Abstract

Measurements of the switch-on time statistical properties of a single-mode Ar+ laser modulated by an acousto-optic modulator (AOM) are reported. The mean switch-on time, 〈τ〉, is found to increase linearly with the time of application of the AOM, toff, before reaching a constant value for large values of toff. The switch-on time variance, στ, shows a maximum as a function of toff. These results are explained with the use of a model that includes the spontaneous emission noise and fluctuations in the loss factor caused by the random character of the radio frequency signal driving the AOM. An analytic approximation is developed to obtain the slope of 〈τ〉 versus toff and to characterize the maximum of στ

© 1995 Optical Society of America

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  1. M. Suzuki, in Order of Fluctuations in Equilibrium and Nonequilibrium Statistical Mechanics, G. Nicolis, G. Dewel, and J. Turner, eds. (Wiley, New York, 1980).
  2. F. de Pasquale and P. Tombesi, "The decay of an unstable equilibrium state near a critical point," Phys. Lett. 72 A, 7 (1979); F. de Pasquale, P. Tartaglia, and P. Tombesi, "New expansion technique for the decay of an unstable state," Phys. Rev. A 25, 466 (1982).
    [CrossRef]
  3. G. Ahlers, M. C. Cross, P. C. Hohenberg, and S. Safran, "The amplitude equation near the convective threshold: application to time dependent heating experiments," J. Fluid Mech. 110, 297 (1981); J. B. Swift, P. C. Hohenberg, and G. Ahlers, "Stochastic Landau equation with time-dependent drift," Phys. Rev. A 43, 6572 (1991).
    [CrossRef] [PubMed]
  4. G. Broggi, A. Colombo, L. A. Lugiato, and P. Mandel, "Influence of white noise on delayed bifurcations," Phys. Rev. A 33, 3635 (1986).
    [CrossRef] [PubMed]
  5. M. C. Torrent and M. San Miguel, "Stochastic-dynamical characterization of delayed laser threshold instability with swept control parameter," Phys. Rev. A 38, 245 (1988).
    [CrossRef] [PubMed]
  6. A. Valle, L. Pesquera, and M. A. Rodríguez, "Transient statistics for a good cavity laser with swept losses," Phys. Rev. A 45, 5243 (1992).
    [CrossRef] [PubMed]
  7. W. Scharpf, M. Squicciarini, D. Bromley, C. Green, J. R. Tredicce, and L. M. Narducci, "Experimental observation of a delayed bifurcation at the threshold of an argon laser," Opt. Commun. 63, 344 (1987); W. Scharpf, "Delayed bifurcation at threshold in argon-ion lasers," Ph.D. dissertation (Drexel University, Philadelphia, Pa., 1988).
    [CrossRef]
  8. D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, J. R. Tredicce, and S. Balle, "Anticipation of the switch-off and delay of the switch-on of a laser with a swept parameter," Opt. Commun. 99, 65 (1993).
    [CrossRef]
  9. F. de Pasquale, Z. Racz, M. San Miquel, and P. Tartaglia, "Fluctuations and limit of metastability in a periodically driven unstable system," Phys. Rev. B 30, 5228 (1984).
    [CrossRef]
  10. M. Suzuki, Phys. Lett. A 67, 339 (1978); Prog. Theor. Phys. (Kyoto) 64, 402 (1978).
    [CrossRef]
  11. M. O. Cáceres, A. Becker, and L. Kramer, "Asymptotic probability distribution for a supercritical bifurcation swept periodically in time," Phys. Rev. A 43, 6581 (1991).
    [CrossRef] [PubMed]
  12. A. Valle, M. A. Rodríguez, and L. Pesquera, "Statistical properties of pulses: application to modulated gas lasers," Phys. Rev. A 47, 4176 (1993).
    [CrossRef] [PubMed]
  13. W. Meyer, G. Ahlers, and D. S. Cannell, "Initial stages of pattern formation in Rayleigh–Bernard convection," Phys. Rev. Lett. 59, 1577 (1987).
    [CrossRef] [PubMed]
  14. B. McNamara, K. Wiesenfeld, and R. Roy, "Observation of stochastic resonance in a ring laser," Phys. Rev. Lett. 60, 2626 (1988).
    [CrossRef] [PubMed]
  15. O. Svelto, Principles of Lasers (Plenum, New York, 1982).
  16. K. Petermann, Laser Diode Modulation and Noise (Kluwer, The Netherlands, 1988).
    [CrossRef]
  17. M. R. Young and S. Singh, "Decay of an unstable state," Phys. Rev. A 31, 888 (1985); "Observation of the Brownian motion of the electric field in a laser," Phys. Rev. A 35, 1453 (1987).
    [CrossRef] [PubMed]
  18. F. T. Arecchi, W. Gadomski, R. Meucci, and J. A. Roversi, "Dynamics of laser buildup from quantum noise," Phys. Rev. A 39, 4004 (1989).
    [CrossRef] [PubMed]
  19. R. Roy, A. W. Yu, and S. Zhu, "Quantum fluctuations, pump noise, and the growth of laser radiation," Phys. Rev. Lett. 55, 2794 (1985); S. Zhu, A. W. Yu, and R. Roy, "Statistical fluctuations in laser transients," Phys. Rev. A 34, 4333 (1986).
    [CrossRef] [PubMed]
  20. F. de Pasquale, J. M. Sancho, M. San Miguel, and P. Tartaglia, "Theory of the transient statistics of a dye laser," Phys. Rev. Lett. 56, 2473 (1986).
    [CrossRef] [PubMed]
  21. M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass., 1974).
  22. L. M. Narducci and N. B. Abraham, Laser Physics and Laser Instabilities (World Scientific, N.J., 1988).
    [CrossRef]
  23. J. M. Sancho, M. San Miguel, S. L. Katz, and J. D. Gunton, "Analytical and numerical studies of multiplicative noise," Phys. Rev. A 26, 1589 (1982).
    [CrossRef]
  24. N. Berg and J. Lee, Acousto-Optic Signal Processing. Theory and Implementation (Marcel Dekker, New York, 1983).
  25. A. Valle, M. A. Rodríguez, and C. Mirasso, "Analytical calculation of timing jitter in single mode semiconductor lasers under fast periodic modulation," Opt. Lett. 17, 1523 (1992).
    [CrossRef] [PubMed]
  26. M. San Miguel, "Statistics of laser switch-on," in Laser Noise, R. Roy, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1376, 272–283 (1991).
    [CrossRef]
  27. B. E. A. Saleh and M. C. Teich, Fundamental of Photonics (Addison-Wesley, Reading, Mass., 1991).
    [CrossRef]
  28. F. T. Arecchi, V. Degiorgio, and B. Querzola, "Time-dependent statistical properties of the laser radiation," Phys. Rev. Lett. 19, 1168 (1967); F. T. Arecchi and V. Degiorgio, "Statistical properties of laser radiation during a transient buildup," Phys. Rev. A 3, 1108 (1971).
    [CrossRef]

