroscopy,” in Laser Handbook, F. T. Arrechi and E. O. Schultz-Dubois, eds. (Elsevier, Amsterdam, 1972), Vol. 2, pp. 1089–1096.
  21. J. Gazengel, N. P. Xuan, and G. Rivoire, “Stimulated Raman scattering thresholds for ultra-shot excitation,” Opt. Acta 26, 1245–1255 (1979).
    [CrossRef]
  22. S. Er. Rhaïmini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
    [CrossRef]
  23. R. Loudon, The Quantum Theory of Light (Oxford U. Press, Oxford, 1973).
  24. B. Colombeau, C. Froehly, and M. Vampouille, “Fourier description of the axial structure of speckle,” J. Opt. 10, 65–69 (1979).
    [CrossRef]
  25. J. L. Ferrier, Z. Wu, J. Gazengel, N. P. Xuan, and G. Rivoire, “Backward scatterings in the picosecond range: generation and geometrical conditions for wave front reconstruction,” Opt. Commun. 41, 135–139 (1982).
    [CrossRef]

1998

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

1997

F. Chapeau-Blondeau, “Noise-enhanced capacity via stochastic resonance in an asymmetric binary channel,” Phys. Rev. E 55, 2016–2019 (1997).
[CrossRef]

F. Chapeau-Blondeau and X. Godivier, “Theory of stochastic resonance in signal transmission by static nonlinear systems,” Phys. Rev. E 55, 1478–1495 (1997).
[CrossRef]

X. Godivier, J. Rojas-Varela, and F. Chapeau-Blondeau, “Noise-assisted signal transmission via stochastic resonance in a diode nonlinearity,” Electron. Lett. 33, 1666–1668 (1997).
[CrossRef]

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

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

1996

F. Chapeau-Blondeau and X. Godivier, “Stochastic resonance in nonlinear transmission of spike signals: an exact model and an application to the neuron,” Int. J. Bifurcation Chaos 6, 2069–2076 (1996).
[CrossRef]

A. R. Bulsara and L. Gammaitoni, “Tuning in to noise,” Phys. Today 49(3), 39–45 (1996).
[CrossRef]

1995

K. Wiesenfeld and F. Moss, “Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs,” Nature (London) 373, 33–36 (1995).
[CrossRef]

M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, “Stochastic resonance in perspective,” Nuovo Cimento D 17, 661–683 (1995).
[CrossRef]

J. J. Collins, C. C. Chow, and T. T. Imhoff, “Aperiodic stochastic resonance in excitable systems,” Phys. Rev. E 52, R3321–R3324 (1995).
[CrossRef]

L. Gammaitoni, “Stochastic resonance and the dithering effect in threshold physical systems,” Phys. Rev. E 52, 4691–4698 (1995).
[CrossRef]

1994

P. Jung, “Threshold devices: fractal noise and neural talk,” Phys. Rev. E 50, 2513–2522 (1994).
[CrossRef]

1993

M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
[CrossRef]

S. Er. Rhaïmini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

1989

B. McNamara and K. Wiesenfeld, “Theory of stochastic resonance,” Phys. Rev. A 39, 4854–4869 (1989).
[CrossRef] [PubMed]

L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, and S. Santucci, “Stochastic resonance in bistable systems,” Phys. Rev. Lett. 62, 349–352 (1989).
[CrossRef] [PubMed]

1982

J. L. Ferrier, Z. Wu, J. Gazengel, N. P. Xuan, and G. Rivoire, “Backward scatterings in the picosecond range: generation and geometrical conditions for wave front reconstruction,” Opt. Commun. 41, 135–139 (1982).
[CrossRef]

1981

R. Benzi, A. Sutera, and A. Vulpiani, “The mechanism of stochastic resonance,” J. Phys. A 14, L453–L458 (1981).
[CrossRef]

1979

J. Gazengel, N. P. Xuan, and G. Rivoire, “Stimulated Raman scattering thresholds for ultra-shot excitation,” Opt. Acta 26, 1245–1255 (1979).
[CrossRef]

B. Colombeau, C. Froehly, and M. Vampouille, “Fourier description of the axial structure of speckle,” J. Opt. 10, 65–69 (1979).
[CrossRef]

Benzi, R.

