Abstract

We show the connection between the treatment of the effects of Gaussian-beam averaging on laser instability in some recent papers by Stuut and Sargent [ J. Opt. Soc. Am. B 1, 95 ( 1984)] and ourselves [ Z. Phys. B 50, 171 ( 1983); Opt. Commun. 46, 57 ( 1983)] and review the results obtained for laser instabilities with a Gaussian transverse intensity profile.

© 1985 Optical Society of America

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References

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  1. L. A. Lugiato and M. Milani, “Transverse effects and self-pulsing in optical Instability,” Z. Phys. B 50, 171–179 (1983).
    [CrossRef]
  2. L. A. Lugiato and M. Milani, “Disappearance of laser instabilities in a Gaussian cavity mode,” Opt. Commun. 46, 57–60 (1983).
    [CrossRef]
  3. S. Stuut and M. Sargent, “Effects of Gaussian-beam averaging on phase conjugation and beat-frequency spectroscopy,” J. Opt. Soc. Am. B 1, 95–101 (1984).
    [CrossRef]
  4. H. Haken, “Theory of intensity and phase fluctuations of a homogeneously broadened laser,” Z. Phys. 190, 327–356 (1966).
    [CrossRef]
  5. H. Risken, C. Schmid, and W. Weidlich, “Fokker–Planck equation, distribution and correlation functions for laser noise,” Z. Phys. 194, 337–359 (1966).
    [CrossRef]
  6. H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys. 39, 4662–4672 (1968).
    [CrossRef]
  7. R. Graham and H. Haken, “Quantum theory of light propagation in a fluctuating laser,” Z. Phys. 213, 420–450 (1968).
    [CrossRef]
  8. R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21, 510–516 (1978).
    [CrossRef]
  9. L. W. Hillman, J. Y. Yuan, K. Koch, J. Krasinski, and C. R. Stroud, “Behavior of homogeneously broadened lasers operating far above threshold,” J. Opt. Soc. Am. B 1, 440–441 (1984).
  10. L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, “Instabilities in active and passive optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A (to be published).
  11. See, e.g., N. B. Abraham, D. Dangoisse, P. Glorieux, and P. Mandel, “Observation of undamped pulsations in a low-pressure, far-infrared laser and comparison with a simple theoretical model,” J. Opt. Soc. Am. B 2, 23–34 (1985);L. W. Casperson, “Spontaneous coherent pulsations in ring-laser oscillators,” J. Opt. Soc. Am. B 2, 62–72 (1985);L. W. Casperson, “Spontaneous coherent pulsations in ring-laser oscillators: simplified models,” J. Opt. Soc. Am. B 2, 73–80 (1985);C. O. Weiss, “Observation of instabilities and chaos in optically pumped far-infrared lasers,” J. Opt. Soc. Am. B 2, 137–140 (1985).
    [CrossRef]

1985 (1)

1984 (2)

S. Stuut and M. Sargent, “Effects of Gaussian-beam averaging on phase conjugation and beat-frequency spectroscopy,” J. Opt. Soc. Am. B 1, 95–101 (1984).
[CrossRef]

L. W. Hillman, J. Y. Yuan, K. Koch, J. Krasinski, and C. R. Stroud, “Behavior of homogeneously broadened lasers operating far above threshold,” J. Opt. Soc. Am. B 1, 440–441 (1984).

1983 (2)

L. A. Lugiato and M. Milani, “Transverse effects and self-pulsing in optical Instability,” Z. Phys. B 50, 171–179 (1983).
[CrossRef]

L. A. Lugiato and M. Milani, “Disappearance of laser instabilities in a Gaussian cavity mode,” Opt. Commun. 46, 57–60 (1983).
[CrossRef]

1978 (1)

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21, 510–516 (1978).
[CrossRef]

1968 (2)

H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys. 39, 4662–4672 (1968).
[CrossRef]

R. Graham and H. Haken, “Quantum theory of light propagation in a fluctuating laser,” Z. Phys. 213, 420–450 (1968).
[CrossRef]

1966 (2)

H. Haken, “Theory of intensity and phase fluctuations of a homogeneously broadened laser,” Z. Phys. 190, 327–356 (1966).
[CrossRef]

H. Risken, C. Schmid, and W. Weidlich, “Fokker–Planck equation, distribution and correlation functions for laser noise,” Z. Phys. 194, 337–359 (1966).
[CrossRef]

Abraham, N. B.

Bonifacio, R.

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21, 510–516 (1978).
[CrossRef]

Dangoisse, D.

Glorieux, P.

Graham, R.

R. Graham and H. Haken, “Quantum theory of light propagation in a fluctuating laser,” Z. Phys. 213, 420–450 (1968).
[CrossRef]

Haken, H.

R. Graham and H. Haken, “Quantum theory of light propagation in a fluctuating laser,” Z. Phys. 213, 420–450 (1968).
[CrossRef]

H. Haken, “Theory of intensity and phase fluctuations of a homogeneously broadened laser,” Z. Phys. 190, 327–356 (1966).
[CrossRef]

Hillman, L. W.

L. W. Hillman, J. Y. Yuan, K. Koch, J. Krasinski, and C. R. Stroud, “Behavior of homogeneously broadened lasers operating far above threshold,” J. Opt. Soc. Am. B 1, 440–441 (1984).

Horowicz, R. J.

L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, “Instabilities in active and passive optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A (to be published).

Koch, K.

L. W. Hillman, J. Y. Yuan, K. Koch, J. Krasinski, and C. R. Stroud, “Behavior of homogeneously broadened lasers operating far above threshold,” J. Opt. Soc. Am. B 1, 440–441 (1984).

Krasinski, J.

