Abstract

Under some conditions, spontaneous coherent pulsations are known to occur in the output beams of inhomogeneously broadened laser oscillators. These lasers typically operate with a Gaussian transverse field distribution, while the corresponding theoretical models assume a uniform-plane-wave field. The effects of a Gaussian field on the stability criteria of single-mode inhomogeneously broadened ring laser oscillators are considered in this study. It is found that in comparison to a plane wave a Gaussian field variation still permits low-threshold spontaneous pulsations but reduces the parameter space over which these pulsations can be observed.

© 2009 Optical Society of America

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References

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  1. N. B. Abraham, L. A. Lugiato, and L. M. Narducci, “Overview of instabilities in laser systems,” J. Opt. Soc. Am. B 2, 7-14 (1985) and references.
    [CrossRef]
  2. H. Haken, “Analogy between higher instabilities in fluids and lasers,” Phys. Lett. A 53, 77-78 (1975).
    [CrossRef]
  3. L. A. Lugiato and M. Milani, “Disappearance of laser instabilities in a Gaussian cavity mode,” Opt. Commun. 46, 57-60 (1983).
    [CrossRef]
  4. S. Stuut and M. Sargent III, “Effects of Gaussian-beam averaging on phase conjugation and beat-frequency spectroscopy,” J. Opt. Soc. Am. B 1, 95-101 (1984).
    [CrossRef]
  5. L. A. Lugiato and M. Milani, “Effects of Gaussian-beam averaging on laser instabilities,” J. Opt. Soc. Am. B 2, 15-17 (1985).
    [CrossRef]
  6. L. A. Lugiato, R. J. Horowicz, and G. Strini, “Instabilities in passive and active optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A 30, 1366-1376 (1984).
    [CrossRef]
  7. D. Y. Tang, C. O. Weiss, E. Roldán, and C. J. de Valcárcel, “Deviation from Lorenz-type dynamics of an NH3 ring laser,” Opt. Commun. 89, 47-53 (1992).
    [CrossRef]
  8. C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
    [CrossRef]
  9. C. P. Smith and R. Dykstra, “Lorenz-like chaos in a Gaussian mode laser with a radially dependent gain,” Opt. Commun. 117, 107-110 (1995).
    [CrossRef]
  10. C. P. Smith and R. Dykstra, “Observation in the two-level spatial Maxwell-Bloch model of the anomalously large first peak as seen in experimental Lorenz-like spiral chaos from the N15H3 laser,” Opt. Commun. 129, 69-74 (1996).
    [CrossRef]
  11. J. F. Urchueguia, G. J. de Valcárcel, and E. Roldán, “Laser instabilities in a Gaussian cavity mode with Gaussian pump profile,” J. Opt. Soc. Am. B 15, 1512-1520 (1998).
    [CrossRef]
  12. J. F. Urchueguia, G. J. de Valcárcel, E. Roldán, and F. Prati, “Transverse effects in ring fiber laser multimode instabilities,” Phys. Rev. A 62, 041801 (2000).
    [CrossRef]
  13. E. Roldán, G. J. de Valcárcel, J. F. Urchueguia, and J. M. Guerra, “Observability of the Risken-Nummedal-Graham-Haken instability in Nd:YAG lasers,” J. Opt. Soc. Am. B 20, 816-824 (2003).
    [CrossRef]
  14. L. W. Casperson, “Spontaneous coherent pulsations in laser oscillators,” IEEE J. Quantum Electron. QE-14, 756-761 (1978).
    [CrossRef]
  15. L. W. Casperson, Laser Physics, J.D.Harvey and D.F.Walls, eds., Vol. 182 of Springer Lecture Notes in Physics (Springer-Verlag, 1983), pp. 88-106.
    [CrossRef]
  16. J. Bentley and N. B. Abraham, “Mode-pulling, mode-splitting and pulsing in high-gain lasers,” J. Opt. Soc. Am. 70, 1622 (1980).
  17. J. Bentley and N. B. Abraham, “Mode-pulling, mode-splitting, and pulsing in a high gain He-Xe laser,” Opt. Commun. 41, 52-56 (1982).
    [CrossRef]
  18. M. Maeda and N. B. Abraham, “Measurements of mode-splitting self-pulsing in a single-mode, Fabry-Perot laser,” Phys. Rev. A 26, 3395-3403 (1982).
    [CrossRef]
  19. R. S. Gioggia and N. B. Abraham, “Single-mode self-pulsing instabilities at the Lamb dip of a He-Ne 3.39 μm laser,” Opt. Commun. 47, 278-282 (1983).
    [CrossRef]
  20. R. S. Gioggia and N. B. Abraham, “Anomalous mode pulling, instabilities, and chaos in a single mode, standing-wave 3.39-μm He-Ne laser,” Phys. Rev. A 29, 1304-1309 (1984).
    [CrossRef]
  21. P. Chenkosol and L. W. Casperson, “Stability criteria for spontaneously pulsing gas lasers,” J. Opt. Soc. Am. B 26, 939-945 (2009).
    [CrossRef]
  22. L. W. Casperson, “Spontaneous coherent pulsations in ring-laser oscillators,” J. Opt. Soc. Am. B 2, 62-72 (1985).
    [CrossRef]
  23. P. Chenkosol and L. W. Casperson, “Spontaneous coherent pulsations in standing-wave laser oscillators: stability criteria for homogeneous broadening,” J. Opt. Soc. Am. B 10, 817-826 (1993).
    [CrossRef]
  24. L. W. Casperson, “Spontaneous coherent pulsations in ring-laser oscillators: stability criteria,” J. Opt. Soc. Am. 2, 993-997 (1985) and references.
    [CrossRef]
  25. L. W. Casperson, “Laser power calculations: sources of error,” Appl. Opt. 19, 422-434 (1980).
    [CrossRef] [PubMed]
  26. P. Chenkosol and L. W. Casperson, “Spontaneous coherent pulsations in 3.39 μm He-Ne standing-wave laser oscillators,” J. Opt. Soc. Am. B 20, 2539-2547 (2003).
    [CrossRef]