1993

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, J. R. Tredicce, and S. Balle, "Anticipation of the switch-off and delay of the switch-on of a laser with a swept parameter," Opt. Commun. 99, 65 (1993).
[CrossRef]

A. Valle, M. A. Rodríguez, and L. Pesquera, "Statistical properties of pulses: application to modulated gas lasers," Phys. Rev. A 47, 4176 (1993).
[CrossRef] [PubMed]

1992

1991

M. O. Cáceres, A. Becker, and L. Kramer, "Asymptotic probability distribution for a supercritical bifurcation swept periodically in time," Phys. Rev. A 43, 6581 (1991).
[CrossRef] [PubMed]

1989

F. T. Arecchi, W. Gadomski, R. Meucci, and J. A. Roversi, "Dynamics of laser buildup from quantum noise," Phys. Rev. A 39, 4004 (1989).
[CrossRef] [PubMed]

1988

B. McNamara, K. Wiesenfeld, and R. Roy, "Observation of stochastic resonance in a ring laser," Phys. Rev. Lett. 60, 2626 (1988).
[CrossRef] [PubMed]

M. C. Torrent and M. San Miguel, "Stochastic-dynamical characterization of delayed laser threshold instability with swept control parameter," Phys. Rev. A 38, 245 (1988).
[CrossRef] [PubMed]

1987

W. Scharpf, M. Squicciarini, D. Bromley, C. Green, J. R. Tredicce, and L. M. Narducci, "Experimental observation of a delayed bifurcation at the threshold of an argon laser," Opt. Commun. 63, 344 (1987); W. Scharpf, "Delayed bifurcation at threshold in argon-ion lasers," Ph.D. dissertation (Drexel University, Philadelphia, Pa., 1988).
[CrossRef]

W. Meyer, G. Ahlers, and D. S. Cannell, "Initial stages of pattern formation in Rayleigh–Bernard convection," Phys. Rev. Lett. 59, 1577 (1987).
[CrossRef] [PubMed]

1986

F. de Pasquale, J. M. Sancho, M. San Miguel, and P. Tartaglia, "Theory of the transient statistics of a dye laser," Phys. Rev. Lett. 56, 2473 (1986).
[CrossRef] [PubMed]

G. Broggi, A. Colombo, L. A. Lugiato, and P. Mandel, "Influence of white noise on delayed bifurcations," Phys. Rev. A 33, 3635 (1986).
[CrossRef] [PubMed]

1985

R. Roy, A. W. Yu, and S. Zhu, "Quantum fluctuations, pump noise, and the growth of laser radiation," Phys. Rev. Lett. 55, 2794 (1985); S. Zhu, A. W. Yu, and R. Roy, "Statistical fluctuations in laser transients," Phys. Rev. A 34, 4333 (1986).
[CrossRef] [PubMed]

M. R. Young and S. Singh, "Decay of an unstable state," Phys. Rev. A 31, 888 (1985); "Observation of the Brownian motion of the electric field in a laser," Phys. Rev. A 35, 1453 (1987).
[CrossRef] [PubMed]