R. Benzi, A. Sutera, and A. Vulpiani, “The mechanism of stochastic resonance,” J. Phys. A 14, L453–L458 (1981).
[CrossRef]

Bezrukov, S. M.

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

Bulsara, A. R.

A. R. Bulsara and L. Gammaitoni, “Tuning in to noise,” Phys. Today 49(3), 39–45 (1996).
[CrossRef]

Chapeau-Blondeau, F.

F. Chapeau-Blondeau, “Noise-enhanced capacity via stochastic resonance in an asymmetric binary channel,” Phys. Rev. E 55, 2016–2019 (1997).
[CrossRef]

X. Godivier, J. Rojas-Varela, and F. Chapeau-Blondeau, “Noise-assisted signal transmission via stochastic resonance in a diode nonlinearity,” Electron. Lett. 33, 1666–1668 (1997).
[CrossRef]

F. Chapeau-Blondeau and X. Godivier, “Theory of stochastic resonance in signal transmission by static nonlinear systems,” Phys. Rev. E 55, 1478–1495 (1997).
[CrossRef]

F. Chapeau-Blondeau and X. Godivier, “Stochastic resonance in nonlinear transmission of spike signals: an exact model and an application to the neuron,” Int. J. Bifurcation Chaos 6, 2069–2076 (1996).
[CrossRef]

Chow, C. C.

J. J. Collins, C. C. Chow, and T. T. Imhoff, “Aperiodic stochastic resonance in excitable systems,” Phys. Rev. E 52, R3321–R3324 (1995).
[CrossRef]

Collins, J. J.

J. J. Collins, C. C. Chow, and T. T. Imhoff, “Aperiodic stochastic resonance in excitable systems,” Phys. Rev. E 52, R3321–R3324 (1995).
[CrossRef]

Colombeau, B.

B. Colombeau, C. Froehly, and M. Vampouille, “Fourier description of the axial structure of speckle,” J. Opt. 10, 65–69 (1979).
[CrossRef]

Dykman, M. I.

M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, “Stochastic resonance in perspective,” Nuovo Cimento D 17, 661–683 (1995).
[CrossRef]

M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
[CrossRef]

Ferrier, J. L.

J. L. Ferrier, Z. Wu, J. Gazengel, N. P. Xuan, and G. Rivoire, “Backward scatterings in the picosecond range: generation and geometrical conditions for wave front reconstruction,” Opt. Commun. 41, 135–139 (1982).
[CrossRef]

Froehly, C.

B. Colombeau, C. Froehly, and M. Vampouille, “Fourier description of the axial structure of speckle,” J. Opt. 10, 65–69 (1979).
[CrossRef]

Gammaitoni, L.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

A. R. Bulsara and L. Gammaitoni, “Tuning in to noise,” Phys. Today 49(3), 39–45 (1996).
[CrossRef]

L. Gammaitoni, “Stochastic resonance and the dithering effect in threshold physical systems,” Phys. Rev. E 52, 4691–4698 (1995).
[CrossRef]

L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, and S. Santucci, “Stochastic resonance in bistable systems,” Phys. Rev. Lett. 62, 349–352 (1989).
[CrossRef] [PubMed]

Gazengel, J.

J. L. Ferrier, Z. Wu, J. Gazengel, N. P. Xuan, and G. Rivoire, “Backward scatterings in the picosecond range: generation and geometrical conditions for wave front reconstruction,” Opt. Commun. 41, 135–139 (1982).
[CrossRef]

J. Gazengel, N. P. Xuan, and G. Rivoire, “Stimulated Raman scattering thresholds for ultra-shot excitation,” Opt. Acta 26, 1245–1255 (1979).
[CrossRef]

Godivier, X.

F. Chapeau-Blondeau and X. Godivier, “Theory of stochastic resonance in signal transmission by static nonlinear systems,” Phys. Rev. E 55, 1478–1495 (1997).
[CrossRef]

X. Godivier, J. Rojas-Varela, and F. Chapeau-Blondeau, “Noise-assisted signal transmission via stochastic resonance in a diode nonlinearity,” Electron. Lett. 33, 1666–1668 (1997).
[CrossRef]

F. Chapeau-Blondeau and X. Godivier, “Stochastic resonance in nonlinear transmission of spike signals: an exact model and an application to the neuron,” Int. J. Bifurcation Chaos 6, 2069–2076 (1996).
[CrossRef]

Haken, H.