2009 (1)

2003 (2)

2000 (1)

J. F. Urchueguia, G. J. de Valcárcel, E. Roldán, and F. Prati, “Transverse effects in ring fiber laser multimode instabilities,” Phys. Rev. A 62, 041801 (2000).
[CrossRef]

1998 (1)

1996 (1)

C. P. Smith and R. Dykstra, “Observation in the two-level spatial Maxwell-Bloch model of the anomalously large first peak as seen in experimental Lorenz-like spiral chaos from the N15H3 laser,” Opt. Commun. 129, 69-74 (1996).
[CrossRef]

1995 (2)

C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
[CrossRef]

C. P. Smith and R. Dykstra, “Lorenz-like chaos in a Gaussian mode laser with a radially dependent gain,” Opt. Commun. 117, 107-110 (1995).
[CrossRef]

1993 (1)

1992 (1)

D. Y. Tang, C. O. Weiss, E. Roldán, and C. J. de Valcárcel, “Deviation from Lorenz-type dynamics of an NH3 ring laser,” Opt. Commun. 89, 47-53 (1992).
[CrossRef]

1985 (4)

1984 (3)

R. S. Gioggia and N. B. Abraham, “Anomalous mode pulling, instabilities, and chaos in a single mode, standing-wave 3.39-μm He-Ne laser,” Phys. Rev. A 29, 1304-1309 (1984).
[CrossRef]

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

L. A. Lugiato, R. J. Horowicz, and G. Strini, “Instabilities in passive and active optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A 30, 1366-1376 (1984).
[CrossRef]

1983 (2)

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

R. S. Gioggia and N. B. Abraham, “Single-mode self-pulsing instabilities at the Lamb dip of a He-Ne 3.39 μm laser,” Opt. Commun. 47, 278-282 (1983).
[CrossRef]

1982 (2)

J. Bentley and N. B. Abraham, “Mode-pulling, mode-splitting, and pulsing in a high gain He-Xe laser,” Opt. Commun. 41, 52-56 (1982).
[CrossRef]

M. Maeda and N. B. Abraham, “Measurements of mode-splitting self-pulsing in a single-mode, Fabry-Perot laser,” Phys. Rev. A 26, 3395-3403 (1982).
[CrossRef]

1980 (2)

J. Bentley and N. B. Abraham, “Mode-pulling, mode-splitting and pulsing in high-gain lasers,” J. Opt. Soc. Am. 70, 1622 (1980).

L. W. Casperson, “Laser power calculations: sources of error,” Appl. Opt. 19, 422-434 (1980).
[CrossRef] [PubMed]

1978 (1)

L. W. Casperson, “Spontaneous coherent pulsations in laser oscillators,” IEEE J. Quantum Electron. QE-14, 756-761 (1978).
[CrossRef]

1975 (1)

H. Haken, “Analogy between higher instabilities in fluids and lasers,” Phys. Lett. A 53, 77-78 (1975).
[CrossRef]

Abraham, N. B.