1984

F. de Pasquale, Z. Racz, M. San Miquel, and P. Tartaglia, "Fluctuations and limit of metastability in a periodically driven unstable system," Phys. Rev. B 30, 5228 (1984).
[CrossRef]

1982

J. M. Sancho, M. San Miguel, S. L. Katz, and J. D. Gunton, "Analytical and numerical studies of multiplicative noise," Phys. Rev. A 26, 1589 (1982).
[CrossRef]

1981

G. Ahlers, M. C. Cross, P. C. Hohenberg, and S. Safran, "The amplitude equation near the convective threshold: application to time dependent heating experiments," J. Fluid Mech. 110, 297 (1981); J. B. Swift, P. C. Hohenberg, and G. Ahlers, "Stochastic Landau equation with time-dependent drift," Phys. Rev. A 43, 6572 (1991).
[CrossRef] [PubMed]

1979

F. de Pasquale and P. Tombesi, "The decay of an unstable equilibrium state near a critical point," Phys. Lett. 72 A, 7 (1979); F. de Pasquale, P. Tartaglia, and P. Tombesi, "New expansion technique for the decay of an unstable state," Phys. Rev. A 25, 466 (1982).
[CrossRef]

1967

F. T. Arecchi, V. Degiorgio, and B. Querzola, "Time-dependent statistical properties of the laser radiation," Phys. Rev. Lett. 19, 1168 (1967); F. T. Arecchi and V. Degiorgio, "Statistical properties of laser radiation during a transient buildup," Phys. Rev. A 3, 1108 (1971).
[CrossRef]

Abraham, N. B.

L. M. Narducci and N. B. Abraham, Laser Physics and Laser Instabilities (World Scientific, N.J., 1988).
[CrossRef]

Ahlers, G.

W. Meyer, G. Ahlers, and D. S. Cannell, "Initial stages of pattern formation in Rayleigh–Bernard convection," Phys. Rev. Lett. 59, 1577 (1987).
[CrossRef] [PubMed]

G. Ahlers, M. C. Cross, P. C. Hohenberg, and S. Safran, "The amplitude equation near the convective threshold: application to time dependent heating experiments," J. Fluid Mech. 110, 297 (1981); J. B. Swift, P. C. Hohenberg, and G. Ahlers, "Stochastic Landau equation with time-dependent drift," Phys. Rev. A 43, 6572 (1991).
[CrossRef] [PubMed]

Arecchi, F. T.

F. T. Arecchi, W. Gadomski, R. Meucci, and J. A. Roversi, "Dynamics of laser buildup from quantum noise," Phys. Rev. A 39, 4004 (1989).
[CrossRef] [PubMed]

F. T. Arecchi, V. Degiorgio, and B. Querzola, "Time-dependent statistical properties of the laser radiation," Phys. Rev. Lett. 19, 1168 (1967); F. T. Arecchi and V. Degiorgio, "Statistical properties of laser radiation during a transient buildup," Phys. Rev. A 3, 1108 (1971).
[CrossRef]

Balle, S.

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, J. R. Tredicce, and S. Balle, "Anticipation of the switch-off and delay of the switch-on of a laser with a swept parameter," Opt. Commun. 99, 65 (1993).
[CrossRef]

Becker, A.

M. O. Cáceres, A. Becker, and L. Kramer, "Asymptotic probability distribution for a supercritical bifurcation swept periodically in time," Phys. Rev. A 43, 6581 (1991).
[CrossRef] [PubMed]

Berg, N.

N. Berg and J. Lee, Acousto-Optic Signal Processing. Theory and Implementation (Marcel Dekker, New York, 1983).

Broggi, G.

G. Broggi, A. Colombo, L. A. Lugiato, and P. Mandel, "Influence of white noise on delayed bifurcations," Phys. Rev. A 33, 3635 (1986).
[CrossRef] [PubMed]

Bromley, D.

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, J. R. Tredicce, and S. Balle, "Anticipation of the switch-off and delay of the switch-on of a laser with a swept parameter," Opt. Commun. 99, 65 (1993).
[CrossRef]

W. Scharpf, M. Squicciarini, D. Bromley, C. Green, J. R. Tredicce, and L. M. Narducci, "Experimental observation of a delayed bifurcation at the threshold of an argon laser," Opt. Commun. 63, 344 (1987); W. Scharpf, "Delayed bifurcation at threshold in argon-ion lasers," Ph.D. dissertation (Drexel University, Philadelphia, Pa., 1988).
[CrossRef]

Cáceres, M. O.

M. O. Cáceres, A. Becker, and L. Kramer, "Asymptotic probability distribution for a supercritical bifurcation swept periodically in time," Phys. Rev. A 43, 6581 (1991).
[CrossRef] [PubMed]

Cannell, D. S.

W. Meyer, G. Ahlers, and D. S. Cannell, "Initial stages of pattern formation in Rayleigh–Bernard convection," Phys. Rev. Lett. 59, 1577 (1987).
[CrossRef] [PubMed]

Colombo, A.

G. Broggi, A. Colombo, L. A. Lugiato, and P. Mandel, "Influence of white noise on delayed bifurcations," Phys. Rev. A 33, 3635 (1986).
[CrossRef] [PubMed]

Cross, M. C.

