Abstract

The occurrence of pure rotational-to-rotational lasing from high J levels suggests that present rotational nonequilibrium mechanisms are inadequate to explain all lasing behavior of the HF laser. A possible mechanism for explaining this behavior is vibrational-to-rotational energy transfer. The usual assumption that vibrational relaxation occurs with rotational levels at equilibrium at the translational temperature is replaced with a near resonant multiquanta VR process that results in the formation of highly excited rotational states. Computer simulations incorporating VR relaxation predicted significant occurrence of rotational lasing. A simpler model that produced rotational nonequilibrium from pumping and P-branch lasing did not exhibit rotational lasing. Rotational lasing did not decrease energy available to P-branch lasing and produced effects resembling an increase in rotational relaxation rates. Rotational lasing is very sensitive to kinetics for both VR energy exchange and rotational relaxation.

© 1980 Optical Society of America

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References

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  1. R. L. Kerber, J. J. T. Hough, Appl. Opt. 17, 2369. (1978).
    [CrossRef] [PubMed]
  2. J. J. T. Hough, R. L. Kerber, Appl. Opt. 14, 2960 (1975).
    [CrossRef] [PubMed]
  3. J. R. Creighton, “A Numerical Investigation of the Pulsed NF3 + H2 Chemical Laser Using a Model Which Includes Rotational Relaxation and Semi-Classical Laser Equations,” Technical Report UCRL 51931, Lawrence Livermore Laboratory, University of California/Livermore, 1Sept.1975.
  4. J. Moreno, “Computer Model for the H2 + F2 Super Radiant Laser,” AIAA paper 75-36, Thirteenth Aerospace Sciences Meeting, Pasadena, Calif., 20–22 Jan. 1975.
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    [CrossRef]
  6. L. H. Sentman, Appl. Opt. 15, 744 (1976); J. Chem. Phys. 62, 3523 (1975).
    [CrossRef]
  7. J. G. Skifstad, C. M. Chao, Appl. Opt. 14, 1713 (1975).
    [CrossRef] [PubMed]
  8. A. Ben-Shaul, K. L. Kompa, U. Schmailzl, J. Chem. Phys. 65, 1711 (1976).
    [CrossRef]
  9. R. F. Deutsch, Appl. Phys. Lett. 11, 18 (1967).
    [CrossRef]
  10. E. R. Sirkin, E. Cuellar, G. C. Pimentel, “Laser emission between high rotational states of HX resulting from photoelimination of halogenated olefins,” presented at the Fifth Conference of Chemical and Molecular Lasers, St. Louis, Mo., 18–20 Apr. 1977.
  11. N. Skribanowitz, I. P. Herman, R. M. Osgood, M. S. Feld, A. Javan, Appl. Phys. Lett. 20, 428 (1972).
    [CrossRef]
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    [CrossRef]
  13. D. P. Akitt, J. T. Yardley, IEEE J. Quantum Electron. QE-6, 113 (1972).
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    [CrossRef]
  15. W. W. Rice, R. C. Oldenborg, IEEE J. Quantum Electron. QE-13, 86 (1977).
    [CrossRef]
  16. J. J. Hinchen, R. H. Hobbs, J. Appl. Phys. 50, 628 (1979).
    [CrossRef]
  17. R. W. F. Gross, J. F. Bott, Handbook of Chemical Lasers (Wiley, New York, 1976).
  18. R. L. Wilkins, J. Chem. Phys. 67, 5838 (1977).
    [CrossRef]
  19. R. L. Wilkins, M. A. Kwok, “Temperature Dependence of HF (v1 = 1) + HF (v2 = 0) Vibrational Relaxation,” Technical Report SAMSO-TR-78-76, Aerospace Corp., El Segundo, Calif. (Aug.1978).
  20. J. J. Hinchen, R. H. Hobbs, J. Chem. Phys. 65, 2732 (1976).
    [CrossRef]
  21. N. Cohen, A Review of Rate Coefficients for Reactions in the H2–F2 Laser System, Technical Report TR-0073 (3430)-9, Aerospace Corp., Los Angeles, Calif. (Nov.1972).
  22. J. J. T. Hough, Appl. Opt. 16, 2297 (1977).
    [CrossRef] [PubMed]
  23. R. E. Meredith, F. G. Smith, “Investigations of Fundamental Laser Processes Vol. II: Computation of Electric Dipole Matrix Elements for Hydrogen Fluoride and Deuterium Fluoride,” Technical Report 84130-39-T (II), Environmental Research Institute of Michigan, Ann Arbor (1971).
  24. L. F. Shampine, H. A. Watts, “Practical Solution of Ordinary Differential Equations by Runge-Kutta Methods,” SAND76-0585, Sandia Laboratories, Albuquerque, N. Mex. (Dec.1976).
  25. J. C. Polanyi, K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).
    [CrossRef]
  26. J. C. Polanyi, J. J. Sloan, J. Chem. Phys. 57, 4988 (1972).
    [CrossRef]
  27. M. A. Kwok, Aerospace Corp.; private communication (1975).