C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
[CrossRef]

N. B. Abraham, L. A. Lugiato, and L. M. Narducci, “Overview of instabilities in laser systems,” J. Opt. Soc. Am. B 2, 7-14 (1985) and references.
[CrossRef]

R. S. Gioggia and N. B. Abraham, “Anomalous mode pulling, instabilities, and chaos in a single mode, standing-wave 3.39-μm He-Ne laser,” Phys. Rev. A 29, 1304-1309 (1984).
[CrossRef]

R. S. Gioggia and N. B. Abraham, “Single-mode self-pulsing instabilities at the Lamb dip of a He-Ne 3.39 μm laser,” Opt. Commun. 47, 278-282 (1983).
[CrossRef]

M. Maeda and N. B. Abraham, “Measurements of mode-splitting self-pulsing in a single-mode, Fabry-Perot laser,” Phys. Rev. A 26, 3395-3403 (1982).
[CrossRef]

J. Bentley and N. B. Abraham, “Mode-pulling, mode-splitting, and pulsing in a high gain He-Xe laser,” Opt. Commun. 41, 52-56 (1982).
[CrossRef]

J. Bentley and N. B. Abraham, “Mode-pulling, mode-splitting and pulsing in high-gain lasers,” J. Opt. Soc. Am. 70, 1622 (1980).

Bentley, J.

J. Bentley and N. B. Abraham, “Mode-pulling, mode-splitting, and pulsing in a high gain He-Xe laser,” Opt. Commun. 41, 52-56 (1982).
[CrossRef]

J. Bentley and N. B. Abraham, “Mode-pulling, mode-splitting and pulsing in high-gain lasers,” J. Opt. Soc. Am. 70, 1622 (1980).

Casperson, L. W.

Chenkosol, P.

Corbalin, R.

C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
[CrossRef]

de Valcárcel, C. J.

D. Y. Tang, C. O. Weiss, E. Roldán, and C. J. de Valcárcel, “Deviation from Lorenz-type dynamics of an NH3 ring laser,” Opt. Commun. 89, 47-53 (1992).
[CrossRef]

de Valcárcel, G. J.

E. Roldán, G. J. de Valcárcel, J. F. Urchueguia, and J. M. Guerra, “Observability of the Risken-Nummedal-Graham-Haken instability in Nd:YAG lasers,” J. Opt. Soc. Am. B 20, 816-824 (2003).
[CrossRef]

J. F. Urchueguia, G. J. de Valcárcel, E. Roldán, and F. Prati, “Transverse effects in ring fiber laser multimode instabilities,” Phys. Rev. A 62, 041801 (2000).
[CrossRef]

J. F. Urchueguia, G. J. de Valcárcel, and E. Roldán, “Laser instabilities in a Gaussian cavity mode with Gaussian pump profile,” J. Opt. Soc. Am. B 15, 1512-1520 (1998).
[CrossRef]

C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
[CrossRef]

Dykstra, R.

C. P. Smith and R. Dykstra, “Observation in the two-level spatial Maxwell-Bloch model of the anomalously large first peak as seen in experimental Lorenz-like spiral chaos from the N15H3 laser,” Opt. Commun. 129, 69-74 (1996).
[CrossRef]

C. P. Smith and R. Dykstra, “Lorenz-like chaos in a Gaussian mode laser with a radially dependent gain,” Opt. Commun. 117, 107-110 (1995).
[CrossRef]

Gioggia, R. S.

R. S. Gioggia and N. B. Abraham, “Anomalous mode pulling, instabilities, and chaos in a single mode, standing-wave 3.39-μm He-Ne laser,” Phys. Rev. A 29, 1304-1309 (1984).
[CrossRef]

R. S. Gioggia and N. B. Abraham, “Single-mode self-pulsing instabilities at the Lamb dip of a He-Ne 3.39 μm laser,” Opt. Commun. 47, 278-282 (1983).
[CrossRef]

Guerra, J. M.

Haken, H.

H. Haken, “Analogy between higher instabilities in fluids and lasers,” Phys. Lett. A 53, 77-78 (1975).
[CrossRef]

Horowicz, R. J.

L. A. Lugiato, R. J. Horowicz, and G. Strini, “Instabilities in passive and active optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A 30, 1366-1376 (1984).
[CrossRef]

Hübner, U.

C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
[CrossRef]

Lugiato, L. A.

N. B. Abraham, L. A. Lugiato, and L. M. Narducci, “Overview of instabilities in laser systems,” J. Opt. Soc. Am. B 2, 7-14 (1985) and references.
[CrossRef]

L. A. Lugiato and M. Milani, “Effects of Gaussian-beam averaging on laser instabilities,” J. Opt. Soc. Am. B 2, 15-17 (1985).
[CrossRef]

L. A. Lugiato, R. J. Horowicz, and G. Strini, “Instabilities in passive and active optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A 30, 1366-1376 (1984).
[CrossRef]

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

Maeda, M.

M. Maeda and N. B. Abraham, “Measurements of mode-splitting self-pulsing in a single-mode, Fabry-Perot laser,” Phys. Rev. A 26, 3395-3403 (1982).
[CrossRef]

Milani, M.

L. A. Lugiato and M. Milani, “Effects of Gaussian-beam averaging on laser instabilities,” J. Opt. Soc. Am. B 2, 15-17 (1985).
[CrossRef]

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

Narducci, L. M.