M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
[CrossRef]

Hänggi, P.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

Hu, G.

M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
[CrossRef]

Imhoff, T. T.

J. J. Collins, C. C. Chow, and T. T. Imhoff, “Aperiodic stochastic resonance in excitable systems,” Phys. Rev. E 52, R3321–R3324 (1995).
[CrossRef]

Jung, P.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

P. Jung, “Threshold devices: fractal noise and neural talk,” Phys. Rev. E 50, 2513–2522 (1994).
[CrossRef]

Lecoq, J. P.

S. Er. Rhaïmini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

Luchinsky, D. G.

M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, “Stochastic resonance in perspective,” Nuovo Cimento D 17, 661–683 (1995).
[CrossRef]

M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
[CrossRef]

Mannella, R.

M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, “Stochastic resonance in perspective,” Nuovo Cimento D 17, 661–683 (1995).
[CrossRef]

M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
[CrossRef]

Marchesoni, F.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, and S. Santucci, “Stochastic resonance in bistable systems,” Phys. Rev. Lett. 62, 349–352 (1989).
[CrossRef] [PubMed]

McClintock, P. V. E.

M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, “Stochastic resonance in perspective,” Nuovo Cimento D 17, 661–683 (1995).
[CrossRef]

M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
[CrossRef]

McNamara, B.

B. McNamara and K. Wiesenfeld, “Theory of stochastic resonance,” Phys. Rev. A 39, 4854–4869 (1989).
[CrossRef] [PubMed]

Menichella-Saetta, E.

L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, and S. Santucci, “Stochastic resonance in bistable systems,” Phys. Rev. Lett. 62, 349–352 (1989).
[CrossRef] [PubMed]

Moss, F.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

K. Wiesenfeld and F. Moss, “Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs,” Nature (London) 373, 33–36 (1995).
[CrossRef]

Ning, C. Z.

M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
[CrossRef]

Rhaïmini, S. Er.

S. Er. Rhaïmini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

Riani, M.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

Rivoire, G.

S. Er. Rhaïmini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

J. L. Ferrier, Z. Wu, J. Gazengel, N. P. Xuan, and G. Rivoire, “Backward scatterings in the picosecond range: generation and geometrical conditions for wave front reconstruction,” Opt. Commun. 41, 135–139 (1982).
[CrossRef]

J. Gazengel, N. P. Xuan, and G. Rivoire, “Stimulated Raman scattering thresholds for ultra-shot excitation,” Opt. Acta 26, 1245–1255 (1979).
[CrossRef]

Roberts, M.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

Rojas-Varela, J.

X. Godivier, J. Rojas-Varela, and F. Chapeau-Blondeau, “Noise-assisted signal transmission via stochastic resonance in a diode nonlinearity,” Electron. Lett. 33, 1666–1668 (1997).
[CrossRef]

Santucci, S.

L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, and S. Santucci, “Stochastic resonance in bistable systems,” Phys. Rev. Lett. 62, 349–352 (1989).
[CrossRef] [PubMed]

Seife, C.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

Simonotto, E.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

Stein, N. D.

M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, “Stochastic resonance in perspective,” Nuovo Cimento D 17, 661–683 (1995).
[CrossRef]

M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
[CrossRef]

Stocks, N. G.

M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, “Stochastic resonance in perspective,” Nuovo Cimento D 17, 661–683 (1995).
[CrossRef]

M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
[CrossRef]

Sutera, A.

R. Benzi, A. Sutera, and A. Vulpiani, “The mechanism of stochastic resonance,” J. Phys. A 14, L453–L458 (1981).
[CrossRef]

Tcherniega, N.

S. Er. Rhaïmini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

Twitty, J.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

Vampouille, M.

B. Colombeau, C. Froehly, and M. Vampouille, “Fourier description of the axial structure of speckle,” J. Opt. 10, 65–69 (1979).
[CrossRef]

Vodyanoy, I.

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

Vulpiani, A.

