Abstract

Several types of instability in passive Q switching and optical bistability are observed in a number of 10-μm laser lines in a N2O laser with intracavity saturable absorbers such as NH3, SF6, C2H4, C2H3Cl, and CCl2F2. The observed pulse shapes are reproduced well by a calculation based on the recently proposed rate-equation model. Characteristic dependences of passive Q switching and bistability on the laser parameters are explained with a phase diagram derived theoretically.

© 1988 Optical Society of America

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  1. O. R. Wood, S. E. Schwarz, “Passive Q-switching of a CO2laser,” Appl. Phys. Lett. 11, 88 (1967).
    [CrossRef]
  2. C. O. Weiss, W. Klische, P. S. Ering, M. Cooper, “Instabilities and chaos of a single mode NH3ring laser,” Opt. Commun. 52, 405 (1985).
    [CrossRef]
  3. H. Haken, “Analogy between higher instabilities in fluids and lasers,” Phys. Lett. 53A, 77 (1975).
  4. L. W. Casperson, “Spontaneous coherent pulsations in laser oscillator,” IEEE J. Quantum Electron. QE-14, 756 (1978).
    [CrossRef]
  5. M.-L. Shin, P. W. Milonni, J. R. Ackerhalt, “Modeling laser instabilities and chaos,” J. Opt. Soc. Am. B 2, 130 (1985).
    [CrossRef]
  6. R. S. Gioggia, N. Abraham, “Routes to chaotic output from a single-mode, dc-excited laser,” Phys. Rev. Lett. 51, 650 (1983).
    [CrossRef]
  7. M. Tachikawa, K. Tanii, M. Kajita, T. Shimizu, “Undamped undulation superposed on the passive Q-switching pulse of a CO2laser,” Appl. Phys. B 39, 83 (1986).
    [CrossRef]
  8. M. Tachikawa, K. Tanii, T. Shimizu, “Comprehensive interpretation of passive Q switching and optical bistability in a CO2laser with an intracavity saturable absorber,” J. Opt. Soc. Am. B 4, 387 (1987).
    [CrossRef]
  9. E. Arimondo, P. Bootz, P. Glorieux, E. Menchi, “Pulse shape and phase diagram in the passive Q switching of CO2lasers,” J. Opt. Soc. Am. B 2, 193 (1985).
    [CrossRef]
  10. H. Brunet, F. Voignier, “Passive Q-switching of a N2O laser using ethylene,” Appl. Phys. Lett. 15, 423 (1969).
    [CrossRef]
  11. A. Tanaka, A. Mori, Y. Homma, M. Yamanaka, “Characteristics of 10.8-μ m N2O lasers in cw and Q-switching operations,” Jpn. J. Appl. Phys. 13, 2009 (1974).
    [CrossRef]
  12. J. H. McCoy, “Passive Q-switched N2O laser,” IEEE J. Quantum Electron. QE-6, 567 (1970).
    [CrossRef]
  13. C. O. Weiss, “Optically bistable N2O-laser,” Opt. Commun. 42, 291 (1982).
    [CrossRef]

1987 (1)

1986 (1)

M. Tachikawa, K. Tanii, M. Kajita, T. Shimizu, “Undamped undulation superposed on the passive Q-switching pulse of a CO2laser,” Appl. Phys. B 39, 83 (1986).
[CrossRef]

1985 (3)

1983 (1)

R. S. Gioggia, N. Abraham, “Routes to chaotic output from a single-mode, dc-excited laser,” Phys. Rev. Lett. 51, 650 (1983).
[CrossRef]

1982 (1)

C. O. Weiss, “Optically bistable N2O-laser,” Opt. Commun. 42, 291 (1982).
[CrossRef]

1978 (1)

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

1975 (1)

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

1974 (1)

A. Tanaka, A. Mori, Y. Homma, M. Yamanaka, “Characteristics of 10.8-μ m N2O lasers in cw and Q-switching operations,” Jpn. J. Appl. Phys. 13, 2009 (1974).
[CrossRef]

1970 (1)

J. H. McCoy, “Passive Q-switched N2O laser,” IEEE J. Quantum Electron. QE-6, 567 (1970).
[CrossRef]

1969 (1)

H. Brunet, F. Voignier, “Passive Q-switching of a N2O laser using ethylene,” Appl. Phys. Lett. 15, 423 (1969).
[CrossRef]

1967 (1)

O. R. Wood, S. E. Schwarz, “Passive Q-switching of a CO2laser,” Appl. Phys. Lett. 11, 88 (1967).
[CrossRef]

Abraham, N.

R. S. Gioggia, N. Abraham, “Routes to chaotic output from a single-mode, dc-excited laser,” Phys. Rev. Lett. 51, 650 (1983).
[CrossRef]

Ackerhalt, J. R.