Prati, F.

J. F. Urchueguia, G. J. de Valcárcel, E. Roldán, and F. Prati, “Transverse effects in ring fiber laser multimode instabilities,” Phys. Rev. A 62, 041801 (2000).
[CrossRef]

Pujol, J.

C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
[CrossRef]

Roldán, E.

E. Roldán, G. J. de Valcárcel, J. F. Urchueguia, and J. M. Guerra, “Observability of the Risken-Nummedal-Graham-Haken instability in Nd:YAG lasers,” J. Opt. Soc. Am. B 20, 816-824 (2003).
[CrossRef]

J. F. Urchueguia, G. J. de Valcárcel, E. Roldán, and F. Prati, “Transverse effects in ring fiber laser multimode instabilities,” Phys. Rev. A 62, 041801 (2000).
[CrossRef]

J. F. Urchueguia, G. J. de Valcárcel, and E. Roldán, “Laser instabilities in a Gaussian cavity mode with Gaussian pump profile,” J. Opt. Soc. Am. B 15, 1512-1520 (1998).
[CrossRef]

C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
[CrossRef]

D. Y. Tang, C. O. Weiss, E. Roldán, and C. J. de Valcárcel, “Deviation from Lorenz-type dynamics of an NH3 ring laser,” Opt. Commun. 89, 47-53 (1992).
[CrossRef]

Sargent, M.

Smith, C. P.

C. P. Smith and R. Dykstra, “Observation in the two-level spatial Maxwell-Bloch model of the anomalously large first peak as seen in experimental Lorenz-like spiral chaos from the N15H3 laser,” Opt. Commun. 129, 69-74 (1996).
[CrossRef]

C. P. Smith and R. Dykstra, “Lorenz-like chaos in a Gaussian mode laser with a radially dependent gain,” Opt. Commun. 117, 107-110 (1995).
[CrossRef]

Strini, G.

L. A. Lugiato, R. J. Horowicz, and G. Strini, “Instabilities in passive and active optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A 30, 1366-1376 (1984).
[CrossRef]

Stuut, S.

Tang, D. Y.

C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
[CrossRef]

D. Y. Tang, C. O. Weiss, E. Roldán, and C. J. de Valcárcel, “Deviation from Lorenz-type dynamics of an NH3 ring laser,” Opt. Commun. 89, 47-53 (1992).
[CrossRef]

Urchueguia, J. F.

Vilaseca, R.

C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
[CrossRef]

Weiss, C. O.

C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
[CrossRef]

D. Y. Tang, C. O. Weiss, E. Roldán, and C. J. de Valcárcel, “Deviation from Lorenz-type dynamics of an NH3 ring laser,” Opt. Commun. 89, 47-53 (1992).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

C. O. Weiss, R. Vilaseca, N. B. Abraham, R. Corbalin, E. Roldán, G. J. de Valcárcel, J. Pujol, U. Hübner, and D. Y. Tang, “Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model,” Appl. Phys. B 61, 223-242 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. W. Casperson, “Spontaneous coherent pulsations in laser oscillators,” IEEE J. Quantum Electron. QE-14, 756-761 (1978).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Bentley and N. B. Abraham, “Mode-pulling, mode-splitting and pulsing in high-gain lasers,” J. Opt. Soc. Am. 70, 1622 (1980).

L. W. Casperson, “Spontaneous coherent pulsations in ring-laser oscillators: stability criteria,” J. Opt. Soc. Am. 2, 993-997 (1985) and references.
[CrossRef]

J. Opt. Soc. Am. B (9)

E. Roldán, G. J. de Valcárcel, J. F. Urchueguia, and J. M. Guerra, “Observability of the Risken-Nummedal-Graham-Haken instability in Nd:YAG lasers,” J. Opt. Soc. Am. B 20, 816-824 (2003).
[CrossRef]

P. Chenkosol and L. W. Casperson, “Stability criteria for spontaneously pulsing gas lasers,” J. Opt. Soc. Am. B 26, 939-945 (2009).
[CrossRef]

L. W. Casperson, “Spontaneous coherent pulsations in ring-laser oscillators,” J. Opt. Soc. Am. B 2, 62-72 (1985).
[CrossRef]

P. Chenkosol and L. W. Casperson, “Spontaneous coherent pulsations in standing-wave laser oscillators: stability criteria for homogeneous broadening,” J. Opt. Soc. Am. B 10, 817-826 (1993).
[CrossRef]

P. Chenkosol and L. W. Casperson, “Spontaneous coherent pulsations in 3.39 μm He-Ne standing-wave laser oscillators,” J. Opt. Soc. Am. B 20, 2539-2547 (2003).
[CrossRef]