R. Benzi, A. Sutera, and A. Vulpiani, “The mechanism of stochastic resonance,” J. Phys. A 14, L453–L458 (1981).
[CrossRef]

Wiesenfeld, K.

K. Wiesenfeld and F. Moss, “Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs,” Nature (London) 373, 33–36 (1995).
[CrossRef]

B. McNamara and K. Wiesenfeld, “Theory of stochastic resonance,” Phys. Rev. A 39, 4854–4869 (1989).
[CrossRef] [PubMed]

Wu, Z.

J. L. Ferrier, Z. Wu, J. Gazengel, N. P. Xuan, and G. Rivoire, “Backward scatterings in the picosecond range: generation and geometrical conditions for wave front reconstruction,” Opt. Commun. 41, 135–139 (1982).
[CrossRef]

Xuan, N. P.

S. Er. Rhaïmini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

J. L. Ferrier, Z. Wu, J. Gazengel, N. P. Xuan, and G. Rivoire, “Backward scatterings in the picosecond range: generation and geometrical conditions for wave front reconstruction,” Opt. Commun. 41, 135–139 (1982).
[CrossRef]

J. Gazengel, N. P. Xuan, and G. Rivoire, “Stimulated Raman scattering thresholds for ultra-shot excitation,” Opt. Acta 26, 1245–1255 (1979).
[CrossRef]

Electron. Lett.

X. Godivier, J. Rojas-Varela, and F. Chapeau-Blondeau, “Noise-assisted signal transmission via stochastic resonance in a diode nonlinearity,” Electron. Lett. 33, 1666–1668 (1997).
[CrossRef]

Int. J. Bifurcation Chaos

F. Chapeau-Blondeau and X. Godivier, “Stochastic resonance in nonlinear transmission of spike signals: an exact model and an application to the neuron,” Int. J. Bifurcation Chaos 6, 2069–2076 (1996).
[CrossRef]

J. Opt.

B. Colombeau, C. Froehly, and M. Vampouille, “Fourier description of the axial structure of speckle,” J. Opt. 10, 65–69 (1979).
[CrossRef]

J. Phys. A

R. Benzi, A. Sutera, and A. Vulpiani, “The mechanism of stochastic resonance,” J. Phys. A 14, L453–L458 (1981).
[CrossRef]

Nature (London)

K. Wiesenfeld and F. Moss, “Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs,” Nature (London) 373, 33–36 (1995).
[CrossRef]

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

Nuovo Cimento D

M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, “Stochastic resonance in perspective,” Nuovo Cimento D 17, 661–683 (1995).
[CrossRef]

Opt. Acta

J. Gazengel, N. P. Xuan, and G. Rivoire, “Stimulated Raman scattering thresholds for ultra-shot excitation,” Opt. Acta 26, 1245–1255 (1979).
[CrossRef]

Opt. Commun.

S. Er. Rhaïmini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

J. L. Ferrier, Z. Wu, J. Gazengel, N. P. Xuan, and G. Rivoire, “Backward scatterings in the picosecond range: generation and geometrical conditions for wave front reconstruction,” Opt. Commun. 41, 135–139 (1982).
[CrossRef]

Phys. Lett. A

M. I. Dykman, H. Haken, G. Hu, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, C. Z. Ning, N. D. Stein, and N. G. Stocks, “Linear response theory in stochastic resonance,” Phys. Lett. A 180, 332–336 (1993).
[CrossRef]

Phys. Rev. A

B. McNamara and K. Wiesenfeld, “Theory of stochastic resonance,” Phys. Rev. A 39, 4854–4869 (1989).
[CrossRef] [PubMed]

Phys. Rev. E

J. J. Collins, C. C. Chow, and T. T. Imhoff, “Aperiodic stochastic resonance in excitable systems,” Phys. Rev. E 52, R3321–R3324 (1995).
[CrossRef]

F. Chapeau-Blondeau, “Noise-enhanced capacity via stochastic resonance in an asymmetric binary channel,” Phys. Rev. E 55, 2016–2019 (1997).
[CrossRef]

F. Chapeau-Blondeau and X. Godivier, “Theory of stochastic resonance in signal transmission by static nonlinear systems,” Phys. Rev. E 55, 1478–1495 (1997).
[CrossRef]