Arimondo, E.

Bootz, P.

Brunet, H.

H. Brunet, F. Voignier, “Passive Q-switching of a N2O laser using ethylene,” Appl. Phys. Lett. 15, 423 (1969).
[CrossRef]

Casperson, L. W.

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

Cooper, M.

C. O. Weiss, W. Klische, P. S. Ering, M. Cooper, “Instabilities and chaos of a single mode NH3ring laser,” Opt. Commun. 52, 405 (1985).
[CrossRef]

Ering, P. S.

C. O. Weiss, W. Klische, P. S. Ering, M. Cooper, “Instabilities and chaos of a single mode NH3ring laser,” Opt. Commun. 52, 405 (1985).
[CrossRef]

Gioggia, R. S.

R. S. Gioggia, N. Abraham, “Routes to chaotic output from a single-mode, dc-excited laser,” Phys. Rev. Lett. 51, 650 (1983).
[CrossRef]

Glorieux, P.

Haken, H.

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

Homma, Y.

A. Tanaka, A. Mori, Y. Homma, M. Yamanaka, “Characteristics of 10.8-μ m N2O lasers in cw and Q-switching operations,” Jpn. J. Appl. Phys. 13, 2009 (1974).
[CrossRef]

Kajita, M.

M. Tachikawa, K. Tanii, M. Kajita, T. Shimizu, “Undamped undulation superposed on the passive Q-switching pulse of a CO2laser,” Appl. Phys. B 39, 83 (1986).
[CrossRef]

Klische, W.

C. O. Weiss, W. Klische, P. S. Ering, M. Cooper, “Instabilities and chaos of a single mode NH3ring laser,” Opt. Commun. 52, 405 (1985).
[CrossRef]

McCoy, J. H.

J. H. McCoy, “Passive Q-switched N2O laser,” IEEE J. Quantum Electron. QE-6, 567 (1970).
[CrossRef]

Menchi, E.

Milonni, P. W.

Mori, A.

A. Tanaka, A. Mori, Y. Homma, M. Yamanaka, “Characteristics of 10.8-μ m N2O lasers in cw and Q-switching operations,” Jpn. J. Appl. Phys. 13, 2009 (1974).
[CrossRef]

Schwarz, S. E.

O. R. Wood, S. E. Schwarz, “Passive Q-switching of a CO2laser,” Appl. Phys. Lett. 11, 88 (1967).
[CrossRef]

Shimizu, T.

M. Tachikawa, K. Tanii, T. Shimizu, “Comprehensive interpretation of passive Q switching and optical bistability in a CO2laser with an intracavity saturable absorber,” J. Opt. Soc. Am. B 4, 387 (1987).
[CrossRef]

M. Tachikawa, K. Tanii, M. Kajita, T. Shimizu, “Undamped undulation superposed on the passive Q-switching pulse of a CO2laser,” Appl. Phys. B 39, 83 (1986).
[CrossRef]

Shin, M.-L.

Tachikawa, M.

M. Tachikawa, K. Tanii, T. Shimizu, “Comprehensive interpretation of passive Q switching and optical bistability in a CO2laser with an intracavity saturable absorber,” J. Opt. Soc. Am. B 4, 387 (1987).
[CrossRef]

M. Tachikawa, K. Tanii, M. Kajita, T. Shimizu, “Undamped undulation superposed on the passive Q-switching pulse of a CO2laser,” Appl. Phys. B 39, 83 (1986).
[CrossRef]

Tanaka, A.

A. Tanaka, A. Mori, Y. Homma, M. Yamanaka, “Characteristics of 10.8-μ m N2O lasers in cw and Q-switching operations,” Jpn. J. Appl. Phys. 13, 2009 (1974).
[CrossRef]

Tanii, K.

M. Tachikawa, K. Tanii, T. Shimizu, “Comprehensive interpretation of passive Q switching and optical bistability in a CO2laser with an intracavity saturable absorber,” J. Opt. Soc. Am. B 4, 387 (1987).
[CrossRef]

M. Tachikawa, K. Tanii, M. Kajita, T. Shimizu, “Undamped undulation superposed on the passive Q-switching pulse of a CO2laser,” Appl. Phys. B 39, 83 (1986).
[CrossRef]

Voignier, F.

H. Brunet, F. Voignier, “Passive Q-switching of a N2O laser using ethylene,” Appl. Phys. Lett. 15, 423 (1969).
[CrossRef]

Weiss, C. O.

C. O. Weiss, W. Klische, P. S. Ering, M. Cooper, “Instabilities and chaos of a single mode NH3ring laser,” Opt. Commun. 52, 405 (1985).
[CrossRef]

C. O. Weiss, “Optically bistable N2O-laser,” Opt. Commun. 42, 291 (1982).
[CrossRef]

Wood, O. R.