G. Ahlers, M. C. Cross, P. C. Hohenberg, and S. Safran, "The amplitude equation near the convective threshold: application to time dependent heating experiments," J. Fluid Mech. 110, 297 (1981); J. B. Swift, P. C. Hohenberg, and G. Ahlers, "Stochastic Landau equation with time-dependent drift," Phys. Rev. A 43, 6572 (1991).
[CrossRef] [PubMed]

D'Angelo, E. J.

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, J. R. Tredicce, and S. Balle, "Anticipation of the switch-off and delay of the switch-on of a laser with a swept parameter," Opt. Commun. 99, 65 (1993).
[CrossRef]

Degiorgio, V.

F. T. Arecchi, V. Degiorgio, and B. Querzola, "Time-dependent statistical properties of the laser radiation," Phys. Rev. Lett. 19, 1168 (1967); F. T. Arecchi and V. Degiorgio, "Statistical properties of laser radiation during a transient buildup," Phys. Rev. A 3, 1108 (1971).
[CrossRef]

Gadomski, W.

F. T. Arecchi, W. Gadomski, R. Meucci, and J. A. Roversi, "Dynamics of laser buildup from quantum noise," Phys. Rev. A 39, 4004 (1989).
[CrossRef] [PubMed]

Grassi, H.

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, J. R. Tredicce, and S. Balle, "Anticipation of the switch-off and delay of the switch-on of a laser with a swept parameter," Opt. Commun. 99, 65 (1993).
[CrossRef]

Green, C.

W. Scharpf, M. Squicciarini, D. Bromley, C. Green, J. R. Tredicce, and L. M. Narducci, "Experimental observation of a delayed bifurcation at the threshold of an argon laser," Opt. Commun. 63, 344 (1987); W. Scharpf, "Delayed bifurcation at threshold in argon-ion lasers," Ph.D. dissertation (Drexel University, Philadelphia, Pa., 1988).
[CrossRef]

Gunton, J. D.

J. M. Sancho, M. San Miguel, S. L. Katz, and J. D. Gunton, "Analytical and numerical studies of multiplicative noise," Phys. Rev. A 26, 1589 (1982).
[CrossRef]

Hohenberg, P. C.

G. Ahlers, M. C. Cross, P. C. Hohenberg, and S. Safran, "The amplitude equation near the convective threshold: application to time dependent heating experiments," J. Fluid Mech. 110, 297 (1981); J. B. Swift, P. C. Hohenberg, and G. Ahlers, "Stochastic Landau equation with time-dependent drift," Phys. Rev. A 43, 6572 (1991).
[CrossRef] [PubMed]

Katz, S. L.

J. M. Sancho, M. San Miguel, S. L. Katz, and J. D. Gunton, "Analytical and numerical studies of multiplicative noise," Phys. Rev. A 26, 1589 (1982).
[CrossRef]

Kramer, L.

M. O. Cáceres, A. Becker, and L. Kramer, "Asymptotic probability distribution for a supercritical bifurcation swept periodically in time," Phys. Rev. A 43, 6581 (1991).
[CrossRef] [PubMed]

Lamb, W. E.

M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass., 1974).

Lee, J.

N. Berg and J. Lee, Acousto-Optic Signal Processing. Theory and Implementation (Marcel Dekker, New York, 1983).

Lugiato, L. A.

G. Broggi, A. Colombo, L. A. Lugiato, and P. Mandel, "Influence of white noise on delayed bifurcations," Phys. Rev. A 33, 3635 (1986).
[CrossRef] [PubMed]

Mandel, P.

G. Broggi, A. Colombo, L. A. Lugiato, and P. Mandel, "Influence of white noise on delayed bifurcations," Phys. Rev. A 33, 3635 (1986).
[CrossRef] [PubMed]

Mathis, C.

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, J. R. Tredicce, and S. Balle, "Anticipation of the switch-off and delay of the switch-on of a laser with a swept parameter," Opt. Commun. 99, 65 (1993).
[CrossRef]

McNamara, B.

B. McNamara, K. Wiesenfeld, and R. Roy, "Observation of stochastic resonance in a ring laser," Phys. Rev. Lett. 60, 2626 (1988).
[CrossRef] [PubMed]

Meucci, R.

F. T. Arecchi, W. Gadomski, R. Meucci, and J. A. Roversi, "Dynamics of laser buildup from quantum noise," Phys. Rev. A 39, 4004 (1989).
[CrossRef] [PubMed]

Meyer, W.