J. F. Urchueguia, G. J. de Valcárcel, and E. Roldán, “Laser instabilities in a Gaussian cavity mode with Gaussian pump profile,” J. Opt. Soc. Am. B 15, 1512-1520 (1998).
[CrossRef]

N. B. Abraham, L. A. Lugiato, and L. M. Narducci, “Overview of instabilities in laser systems,” J. Opt. Soc. Am. B 2, 7-14 (1985) and references.
[CrossRef]

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

L. A. Lugiato and M. Milani, “Effects of Gaussian-beam averaging on laser instabilities,” J. Opt. Soc. Am. B 2, 15-17 (1985).
[CrossRef]

Opt. Commun. (6)

C. P. Smith and R. Dykstra, “Lorenz-like chaos in a Gaussian mode laser with a radially dependent gain,” Opt. Commun. 117, 107-110 (1995).
[CrossRef]

C. P. Smith and R. Dykstra, “Observation in the two-level spatial Maxwell-Bloch model of the anomalously large first peak as seen in experimental Lorenz-like spiral chaos from the N15H3 laser,” Opt. Commun. 129, 69-74 (1996).
[CrossRef]

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

D. Y. Tang, C. O. Weiss, E. Roldán, and C. J. de Valcárcel, “Deviation from Lorenz-type dynamics of an NH3 ring laser,” Opt. Commun. 89, 47-53 (1992).
[CrossRef]

J. Bentley and N. B. Abraham, “Mode-pulling, mode-splitting, and pulsing in a high gain He-Xe laser,” Opt. Commun. 41, 52-56 (1982).
[CrossRef]

R. S. Gioggia and N. B. Abraham, “Single-mode self-pulsing instabilities at the Lamb dip of a He-Ne 3.39 μm laser,” Opt. Commun. 47, 278-282 (1983).
[CrossRef]

Phys. Lett. A (1)

H. Haken, “Analogy between higher instabilities in fluids and lasers,” Phys. Lett. A 53, 77-78 (1975).
[CrossRef]

Phys. Rev. A (4)

L. A. Lugiato, R. J. Horowicz, and G. Strini, “Instabilities in passive and active optical systems with a Gaussian transverse intensity profile,” Phys. Rev. A 30, 1366-1376 (1984).
[CrossRef]

R. S. Gioggia and N. B. Abraham, “Anomalous mode pulling, instabilities, and chaos in a single mode, standing-wave 3.39-μm He-Ne laser,” Phys. Rev. A 29, 1304-1309 (1984).
[CrossRef]

M. Maeda and N. B. Abraham, “Measurements of mode-splitting self-pulsing in a single-mode, Fabry-Perot laser,” Phys. Rev. A 26, 3395-3403 (1982).
[CrossRef]

J. F. Urchueguia, G. J. de Valcárcel, E. Roldán, and F. Prati, “Transverse effects in ring fiber laser multimode instabilities,” Phys. Rev. A 62, 041801 (2000).
[CrossRef]

Other (1)

L. W. Casperson, Laser Physics, J.D.Harvey and D.F.Walls, eds., Vol. 182 of Springer Lecture Notes in Physics (Springer-Verlag, 1983), pp. 88-106.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Type 1 stability boundaries for inhomogeneously broadened unidirectional ring-laser oscillators with Gaussian-beam electromagnetic fields.

Fig. 2
Fig. 2

Type 1 stability boundaries for inhomogeneously broadened unidirectional ring-laser oscillators with uniform-plane-wave electric fields (after [21]).

Equations (63)