1979 (1)

J. J. Hinchen, R. H. Hobbs, J. Appl. Phys. 50, 628 (1979).
[CrossRef]

1978 (1)

1977 (3)

R. L. Wilkins, J. Chem. Phys. 67, 5838 (1977).
[CrossRef]

J. J. T. Hough, Appl. Opt. 16, 2297 (1977).
[CrossRef] [PubMed]

W. W. Rice, R. C. Oldenborg, IEEE J. Quantum Electron. QE-13, 86 (1977).
[CrossRef]

1976 (4)

J. J. Hinchen, R. H. Hobbs, J. Chem. Phys. 65, 2732 (1976).
[CrossRef]

R. J. Hall, IEEE J. Quantum Electron. QE-12, 453 (1976).
[CrossRef]

L. H. Sentman, Appl. Opt. 15, 744 (1976); J. Chem. Phys. 62, 3523 (1975).
[CrossRef]

A. Ben-Shaul, K. L. Kompa, U. Schmailzl, J. Chem. Phys. 65, 1711 (1976).
[CrossRef]

1975 (2)

1974 (2)

H. Chen, R. L. Taylor, J. Wilson, P. Lewis, W. Fyfe, J. Chem. Phys. 61, 306 (1974).
[CrossRef]

E. Cuellar, J. H. Parker, G. C. Pimentel, J. Chem. Phys. 61, 422 (1974).
[CrossRef]

1972 (4)

N. Skribanowitz, I. P. Herman, R. M. Osgood, M. S. Feld, A. Javan, Appl. Phys. Lett. 20, 428 (1972).
[CrossRef]

J. C. Polanyi, K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).
[CrossRef]

J. C. Polanyi, J. J. Sloan, J. Chem. Phys. 57, 4988 (1972).
[CrossRef]

D. P. Akitt, J. T. Yardley, IEEE J. Quantum Electron. QE-6, 113 (1972).

1967 (1)

R. F. Deutsch, Appl. Phys. Lett. 11, 18 (1967).
[CrossRef]

Akitt, D. P.

D. P. Akitt, J. T. Yardley, IEEE J. Quantum Electron. QE-6, 113 (1972).

Ben-Shaul, A.

A. Ben-Shaul, K. L. Kompa, U. Schmailzl, J. Chem. Phys. 65, 1711 (1976).
[CrossRef]

Bott, J. F.

R. W. F. Gross, J. F. Bott, Handbook of Chemical Lasers (Wiley, New York, 1976).

Chao, C. M.

Chen, H.

H. Chen, R. L. Taylor, J. Wilson, P. Lewis, W. Fyfe, J. Chem. Phys. 61, 306 (1974).
[CrossRef]

Cohen, N.

N. Cohen, A Review of Rate Coefficients for Reactions in the H2–F2 Laser System, Technical Report TR-0073 (3430)-9, Aerospace Corp., Los Angeles, Calif. (Nov.1972).

Creighton, J. R.