W. Meyer, G. Ahlers, and D. S. Cannell, "Initial stages of pattern formation in Rayleigh–Bernard convection," Phys. Rev. Lett. 59, 1577 (1987).
[CrossRef] [PubMed]

Miguel, M. San

M. C. Torrent and M. San Miguel, "Stochastic-dynamical characterization of delayed laser threshold instability with swept control parameter," Phys. Rev. A 38, 245 (1988).
[CrossRef] [PubMed]

F. de Pasquale, J. M. Sancho, M. San Miguel, and P. Tartaglia, "Theory of the transient statistics of a dye laser," Phys. Rev. Lett. 56, 2473 (1986).
[CrossRef] [PubMed]

J. M. Sancho, M. San Miguel, S. L. Katz, and J. D. Gunton, "Analytical and numerical studies of multiplicative noise," Phys. Rev. A 26, 1589 (1982).
[CrossRef]

M. San Miguel, "Statistics of laser switch-on," in Laser Noise, R. Roy, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1376, 272–283 (1991).
[CrossRef]

Miquel, M. San

F. de Pasquale, Z. Racz, M. San Miquel, and P. Tartaglia, "Fluctuations and limit of metastability in a periodically driven unstable system," Phys. Rev. B 30, 5228 (1984).
[CrossRef]

Mirasso, C.

Narducci, L. M.

W. Scharpf, M. Squicciarini, D. Bromley, C. Green, J. R. Tredicce, and L. M. Narducci, "Experimental observation of a delayed bifurcation at the threshold of an argon laser," Opt. Commun. 63, 344 (1987); W. Scharpf, "Delayed bifurcation at threshold in argon-ion lasers," Ph.D. dissertation (Drexel University, Philadelphia, Pa., 1988).
[CrossRef]

L. M. Narducci and N. B. Abraham, Laser Physics and Laser Instabilities (World Scientific, N.J., 1988).
[CrossRef]

Pasquale, F. de

F. de Pasquale, J. M. Sancho, M. San Miguel, and P. Tartaglia, "Theory of the transient statistics of a dye laser," Phys. Rev. Lett. 56, 2473 (1986).
[CrossRef] [PubMed]

F. de Pasquale, Z. Racz, M. San Miquel, and P. Tartaglia, "Fluctuations and limit of metastability in a periodically driven unstable system," Phys. Rev. B 30, 5228 (1984).
[CrossRef]

F. de Pasquale and P. Tombesi, "The decay of an unstable equilibrium state near a critical point," Phys. Lett. 72 A, 7 (1979); F. de Pasquale, P. Tartaglia, and P. Tombesi, "New expansion technique for the decay of an unstable state," Phys. Rev. A 25, 466 (1982).
[CrossRef]

Pesquera, L.

A. Valle, M. A. Rodríguez, and L. Pesquera, "Statistical properties of pulses: application to modulated gas lasers," Phys. Rev. A 47, 4176 (1993).
[CrossRef] [PubMed]

A. Valle, L. Pesquera, and M. A. Rodríguez, "Transient statistics for a good cavity laser with swept losses," Phys. Rev. A 45, 5243 (1992).
[CrossRef] [PubMed]

Petermann, K.

K. Petermann, Laser Diode Modulation and Noise (Kluwer, The Netherlands, 1988).
[CrossRef]

Querzola, B.

F. T. Arecchi, V. Degiorgio, and B. Querzola, "Time-dependent statistical properties of the laser radiation," Phys. Rev. Lett. 19, 1168 (1967); F. T. Arecchi and V. Degiorgio, "Statistical properties of laser radiation during a transient buildup," Phys. Rev. A 3, 1108 (1971).
[CrossRef]

Racz, Z.

F. de Pasquale, Z. Racz, M. San Miquel, and P. Tartaglia, "Fluctuations and limit of metastability in a periodically driven unstable system," Phys. Rev. B 30, 5228 (1984).
[CrossRef]

Rodríguez, M. A.

A. Valle, M. A. Rodríguez, and L. Pesquera, "Statistical properties of pulses: application to modulated gas lasers," Phys. Rev. A 47, 4176 (1993).
[CrossRef] [PubMed]

A. Valle, L. Pesquera, and M. A. Rodríguez, "Transient statistics for a good cavity laser with swept losses," Phys. Rev. A 45, 5243 (1992).
[CrossRef] [PubMed]

A. Valle, M. A. Rodríguez, and C. Mirasso, "Analytical calculation of timing jitter in single mode semiconductor lasers under fast periodic modulation," Opt. Lett. 17, 1523 (1992).
[CrossRef] [PubMed]

Roversi, J. A.

F. T. Arecchi, W. Gadomski, R. Meucci, and J. A. Roversi, "Dynamics of laser buildup from quantum noise," Phys. Rev. A 39, 4004 (1989).
[CrossRef] [PubMed]

Roy, R.

B. McNamara, K. Wiesenfeld, and R. Roy, "Observation of stochastic resonance in a ring laser," Phys. Rev. Lett. 60, 2626 (1988).
[CrossRef] [PubMed]

R. Roy, A. W. Yu, and S. Zhu, "Quantum fluctuations, pump noise, and the growth of laser radiation," Phys. Rev. Lett. 55, 2794 (1985); S. Zhu, A. W. Yu, and R. Roy, "Statistical fluctuations in laser transients," Phys. Rev. A 34, 4333 (1986).
[CrossRef] [PubMed]

Safran, S.