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

P r ( V , r , t ) t = γ [ P r ( V , r , t ) V P i ( V , r , t ) ] ,
P i ( V , r , t ) t = γ { P i ( V , r , t ) + V P r ( V , r , t ) + G ( r ) A ( t ) [ D 0 + D ( V , r , t ) ] } ,
D ( V , r , t ) t = γ d [ D ( V , r , t ) G ( r ) A ( t ) P i ( V , r , t ) ] ,
d A ( t ) d t = γ c [ A ( t ) + 0 G ( r ) P i ( V , r , t ) d V r d r ] .
P r s ( V , r ) = V P i s ( V , r ) ,
P i s ( V , r ) = V P r s ( V , r ) G ( r ) A s ( D 0 + D s ( V , r ) ) ,
D s ( V , r ) = G ( r ) A s P i s ( V , r ) ,
A s = 0 G ( r ) P i s ( V , r ) d V r d r .
P i s ( V , r ) = G ( r ) A s D 0 1 + V 2 + G 2 ( r ) A s 2 .
A s = 0 G ( r ) [ G ( r ) A s D 0 1 + V 2 + G 2 ( r ) A s 2 ] d V r d r ,
1 = D 0 0 G 2 ( r ) d V 1 + V 2 + G 2 ( r ) A s 2 r d r = π D 0 0 G 2 ( r ) r d r 1 + G 2 ( r ) A s 2 = π D 0 0 ( 2 / π ) exp ( 2 ( r / w ) 2 ) r d r 1 + ( 2 / π ) exp ( 2 ( r / w ) 2 ) A s 2 = w 2 D 0 2 0 exp ( 2 ( r / w ) 2 ) d ( 2 ( r / w ) 2 ) 1 + ( 2 / π ) exp ( 2 ( r / w ) 2 ) A s 2 = w 2 D 0 2 π A s 2 [ 1 + 2 A s 2 π 1 ] .
D 0 = 2 A s 2 π w 2 [ 1 + 2 A s 2 π 1 ] 1 .
D 0 , th = lim A s 0 2 A s 2 π w 2 [ 1 + 2 A s 2 π 1 ] 1 2 A s 2 π w 2 [ 1 + ( 1 2 ) 2 A s 2 π 1 ] 1 = 2 w 2 .
R = D 0 D 0 , th = D 0 2 w 2 .
1 = ( R π A s 2 ) [ 1 + 2 A s 2 π 1 ] ,
[ A s 2 R π + 1 ] 2 = 1 + 2 A s 2 π ,
A s 4 ( R π ) 2 + 2 A s 2 R π + 1 = 1 + 2 A s 2 π ,
A s 2 ( R π ) 2 + 2 R π = 2 π ,
A s 2 = 2 R π ( R 1 ) .
P i ( V , r , t ) t = γ [ P i ( V , r , t ) + V P r ( V , r , t ) + G ( r ) A ( t ) ( 2 R w 2 + D ( V , r , t ) ) ] .
P r ( V , r , t ) = P r s ( V , r ) + P r ( V , r , t ) ,
P i ( V , r , t ) = P i s ( V , r ) + P i ( V , r , t ) ,
D ( V , r , t ) = D s ( V , r ) + D ( V , r , t ) ,
A ( t ) = A s + A ( t ) ,
P r ( V , r , t ) t = γ [ ( P r s ( V , r ) + P r ( V , r , t ) ) V ( P i s ( V , r ) + P i ( V , r , t ) ) ] = γ [ P r ( V , r , t ) V P i ( V , r , t ) ] ,
P i ( V , r , t ) t = γ [ ( P i s ( V , r ) + P i ( V , r , t ) ) + V ( P r s ( V , r ) + P r ( V , r , t ) ) + G ( r ) ( A s + A ( t ) ) ( 2 R w 2 + D s ( V , r ) + D ( V , r , t ) ) ] γ [ P i ( V , r , t ) + V P r ( V , r , t ) + G ( r ) ( A s D ( V , r , t ) + A ( t ) [ 2 R w 2 + D s ( V , r ) ] ) ] ,
D ( V , r , t ) t = γ d [ ( D s ( V , r ) + D ( V , r , t ) ) G ( r ) ( A s + A ( t ) ) ( P i s ( V , r ) + P i ( V , r , t ) ) ] γ d [ D ( V , r , t ) G ( r ) ( A s P i ( V , r , t ) + A ( t ) P i s ( V , r ) ) ] ,
d A s ( t ) d t = γ c [ ( A s + A ( t ) ) + 0 G ( r ) ( P i s ( V , r ) + P i ( V , r , t ) ) d V r d r ] = γ c [ A ( t ) + 0 G ( r ) P i ( V , r , t ) d V r d r ] ,