J. R. Creighton, “A Numerical Investigation of the Pulsed NF3 + H2 Chemical Laser Using a Model Which Includes Rotational Relaxation and Semi-Classical Laser Equations,” Technical Report UCRL 51931, Lawrence Livermore Laboratory, University of California/Livermore, 1Sept.1975.

Cuellar, E.

E. Cuellar, J. H. Parker, G. C. Pimentel, J. Chem. Phys. 61, 422 (1974).
[CrossRef]

E. R. Sirkin, E. Cuellar, G. C. Pimentel, “Laser emission between high rotational states of HX resulting from photoelimination of halogenated olefins,” presented at the Fifth Conference of Chemical and Molecular Lasers, St. Louis, Mo., 18–20 Apr. 1977.

Deutsch, R. F.

R. F. Deutsch, Appl. Phys. Lett. 11, 18 (1967).
[CrossRef]

Feld, M. S.

N. Skribanowitz, I. P. Herman, R. M. Osgood, M. S. Feld, A. Javan, Appl. Phys. Lett. 20, 428 (1972).
[CrossRef]

Fyfe, W.

H. Chen, R. L. Taylor, J. Wilson, P. Lewis, W. Fyfe, J. Chem. Phys. 61, 306 (1974).
[CrossRef]

Gross, R. W. F.

R. W. F. Gross, J. F. Bott, Handbook of Chemical Lasers (Wiley, New York, 1976).

Hall, R. J.

R. J. Hall, IEEE J. Quantum Electron. QE-12, 453 (1976).
[CrossRef]

Herman, I. P.

N. Skribanowitz, I. P. Herman, R. M. Osgood, M. S. Feld, A. Javan, Appl. Phys. Lett. 20, 428 (1972).
[CrossRef]

Hinchen, J. J.

J. J. Hinchen, R. H. Hobbs, J. Appl. Phys. 50, 628 (1979).
[CrossRef]

J. J. Hinchen, R. H. Hobbs, J. Chem. Phys. 65, 2732 (1976).
[CrossRef]

Hobbs, R. H.

J. J. Hinchen, R. H. Hobbs, J. Appl. Phys. 50, 628 (1979).
[CrossRef]

J. J. Hinchen, R. H. Hobbs, J. Chem. Phys. 65, 2732 (1976).
[CrossRef]

Hough, J. J. T.

Javan, A.

N. Skribanowitz, I. P. Herman, R. M. Osgood, M. S. Feld, A. Javan, Appl. Phys. Lett. 20, 428 (1972).
[CrossRef]

Kerber, R. L.

Kompa, K. L.

A. Ben-Shaul, K. L. Kompa, U. Schmailzl, J. Chem. Phys. 65, 1711 (1976).
[CrossRef]

Kwok, M. A.

R. L. Wilkins, M. A. Kwok, “Temperature Dependence of HF (v1 = 1) + HF (v2 = 0) Vibrational Relaxation,” Technical Report SAMSO-TR-78-76, Aerospace Corp., El Segundo, Calif. (Aug.1978).

M. A. Kwok, Aerospace Corp.; private communication (1975).

Lewis, P.

H. Chen, R. L. Taylor, J. Wilson, P. Lewis, W. Fyfe, J. Chem. Phys. 61, 306 (1974).
[CrossRef]

Meredith, R. E.

R. E. Meredith, F. G. Smith, “Investigations of Fundamental Laser Processes Vol. II: Computation of Electric Dipole Matrix Elements for Hydrogen Fluoride and Deuterium Fluoride,” Technical Report 84130-39-T (II), Environmental Research Institute of Michigan, Ann Arbor (1971).

Moreno, J.

J. Moreno, “Computer Model for the H2 + F2 Super Radiant Laser,” AIAA paper 75-36, Thirteenth Aerospace Sciences Meeting, Pasadena, Calif., 20–22 Jan. 1975.

Oldenborg, R. C.

W. W. Rice, R. C. Oldenborg, IEEE J. Quantum Electron. QE-13, 86 (1977).
[CrossRef]

Osgood, R. M.