G. Ahlers, M. C. Cross, P. C. Hohenberg, and S. Safran, "The amplitude equation near the convective threshold: application to time dependent heating experiments," J. Fluid Mech. 110, 297 (1981); J. B. Swift, P. C. Hohenberg, and G. Ahlers, "Stochastic Landau equation with time-dependent drift," Phys. Rev. A 43, 6572 (1991).
[CrossRef] [PubMed]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamental of Photonics (Addison-Wesley, Reading, Mass., 1991).
[CrossRef]

Sancho, J. M.

F. de Pasquale, J. M. Sancho, M. San Miguel, and P. Tartaglia, "Theory of the transient statistics of a dye laser," Phys. Rev. Lett. 56, 2473 (1986).
[CrossRef] [PubMed]

J. M. Sancho, M. San Miguel, S. L. Katz, and J. D. Gunton, "Analytical and numerical studies of multiplicative noise," Phys. Rev. A 26, 1589 (1982).
[CrossRef]

Sargent, M.

M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass., 1974).

Scharpf, W.

W. Scharpf, M. Squicciarini, D. Bromley, C. Green, J. R. Tredicce, and L. M. Narducci, "Experimental observation of a delayed bifurcation at the threshold of an argon laser," Opt. Commun. 63, 344 (1987); W. Scharpf, "Delayed bifurcation at threshold in argon-ion lasers," Ph.D. dissertation (Drexel University, Philadelphia, Pa., 1988).
[CrossRef]

Scully, M. O.

M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass., 1974).

Singh, S.

M. R. Young and S. Singh, "Decay of an unstable state," Phys. Rev. A 31, 888 (1985); "Observation of the Brownian motion of the electric field in a laser," Phys. Rev. A 35, 1453 (1987).
[CrossRef] [PubMed]

Squicciarini, M.

W. Scharpf, M. Squicciarini, D. Bromley, C. Green, J. R. Tredicce, and L. M. Narducci, "Experimental observation of a delayed bifurcation at the threshold of an argon laser," Opt. Commun. 63, 344 (1987); W. Scharpf, "Delayed bifurcation at threshold in argon-ion lasers," Ph.D. dissertation (Drexel University, Philadelphia, Pa., 1988).
[CrossRef]

Suzuki, M.

M. Suzuki, Phys. Lett. A 67, 339 (1978); Prog. Theor. Phys. (Kyoto) 64, 402 (1978).
[CrossRef]

M. Suzuki, in Order of Fluctuations in Equilibrium and Nonequilibrium Statistical Mechanics, G. Nicolis, G. Dewel, and J. Turner, eds. (Wiley, New York, 1980).

Svelto, O.

O. Svelto, Principles of Lasers (Plenum, New York, 1982).

Tartaglia, P.

F. de Pasquale, J. M. Sancho, M. San Miguel, and P. Tartaglia, "Theory of the transient statistics of a dye laser," Phys. Rev. Lett. 56, 2473 (1986).
[CrossRef] [PubMed]

F. de Pasquale, Z. Racz, M. San Miquel, and P. Tartaglia, "Fluctuations and limit of metastability in a periodically driven unstable system," Phys. Rev. B 30, 5228 (1984).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamental of Photonics (Addison-Wesley, Reading, Mass., 1991).
[CrossRef]

Tombesi, P.

F. de Pasquale and P. Tombesi, "The decay of an unstable equilibrium state near a critical point," Phys. Lett. 72 A, 7 (1979); F. de Pasquale, P. Tartaglia, and P. Tombesi, "New expansion technique for the decay of an unstable state," Phys. Rev. A 25, 466 (1982).
[CrossRef]

Torrent, M. C.

M. C. Torrent and M. San Miguel, "Stochastic-dynamical characterization of delayed laser threshold instability with swept control parameter," Phys. Rev. A 38, 245 (1988).
[CrossRef] [PubMed]

Tredicce, J. R.

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, J. R. Tredicce, and S. Balle, "Anticipation of the switch-off and delay of the switch-on of a laser with a swept parameter," Opt. Commun. 99, 65 (1993).
[CrossRef]

W. Scharpf, M. Squicciarini, D. Bromley, C. Green, J. R. Tredicce, and L. M. Narducci, "Experimental observation of a delayed bifurcation at the threshold of an argon laser," Opt. Commun. 63, 344 (1987); W. Scharpf, "Delayed bifurcation at threshold in argon-ion lasers," Ph.D. dissertation (Drexel University, Philadelphia, Pa., 1988).
[CrossRef]

Valle, A.

A. Valle, M. A. Rodríguez, and L. Pesquera, "Statistical properties of pulses: application to modulated gas lasers," Phys. Rev. A 47, 4176 (1993).
[CrossRef] [PubMed]

A. Valle, L. Pesquera, and M. A. Rodríguez, "Transient statistics for a good cavity laser with swept losses," Phys. Rev. A 45, 5243 (1992).
[CrossRef] [PubMed]

A. Valle, M. A. Rodríguez, and C. Mirasso, "Analytical calculation of timing jitter in single mode semiconductor lasers under fast periodic modulation," Opt. Lett. 17, 1523 (1992).
[CrossRef] [PubMed]

Wiesenfeld, K.