L. W. Hillman, J. Y. Yuan, K. Koch, J. Krasinski, and C. R. Stroud, “Behavior of homogeneously broadened lasers operating far above threshold,” J. Opt. Soc. Am. B 1, 440–441 (1984).

Lugiato, L. A.

L. A. Lugiato and M. Milani, “Transverse effects and self-pulsing in optical Instability,” Z. Phys. B 50, 171–179 (1983).
[CrossRef]

L. A. Lugiato and M. Milani, “Disappearance of laser instabilities in a Gaussian cavity mode,” Opt. Commun. 46, 57–60 (1983).
[CrossRef]

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21, 510–516 (1978).
[CrossRef]

L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, “Instabilities in active and passive optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A (to be published).

Mandel, P.

Milani, M.

L. A. Lugiato and M. Milani, “Disappearance of laser instabilities in a Gaussian cavity mode,” Opt. Commun. 46, 57–60 (1983).
[CrossRef]

L. A. Lugiato and M. Milani, “Transverse effects and self-pulsing in optical Instability,” Z. Phys. B 50, 171–179 (1983).
[CrossRef]

Narducci, L. M.

L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, “Instabilities in active and passive optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A (to be published).

Nummedal, K.

H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys. 39, 4662–4672 (1968).
[CrossRef]

Risken, H.

H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys. 39, 4662–4672 (1968).
[CrossRef]

H. Risken, C. Schmid, and W. Weidlich, “Fokker–Planck equation, distribution and correlation functions for laser noise,” Z. Phys. 194, 337–359 (1966).
[CrossRef]

Sargent, M.

Schmid, C.

H. Risken, C. Schmid, and W. Weidlich, “Fokker–Planck equation, distribution and correlation functions for laser noise,” Z. Phys. 194, 337–359 (1966).
[CrossRef]

Strini, G.

L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, “Instabilities in active and passive optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A (to be published).

Stroud, C. R.

L. W. Hillman, J. Y. Yuan, K. Koch, J. Krasinski, and C. R. Stroud, “Behavior of homogeneously broadened lasers operating far above threshold,” J. Opt. Soc. Am. B 1, 440–441 (1984).

Stuut, S.

Weidlich, W.

H. Risken, C. Schmid, and W. Weidlich, “Fokker–Planck equation, distribution and correlation functions for laser noise,” Z. Phys. 194, 337–359 (1966).
[CrossRef]

Yuan, J. Y.

L. W. Hillman, J. Y. Yuan, K. Koch, J. Krasinski, and C. R. Stroud, “Behavior of homogeneously broadened lasers operating far above threshold,” J. Opt. Soc. Am. B 1, 440–441 (1984).

J. Appl. Phys. (1)

H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys. 39, 4662–4672 (1968).
[CrossRef]

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

Lett. Nuovo Cimento (1)

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21, 510–516 (1978).
[CrossRef]

Opt. Commun. (1)

L. A. Lugiato and M. Milani, “Disappearance of laser instabilities in a Gaussian cavity mode,” Opt. Commun. 46, 57–60 (1983).
[CrossRef]

Z. Phys. (3)

H. Haken, “Theory of intensity and phase fluctuations of a homogeneously broadened laser,” Z. Phys. 190, 327–356 (1966).
[CrossRef]

H. Risken, C. Schmid, and W. Weidlich, “Fokker–Planck equation, distribution and correlation functions for laser noise,” Z. Phys. 194, 337–359 (1966).
[CrossRef]

R. Graham and H. Haken, “Quantum theory of light propagation in a fluctuating laser,” Z. Phys. 213, 420–450 (1968).
[CrossRef]

Z. Phys. B (1)

L. A. Lugiato and M. Milani, “Transverse effects and self-pulsing in optical Instability,” Z. Phys. B 50, 171–179 (1983).
[CrossRef]

Other (1)

L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, “Instabilities in active and passive optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A (to be published).

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Figures (1)

Fig. 1
Fig. 1

Plot of γ Re H(αn, x2) as a function of α ¯ = α n / γ for x2 = 39, β = γ/γ = 1: a, plane wave; b, Gaussian wave for d/w0 → ∞,

Equations (13)

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

α L 1 , T 1 , C α L / 2 T arbitrary ,
2 C = x 2 / ln ( 1 + x 2 ) ,
2 C = 1 + x 2 .
G ( α n , x 2 ) > 1 ,
G ( α n , x 2 ) = 2 C x 2 γ Re H ( α n , x 2 ) ,
H ( α n , x 2 ) = x 2 K ( α n , x 2 ) ,
K ( α n , x 2 ) = 1 1 + x 2 γ ( 1 x 2 ) i α n ( γ i α n ) ( γ i α n ) + γ γ x 2 .
H ( α n , x 2 ) = x 2 x 2 d υ K ( α n , ν ) ,
x 2 = x 2 exp [ ( d w 0 ) 2 ] .
γ Re H ( α n , x 2 ) = ln ( 1 + x 2 ) [ α ¯ 2 + ( β + 1 ) 2 ] [ h 1 ( α ¯ , x 2 ) h 1 ( α ¯ , x 2 ) + h 2 ( α ¯ , x 2 ) h 2 ( α ¯ , x 2 ) ] ,
α ¯ = α n γ , β = γ γ ,
h 1 ( α ¯ n , x 2 ) = ½ ( α ¯ 2 + β 2 + β + 1 ) × ln ( 1 + x 2 ) 2 β 2 ( 1 + x 2 ) 2 2 α ¯ 2 β ( 1 + x 2 ) + α ¯ 2 [ α ¯ 2 + ( β + 1 ) 2 ] ,
h 2 ( α ¯ , x 2 ) = α ¯ 2 + 2 β ( β + 1 ) α ¯ tan 1 β ( 1 + x 2 ) α ¯ 2 α ¯ ( β + 1 ) .

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