N. Skribanowitz, I. P. Herman, R. M. Osgood, M. S. Feld, A. Javan, Appl. Phys. Lett. 20, 428 (1972).
[CrossRef]

Parker, J. H.

E. Cuellar, J. H. Parker, G. C. Pimentel, J. Chem. Phys. 61, 422 (1974).
[CrossRef]

Pimentel, G. C.

E. Cuellar, J. H. Parker, G. C. Pimentel, J. Chem. Phys. 61, 422 (1974).
[CrossRef]

E. R. Sirkin, E. Cuellar, G. C. Pimentel, “Laser emission between high rotational states of HX resulting from photoelimination of halogenated olefins,” presented at the Fifth Conference of Chemical and Molecular Lasers, St. Louis, Mo., 18–20 Apr. 1977.

Polanyi, J. C.

J. C. Polanyi, J. J. Sloan, J. Chem. Phys. 57, 4988 (1972).
[CrossRef]

J. C. Polanyi, K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).
[CrossRef]

Rice, W. W.

W. W. Rice, R. C. Oldenborg, IEEE J. Quantum Electron. QE-13, 86 (1977).
[CrossRef]

Schmailzl, U.

A. Ben-Shaul, K. L. Kompa, U. Schmailzl, J. Chem. Phys. 65, 1711 (1976).
[CrossRef]

Sentman, L. H.

Shampine, L. F.

L. F. Shampine, H. A. Watts, “Practical Solution of Ordinary Differential Equations by Runge-Kutta Methods,” SAND76-0585, Sandia Laboratories, Albuquerque, N. Mex. (Dec.1976).

Sirkin, E. R.

E. R. Sirkin, E. Cuellar, G. C. Pimentel, “Laser emission between high rotational states of HX resulting from photoelimination of halogenated olefins,” presented at the Fifth Conference of Chemical and Molecular Lasers, St. Louis, Mo., 18–20 Apr. 1977.

Skifstad, J. G.

Skribanowitz, N.

N. Skribanowitz, I. P. Herman, R. M. Osgood, M. S. Feld, A. Javan, Appl. Phys. Lett. 20, 428 (1972).
[CrossRef]

Sloan, J. J.

J. C. Polanyi, J. J. Sloan, J. Chem. Phys. 57, 4988 (1972).
[CrossRef]

Smith, F. G.

R. E. Meredith, F. G. Smith, “Investigations of Fundamental Laser Processes Vol. II: Computation of Electric Dipole Matrix Elements for Hydrogen Fluoride and Deuterium Fluoride,” Technical Report 84130-39-T (II), Environmental Research Institute of Michigan, Ann Arbor (1971).

Taylor, R. L.

H. Chen, R. L. Taylor, J. Wilson, P. Lewis, W. Fyfe, J. Chem. Phys. 61, 306 (1974).
[CrossRef]

Watts, H. A.

L. F. Shampine, H. A. Watts, “Practical Solution of Ordinary Differential Equations by Runge-Kutta Methods,” SAND76-0585, Sandia Laboratories, Albuquerque, N. Mex. (Dec.1976).

Wilkins, R. L.

R. L. Wilkins, J. Chem. Phys. 67, 5838 (1977).
[CrossRef]

R. L. Wilkins, M. A. Kwok, “Temperature Dependence of HF (v1 = 1) + HF (v2 = 0) Vibrational Relaxation,” Technical Report SAMSO-TR-78-76, Aerospace Corp., El Segundo, Calif. (Aug.1978).

Wilson, J.

H. Chen, R. L. Taylor, J. Wilson, P. Lewis, W. Fyfe, J. Chem. Phys. 61, 306 (1974).
[CrossRef]

Woodall, K. B.

J. C. Polanyi, K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).
[CrossRef]

Yardley, J. T.