B. McNamara, K. Wiesenfeld, and R. Roy, "Observation of stochastic resonance in a ring laser," Phys. Rev. Lett. 60, 2626 (1988).
[CrossRef] [PubMed]

Young, M. R.

M. R. Young and S. Singh, "Decay of an unstable state," Phys. Rev. A 31, 888 (1985); "Observation of the Brownian motion of the electric field in a laser," Phys. Rev. A 35, 1453 (1987).
[CrossRef] [PubMed]

Yu, A. W.

R. Roy, A. W. Yu, and S. Zhu, "Quantum fluctuations, pump noise, and the growth of laser radiation," Phys. Rev. Lett. 55, 2794 (1985); S. Zhu, A. W. Yu, and R. Roy, "Statistical fluctuations in laser transients," Phys. Rev. A 34, 4333 (1986).
[CrossRef] [PubMed]

Zhu, S.

R. Roy, A. W. Yu, and S. Zhu, "Quantum fluctuations, pump noise, and the growth of laser radiation," Phys. Rev. Lett. 55, 2794 (1985); S. Zhu, A. W. Yu, and R. Roy, "Statistical fluctuations in laser transients," Phys. Rev. A 34, 4333 (1986).
[CrossRef] [PubMed]

J. Fluid Mech.

G. Ahlers, M. C. Cross, P. C. Hohenberg, and S. Safran, "The amplitude equation near the convective threshold: application to time dependent heating experiments," J. Fluid Mech. 110, 297 (1981); J. B. Swift, P. C. Hohenberg, and G. Ahlers, "Stochastic Landau equation with time-dependent drift," Phys. Rev. A 43, 6572 (1991).
[CrossRef] [PubMed]

Opt. Commun.

W. Scharpf, M. Squicciarini, D. Bromley, C. Green, J. R. Tredicce, and L. M. Narducci, "Experimental observation of a delayed bifurcation at the threshold of an argon laser," Opt. Commun. 63, 344 (1987); W. Scharpf, "Delayed bifurcation at threshold in argon-ion lasers," Ph.D. dissertation (Drexel University, Philadelphia, Pa., 1988).
[CrossRef]

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, J. R. Tredicce, and S. Balle, "Anticipation of the switch-off and delay of the switch-on of a laser with a swept parameter," Opt. Commun. 99, 65 (1993).
[CrossRef]

Opt. Lett.

Phys. Lett.

F. de Pasquale and P. Tombesi, "The decay of an unstable equilibrium state near a critical point," Phys. Lett. 72 A, 7 (1979); F. de Pasquale, P. Tartaglia, and P. Tombesi, "New expansion technique for the decay of an unstable state," Phys. Rev. A 25, 466 (1982).
[CrossRef]

Phys. Rev. A

J. M. Sancho, M. San Miguel, S. L. Katz, and J. D. Gunton, "Analytical and numerical studies of multiplicative noise," Phys. Rev. A 26, 1589 (1982).
[CrossRef]

G. Broggi, A. Colombo, L. A. Lugiato, and P. Mandel, "Influence of white noise on delayed bifurcations," Phys. Rev. A 33, 3635 (1986).
[CrossRef] [PubMed]

M. C. Torrent and M. San Miguel, "Stochastic-dynamical characterization of delayed laser threshold instability with swept control parameter," Phys. Rev. A 38, 245 (1988).
[CrossRef] [PubMed]

A. Valle, L. Pesquera, and M. A. Rodríguez, "Transient statistics for a good cavity laser with swept losses," Phys. Rev. A 45, 5243 (1992).
[CrossRef] [PubMed]

M. O. Cáceres, A. Becker, and L. Kramer, "Asymptotic probability distribution for a supercritical bifurcation swept periodically in time," Phys. Rev. A 43, 6581 (1991).
[CrossRef] [PubMed]

A. Valle, M. A. Rodríguez, and L. Pesquera, "Statistical properties of pulses: application to modulated gas lasers," Phys. Rev. A 47, 4176 (1993).
[CrossRef] [PubMed]

M. R. Young and S. Singh, "Decay of an unstable state," Phys. Rev. A 31, 888 (1985); "Observation of the Brownian motion of the electric field in a laser," Phys. Rev. A 35, 1453 (1987).
[CrossRef] [PubMed]

F. T. Arecchi, W. Gadomski, R. Meucci, and J. A. Roversi, "Dynamics of laser buildup from quantum noise," Phys. Rev. A 39, 4004 (1989).
[CrossRef] [PubMed]

Phys. Rev. B

F. de Pasquale, Z. Racz, M. San Miquel, and P. Tartaglia, "Fluctuations and limit of metastability in a periodically driven unstable system," Phys. Rev. B 30, 5228 (1984).
[CrossRef]

Phys. Rev. Lett.