O. R. Wood, S. E. Schwarz, “Passive Q-switching of a CO2laser,” Appl. Phys. Lett. 11, 88 (1967).
[CrossRef]

Yamanaka, M.

A. Tanaka, A. Mori, Y. Homma, M. Yamanaka, “Characteristics of 10.8-μ m N2O lasers in cw and Q-switching operations,” Jpn. J. Appl. Phys. 13, 2009 (1974).
[CrossRef]

Appl. Phys. B (1)

M. Tachikawa, K. Tanii, M. Kajita, T. Shimizu, “Undamped undulation superposed on the passive Q-switching pulse of a CO2laser,” Appl. Phys. B 39, 83 (1986).
[CrossRef]

Appl. Phys. Lett. (2)

H. Brunet, F. Voignier, “Passive Q-switching of a N2O laser using ethylene,” Appl. Phys. Lett. 15, 423 (1969).
[CrossRef]

O. R. Wood, S. E. Schwarz, “Passive Q-switching of a CO2laser,” Appl. Phys. Lett. 11, 88 (1967).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

J. H. McCoy, “Passive Q-switched N2O laser,” IEEE J. Quantum Electron. QE-6, 567 (1970).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

A. Tanaka, A. Mori, Y. Homma, M. Yamanaka, “Characteristics of 10.8-μ m N2O lasers in cw and Q-switching operations,” Jpn. J. Appl. Phys. 13, 2009 (1974).
[CrossRef]

Opt. Commun. (2)

C. O. Weiss, W. Klische, P. S. Ering, M. Cooper, “Instabilities and chaos of a single mode NH3ring laser,” Opt. Commun. 52, 405 (1985).
[CrossRef]

C. O. Weiss, “Optically bistable N2O-laser,” Opt. Commun. 42, 291 (1982).
[CrossRef]

Phys. Lett. (1)

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

Phys. Rev. Lett. (1)

R. S. Gioggia, N. Abraham, “Routes to chaotic output from a single-mode, dc-excited laser,” Phys. Rev. Lett. 51, 650 (1983).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Observed and (a′) calculated PQS pulse train. The pulse has the form of a single spike.

Fig. 2
Fig. 2

(a)–(e) Observed and (a′)–(e′) calculated characteristic dependence of PQS behavior [type (B)] when the pressure of the absorbing gas and the relaxation rate R, respectively, are varied.

Fig. 3
Fig. 3

(a)–(d) Observed and (a′)–(d′) calculated characteristic dependence of PQS behavior [type (B′)] when the pressure of the absorbing gas and the relaxation rate, respectively, are varied.

Fig. 4
Fig. 4

(a)–(c) Observed and (a′)–(c′) calculated characteristic dependence of PQS behavior [type (C)] when the pressure of the absorbing gas and the relaxation rate, respectively, are varied.

Fig. 5
Fig. 5

Observed hysteresis curve of the laser output on the R(15) line as a function of the SF6 pressure. Bistability is observed in the pressure range between Pon and Poff.

Fig. 6
Fig. 6

Model of the gain medium and the absorbing medium used in the rate-equation analysis.

Fig. 7
Fig. 7

Theoretically obtained phase diagram for the relaxation rate R and the absorption parameter b. The observed six characteristic dependences of the laser oscillation on the absorber pressure are clearly shown.

Fig. 8
Fig. 8

Photon density as steady-state solutions of the rate equations. Photon density is plotted as a function of the relaxation rate R, which is proportional to the pressure of the satu rable absorber. The solid line represents the photon density in the c:w laser oscillation. The laser is unstable at the photon density rep resented by the dashed line. The bistable range is between R2 and R3.

Tables (3)

Tables Icon

Table 1 Laser Lines for Which Six Types of Characteristic Dependence Are Observed for Five Kinds of Saturable Absorber

Tables Icon

Table 2 Notation of the Parameters Used in the Rate Equations

Tables Icon

Table 3 Parameter Values Used in the Phase-Diagram Analysis and the Reproduction of Passive Q-Switching Pulses and Bistable Hysteresis

Equations (2)

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d n / d t = B g f g ( J ) n ( M 1 - M 2 ) l g / L - B a n N l a / L - k n + A M 1 , d M 1 / d t = - B g f g ( J ) n ( M 1 - M 2 ) + P M - ( P + R 10 + R 12 ) × M 1 - P M 2 , d M 2 / d t = B g f g ( J ) n ( M 1 - M 2 ) + R 12 M 1 - R 20 M 2 , d N / d t = - 2 B a N - r ( N - N * ) .
b = B a / ( B g f g ) ,

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