P r ( V , r , t ) t = δ [ P r ( V , r , t ) V P i ( V , r , t ) ] ,
P i ( V , r , t ) t = δ [ P i ( V , r , t ) + V P r ( V , r , t ) + G ( r ) ( A s D ( V , r , t ) + A ( t ) [ 2 R w 2 + D s ( V , r ) ] ) ] ,
D ( V , r , t ) t = δ ρ [ D ( V , r , t ) G ( r ) ( A s P i ( V , r , t ) + A ( t ) P i s ( V , r ) ) ] ,
d A ( t ) d t = [ A ( t ) + 0 G ( r ) P i ( V , r , t ) d V r d r ] .
P r ( V , r , t ) = P r ( V , r ) e λ t ,
P i ( V , r , t ) = P i ( V , r ) e λ t ,
D ( V , r , t ) = D ( V , r ) e λ t ,
A ( t ) = A e λ t ,
λ P r ( V , r ) = δ [ P r ( V , r ) V P i ( V , r ) ] ,
( λ + δ ) P r ( V , r ) = δ V P i ( V , r ) ,
λ P i ( V , r ) = δ [ P i ( V , r ) + V P r ( V , r ) + G ( r ) ( A s D ( V , r ) + A [ 2 R w 2 + D s ( V , r ) ] ) ] ,
( λ + δ ) P i ( V , r ) = δ [ V P r ( V , r ) + G ( r ) ( A s D ( V , r ) + A [ 2 R w 2 + D s ( V , r ) ] ) ] ,
λ D ( V , r ) = δ ρ [ D ( V , r ) G ( r ) ( A s P i ( V , r ) + A P i s ( V , r ) ) ] ,
( λ + δ ρ ) D ( V , r ) = δ ρ G ( r ) ( A s P i ( V , r ) + A P i s ( V , r ) ) ,
λ A = [ A + 0 G ( r ) P i ( V , r ) d V r d r ] ,
( λ + 1 ) A = 0 G ( r ) P i ( V , r ) d V r d r .
( λ + δ ) P i ( V , r ) = δ [ V ( δ V λ + δ ) P i ( V , r ) + G ( r ) ( A s D ( V , r ) + A [ 2 R w 2 + D s ( V , r ) ] ) ] ,
( λ + δ + δ 2 V 2 λ + δ ) P i ( V , r ) = δ G ( r ) ( A s D ( V , r ) + A [ 2 R w 2 + D s ( V , r ) ] ) .
( λ + δ + δ 2 V 2 λ + δ ) P i ( V , r ) = δ G ( r ) ( A s [ δ ρ G ( r ) ( λ + δ ρ ) ( A s P i ( V , r ) + A P i s ( V , r ) ) ] + A [ 2 R w 2 + D s ( V , r ) ] ) ,
( λ + δ + δ 2 V 2 λ + δ + δ 2 ρ G 2 ( r ) A s 2 λ + δ ρ ) P i ( V , r ) = δ 2 ρ G 2 ( r ) A s ( λ + δ ρ ) ( G ( r ) A s ( 2 R / w 2 ) 1 + V 2 + G 2 ( r ) A s 2 ) A δ G ( r ) [ 2 R w 2 G 2 ( r ) A s 2 ( 2 R / w 2 ) 1 + V 2 + G 2 ( r ) A s 2 ] A = δ G ( r ) ( 2 R / w 2 ) A 1 + V 2 + G 2 ( r ) A s 2 ( 1 + V 2 ) + ( δ G ( r ) ( 2 R / w 2 ) A 1 + V 2 + G 2 ( r ) A s 2 ) ( δ ρ G 2 ( r ) A s 2 ( λ + δ ρ ) ) = ( δ G ( r ) ( 2 R / w 2 ) A 1 + V 2 + G 2 ( r ) A s 2 ) ( 1 + V 2 δ ρ G 2 ( r ) A s 2 ( λ + δ ρ ) ) ,
P i ( V , r ) = ( δ G ( r ) ( 2 R / w 2 ) A 1 + V 2 + G 2 ( r ) A s 2 ) ( 1 + V 2 δ ρ G 2 ( r ) A s 2 ( λ + δ ρ ) ) ( λ + δ + δ 2 V 2 ( λ + δ ) + δ 2 ρ G 2 ( r ) A s 2 ( λ + δ ρ ) ) .