R. Roy, A. W. Yu, and S. Zhu, "Quantum fluctuations, pump noise, and the growth of laser radiation," Phys. Rev. Lett. 55, 2794 (1985); S. Zhu, A. W. Yu, and R. Roy, "Statistical fluctuations in laser transients," Phys. Rev. A 34, 4333 (1986).
[CrossRef] [PubMed]

F. de Pasquale, J. M. Sancho, M. San Miguel, and P. Tartaglia, "Theory of the transient statistics of a dye laser," Phys. Rev. Lett. 56, 2473 (1986).
[CrossRef] [PubMed]

W. Meyer, G. Ahlers, and D. S. Cannell, "Initial stages of pattern formation in Rayleigh–Bernard convection," Phys. Rev. Lett. 59, 1577 (1987).
[CrossRef] [PubMed]

B. McNamara, K. Wiesenfeld, and R. Roy, "Observation of stochastic resonance in a ring laser," Phys. Rev. Lett. 60, 2626 (1988).
[CrossRef] [PubMed]

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[CrossRef]

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N. Berg and J. Lee, Acousto-Optic Signal Processing. Theory and Implementation (Marcel Dekker, New York, 1983).

M. San Miguel, "Statistics of laser switch-on," in Laser Noise, R. Roy, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1376, 272–283 (1991).
[CrossRef]

B. E. A. Saleh and M. C. Teich, Fundamental of Photonics (Addison-Wesley, Reading, Mass., 1991).
[CrossRef]

O. Svelto, Principles of Lasers (Plenum, New York, 1982).

K. Petermann, Laser Diode Modulation and Noise (Kluwer, The Netherlands, 1988).
[CrossRef]

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L. M. Narducci and N. B. Abraham, Laser Physics and Laser Instabilities (World Scientific, N.J., 1988).
[CrossRef]

M. Suzuki, Phys. Lett. A 67, 339 (1978); Prog. Theor. Phys. (Kyoto) 64, 402 (1978).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Qualitative time traces of the laser intensity (in logarithmic scale) and loss factor. (a) and (b) plot the laser intensity during one pulse for toff small and large, respectively. In (a) the pulses obtained with and without random cavity losses are plotted with solid and dashed curves, respectively; (b) these are plotted with dotted and dashed–dotted curves, respectively. The loss factors with the two different values of toff are plotted in (c) with dashed (toff small) and dashed–dotted (toff large) curves.

Fig. 3
Fig. 3

Mean value of the switch-on time as obtained from (a) simulation and (b) the experiment for three different laser powers. Triangles and solid curves correspond to the minimum power, 6 mW (g = 7.5 × 106 s−1). Squares and dotted curves represent the results for the intermediate power, 24 mW (g = 2.46 × 107 s−1). Circles and dashed curves correspond to the maximum power, 36 mW (g = 3.64 × 107 s−1). Other parameters are κ0 = 106 s−1, Is = 3.9 × 108 nW2 C−2, D = 5 × 103 N2 C−2 s−1, = 3.2 × 106 s−1, tc = 80 ns, and κm = 5 × 107, 6 × 107, and 7 × 107 s−1 for 6, 24, and 36 mW, respectively.

Fig. 4
Fig. 4

Variance of the switch-on time as obtained from (a) simulation and (b) experiment for three different laser powers. Triangles, solid curves, squares, dotted curves, circles, and dashed curves are as listed in Fig. 3. Other parameters used to obtain the simulation results are also listed in Fig. 3.

Fig. 5
Fig. 5

Variance of the switch-on time as obtained from simulation, symbols, and approximation (3.7); curves for three different loss-noise intensities and for g = 7.5 × 106 s−1. The value of the parameters are = 6 × 106 s−1 (squares and solid curve), = 3 × 106 s−1 (crosses and dashed curve), and = 3 × 105 s−1 (circles and dashed–dotted curve). The other parameters are the same as those in Fig. 3.

Equations (12)

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d E d t = g E 1 + I / I s - κ ( t ) E + ξ ( t ) ,
κ ( t ) = { κ 0 if 0 < t < T - t off κ 0 + κ m + ϕ ( t ) if T - t off < t < T ,
I ( t ) = I L exp 2 - t off + t l t [ g - κ ( s ) ] d s .
τ L = ( κ m + κ 0 - g ) ( g - κ 0 ) ( t off - t l ) + 1 2 ( g - κ 0 ) ln I L I L + ψ ( t off - t l ) ( g - κ 0 ) ,
τ = ( κ m + κ 0 - g ) ( g - κ 0 ) ( t off - t l ) + ln I L - ln I L 2 ( g - κ 0 ) + Δ ,
σ τ 2 ( ( t off - t l ) - t c { 1 - exp [ ( t l - t off ) / t c ] } ) ( g - κ 0 ) 2 + 1 4 ( g - κ 0 ) 2 σ ln I L 2 .
σ τ 2 ( t off - t l ) ( g - κ 0 ) 2 + 1 4 ( g - κ 0 ) 2 σ ln I L 2 .
I ( 0 ) D κ m + κ 0 - g .
t m t l + 1 2 ( κ m + κ 0 - g ) ln I L ( κ m + κ 0 - g ) D .
σ τ = 0.64 ( g - κ 0 ) ,
> 0.41 ( κ m + κ 0 - g ) { ln [ I L ( κ m + κ 0 - g ) / D ] } - 1 .
W on e 0 I s ( g - κ 0 ) v 8 κ 0 ,

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