L. Gammaitoni, “Stochastic resonance and the dithering effect in threshold physical systems,” Phys. Rev. E 52, 4691–4698 (1995).
[CrossRef]

P. Jung, “Threshold devices: fractal noise and neural talk,” Phys. Rev. E 50, 2513–2522 (1994).
[CrossRef]

Phys. Rev. Lett.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, and S. Santucci, “Stochastic resonance in bistable systems,” Phys. Rev. Lett. 62, 349–352 (1989).
[CrossRef] [PubMed]

Phys. Today

A. R. Bulsara and L. Gammaitoni, “Tuning in to noise,” Phys. Today 49(3), 39–45 (1996).
[CrossRef]

Rev. Mod. Phys.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

Other

P. Debye, Polar Molecules (Dover, New York, 1929).

G. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

R. Loudon, The Quantum Theory of Light (Oxford U. Press, Oxford, 1973).

W. Kaiser and M. Maier, “Stimulated Rayleigh, Brillouin and Raman spectroscopy,” in Laser Handbook, F. T. Arrechi and E. O. Schultz-Dubois, eds. (Elsevier, Amsterdam, 1972), Vol. 2, pp. 1089–1096.

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 (9)

Fig. 1
Fig. 1

Output 64×64 image Y(x, y) after transmission according to expressions (1) with θ=1.1. The binary input image S(x, y) represents the letter F, and N(x, y) is zero-mean Gaussian noise with rms amplitudes 0.05 (left), 0.43 (center), and 1 (right).

Fig. 2
Fig. 2

Similarity between input image S(x, y) and output image Y(x, y) as a function of the input noise rms amplitude under the conditions of Fig. 1 with probability p1=0.148. Solid curves, theoretical expressions of the cross correlation RSY of Eq. (7) (upper trace) and the cross covariance CSY of Eq. (8) (lower trace). The two sets of discrete data points are experimental estimations through pixels counting on images.

Fig. 3
Fig. 3

Schematic of the interaction that nonlinearly couples a signal beam and a noise beam to produce an output beam.

Fig. 4
Fig. 4

Output Raman intensity IR (GW/cm2) as a function of input laser intensity IL (GW/cm2) as described by Eq. (10) with g =10-11 m/W, l=16 cm, and V=0.1 cm3.

Fig. 5
Fig. 5

Experimental setup: λ1/2, λ2/2, half-wave plates; P1, P2, polarizers; L1, L2, L3, L4, L5, L6, lenses with foci, respectively, of 50, 10, 50, 15, 30, and 5 cm; G1, phase plate; G2, grid; NL, nonlinear medium; CCD, CCD camera.

Fig. 6
Fig. 6

Image carried by the transverse structure of the signal beam as it is observed on the CCD camera in the absence of both the nonlinear medium and the noise beam.

Fig. 7
Fig. 7

Speckle image carried by the transverse structure of the noise beam as it is observed on the CCD camera in the absence of both the nonlinear medium and the signal beam.

Fig. 8
Fig. 8

a, Input image carried by the signal beam. b–f, Output Raman images obtained with the signal beam added to a speckle of increasing intensities IN of b, 0.30; c, 0.36; d, 0.39; e, 0.41; f, 0.43 GW/cm2. Cross-correlation measure RSY identifies the maximum similarity between the input and output images in e.

Fig. 9
Fig. 9

Similarity between the input and output images defined by the cross correlation RSY of Eq. (2) as a function of noise intensity IN (GW/cm2). Circles, experimental data; solid curve, an interpolation.

Equations (11)

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

IfS(x, y)+N(x, y)>θ,thenY(x, y)=1,
elseY(x, y)=0.
RSY=SYS2Y2,
CSY=(S-S)(Y-Y)[(S-S)2(Y-Y)2]1/2,
q1=p11×p1+p10×(1-p1).
p11=Pr(Y=1|S=1)=1-F(θ-1),
p10=Pr(Y=1|S=0)=1-F(θ).
RSY=p11p1p1q1
CSY=p11p1-p1q1[(p1-p12)(q1-q12)]1/2.
P={i,j,k}={S,N,Y}χ(ωY; ωi, ωj, ωk)EiEj*Ek.
IR=cωDV [exp(Gl)-1]cωVIL exp(Gl)-1,

Metrics