λ + 1 = 0 [ ( δ G 2 ( r ) ( 2 R / w 2 ) 1 + V 2 + G 2 ( r ) A s 2 ) ( 1 + V 2 δ ρ G 2 ( r ) A s 2 λ + δ ρ ) ( λ + δ + δ 2 V 2 ( λ + δ ) + δ 2 ρ G 2 ( r ) A s 2 ( λ + δ ρ ) ) ] d V r d r = ( 2 δ R w 2 ) 0 ( λ + δ ) G 2 ( r ) 1 + V 2 + G 2 ( r ) A s 2 [ ( λ + δ ρ ) ( 1 + V 2 ) δ ρ G 2 ( r ) A s 2 ] [ ( λ + δ ρ ) [ ( λ + δ ) 2 + δ 2 V 2 ] + ( λ + δ ) ( δ 2 ρ G 2 ( r ) A s 2 ) ] d V r d r = ( 2 δ R A s 2 ) ( 1 4 ) ( 2 / π ) A s 2 0 ( λ + δ ) 1 + V 2 + G 2 ( r ) A s 2 [ ( λ + δ ρ ) ( 1 + V 2 ) δ ρ G 2 ( r ) A s 2 ] d V d ( G 2 ( r ) A s 2 ) [ ( λ + δ ρ ) [ ( λ + δ ) 2 + δ 2 V 2 ] + ( λ + δ ) ( δ 2 ρ G 2 ( r ) A s 2 ) ] = ( δ R 2 A s 2 ) 0 ( 2 / π ) A s 2 ( λ + δ ) 1 + V 2 + G 2 ( r ) A s 2 [ ( λ + δ ρ ) ( 1 + V 2 ) δ ρ G 2 ( r ) A s 2 ] d V d ( G 2 ( r ) A s 2 ) [ ( λ + δ ρ ) [ ( λ + δ ) 2 + δ 2 V 2 ] + ( λ + δ ) ( δ 2 ρ G 2 ( r ) A s 2 ) ] = ( δ R 2 A s 2 ) 0 ( 2 / π ) A s 2 ( λ + δ ) 1 + V 2 + K [ ( λ + δ ρ ) ( 1 + V 2 ) δ ρ K ] d V d K [ ( λ + δ ρ ) [ ( λ + δ ) 2 + δ 2 V 2 ] + ( λ + δ ) ( δ 2 ρ K ) ] ,
K = G 2 ( r ) A s 2 ,
G 2 ( r ) = ( 2 π ) exp ( 2 r 2 w 2 ) ,
d G 2 ( r ) d r = ( 4 r w 2 ) G 2 ( r )
λ + 1 = ( δ R ( λ + δ ) A s 2 ) 0 ( 2 / π ) A s 2 0 1 1 + V 2 + K [ ( λ + δ ρ ) ( 1 + V 2 ) δ ρ K ] d V d K [ ( λ + δ ρ ) [ ( λ + δ ) 2 + δ 2 V 2 ] + ( λ + δ ) ( δ 2 ρ K ) ] = ( δ R ( λ + δ ) A s 2 ) 0 ( 2 / π ) A s 2 0 1 1 + V 2 + K [ ( λ + δ ρ δ ρ K ) + ( λ + δ ρ ) V 2 ] d V d K [ ( λ + δ ρ ) ( λ + δ ) 2 + ( λ + δ ) δ 2 ρ K + ( λ + δ ρ ) δ 2 V 2 ] .
A 1 = λ + δ ρ δ ρ K ,
B 1 = λ + δ ρ ,
C 1 = 1 + K ,
D 1 = ( λ + δ ρ ) ( λ + δ ) 2 + ( λ + δ ) δ 2 ρ K ,
E 1 = ( λ + δ ρ ) δ 2 .
0 ( A 1 + B 1 V 2 ) d V ( C 1 + V 2 ) ( D 1 + E 1 V 2 ) = A 1 0 d V ( C 1 + V 2 ) ( D 1 + E 1 V 2 ) + B 1 0 V 2 d V ( C 1 + V 2 ) ( D 1 + E 1 V 2 ) = A 1 [ 1 ( C 1 E 1 D 1 ) { 0 d V C 1 + V 2 + E 1 0 d V ( D 1 + E 1 V 2 ) } ] + B 1 [ 1 ( C 1 E 1 D 1 ) { C 1 0 d V C 1 + V 2 D 1 0 d V D 1 + E 1 V 2 } ] ,
= A 1 [ 1 ( C 1 E 1 D 1 ) { π 2 C 1 + π 2 D 1 / E 1 } ] + B 1 [ 1 ( C 1 E 1 D 1 ) { C 1 π 2 C 1 ( D 1 E 1 ) π 2 D 1 / E 1 } ] = π 2 ( C 1 E 1 D 1 ) [ A 1 ( E 1 D 1 1 C 1 ) + B 1 ( C 1 D 1 E 1 ) ] .
λ + 1 = ( δ R ( λ + δ ) A s 2 ) 0 ( 2 / π ) A s 2 π 2 ( C 1 E 1 D 1 ) [ A 1 ( E 1 D 1 1 C 1 ) + B 1 ( C 1 D 1 E 1 ) ] d K = ( δ R ( λ + δ ) 2 R π ( R 1 ) ) ( π 2 ) 0 4 R ( R 1 ) 1 ( C 1 E 1 D 1 ) [ A 1 ( E 1 D 1 1 C 1 ) + B 1 ( C 1 D 1 E 1 ) ] d K = ( δ ( λ + δ ) 4 ( R 1 ) ) 0 4 R ( R 1 ) 1 ( C 1 E 1 D 1 ) [ A 1 ( E 1 D 1 1 C 1 ) + B 1 ( C 1 D 1 E 1 ) ] d K .
0 = λ + 1 ( δ ( λ + δ ) 4 ( R 1 ) ) 0 4 R ( R 1 ) [ 1 ( 1 + K ) ( λ + δ ρ ) δ 2 ( ( λ + δ ρ ) ( λ + δ ) 2 + ( λ + δ ) δ 2 ρ K ) × { ( λ + δ ρ δ ρ K ) [ ( ( λ + δ ρ ) δ 2 ( λ + δ ρ ) ( λ + δ ) 2 + ( λ + δ ) δ 2 ρ K ) 1 / 2 1 1 + K ] + ( λ + δ ρ ) [ 1 + K ( ( λ + δ ρ ) ( λ + δ ) 2 + ( λ + δ ) δ 2 ρ K ( λ + δ ρ ) δ 2 ) 1 / 2 ] } ] d K .

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