D. P. Akitt, J. T. Yardley, IEEE J. Quantum Electron. QE-6, 113 (1972).

Appl. Opt. (5)

Appl. Phys. Lett. (2)

R. F. Deutsch, Appl. Phys. Lett. 11, 18 (1967).
[CrossRef]

N. Skribanowitz, I. P. Herman, R. M. Osgood, M. S. Feld, A. Javan, Appl. Phys. Lett. 20, 428 (1972).
[CrossRef]

IEEE J. Quantum Electron. (3)

D. P. Akitt, J. T. Yardley, IEEE J. Quantum Electron. QE-6, 113 (1972).

W. W. Rice, R. C. Oldenborg, IEEE J. Quantum Electron. QE-13, 86 (1977).
[CrossRef]

R. J. Hall, IEEE J. Quantum Electron. QE-12, 453 (1976).
[CrossRef]

J. Appl. Phys. (1)

J. J. Hinchen, R. H. Hobbs, J. Appl. Phys. 50, 628 (1979).
[CrossRef]

J. Chem. Phys. (7)

R. L. Wilkins, J. Chem. Phys. 67, 5838 (1977).
[CrossRef]

E. Cuellar, J. H. Parker, G. C. Pimentel, J. Chem. Phys. 61, 422 (1974).
[CrossRef]

H. Chen, R. L. Taylor, J. Wilson, P. Lewis, W. Fyfe, J. Chem. Phys. 61, 306 (1974).
[CrossRef]

A. Ben-Shaul, K. L. Kompa, U. Schmailzl, J. Chem. Phys. 65, 1711 (1976).
[CrossRef]

J. C. Polanyi, K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).
[CrossRef]

J. C. Polanyi, J. J. Sloan, J. Chem. Phys. 57, 4988 (1972).
[CrossRef]

J. J. Hinchen, R. H. Hobbs, J. Chem. Phys. 65, 2732 (1976).
[CrossRef]

Other (9)

N. Cohen, A Review of Rate Coefficients for Reactions in the H2–F2 Laser System, Technical Report TR-0073 (3430)-9, Aerospace Corp., Los Angeles, Calif. (Nov.1972).

R. E. Meredith, F. G. Smith, “Investigations of Fundamental Laser Processes Vol. II: Computation of Electric Dipole Matrix Elements for Hydrogen Fluoride and Deuterium Fluoride,” Technical Report 84130-39-T (II), Environmental Research Institute of Michigan, Ann Arbor (1971).

L. F. Shampine, H. A. Watts, “Practical Solution of Ordinary Differential Equations by Runge-Kutta Methods,” SAND76-0585, Sandia Laboratories, Albuquerque, N. Mex. (Dec.1976).

M. A. Kwok, Aerospace Corp.; private communication (1975).

E. R. Sirkin, E. Cuellar, G. C. Pimentel, “Laser emission between high rotational states of HX resulting from photoelimination of halogenated olefins,” presented at the Fifth Conference of Chemical and Molecular Lasers, St. Louis, Mo., 18–20 Apr. 1977.

J. R. Creighton, “A Numerical Investigation of the Pulsed NF3 + H2 Chemical Laser Using a Model Which Includes Rotational Relaxation and Semi-Classical Laser Equations,” Technical Report UCRL 51931, Lawrence Livermore Laboratory, University of California/Livermore, 1Sept.1975.

J. Moreno, “Computer Model for the H2 + F2 Super Radiant Laser,” AIAA paper 75-36, Thirteenth Aerospace Sciences Meeting, Pasadena, Calif., 20–22 Jan. 1975.

R. L. Wilkins, M. A. Kwok, “Temperature Dependence of HF (v1 = 1) + HF (v2 = 0) Vibrational Relaxation,” Technical Report SAMSO-TR-78-76, Aerospace Corp., El Segundo, Calif. (Aug.1978).

R. W. F. Gross, J. F. Bott, Handbook of Chemical Lasers (Wiley, New York, 1976).

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Figures (3)

Fig. 1
Fig. 1

Typical VR relaxation path. Multiquanta vibrational relaxation is allowed. The values of J′ range from Jmin − 4 to Jmin+ 2, where Jmin is the value of J′ with the smallest energy defect.

Fig. 2
Fig. 2

Effect of kinetics on P-branch lasing energy. Gas mixture:0.02F:0.99F2:1 H2:20He, Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.7, L = 10.0 cm, l = 10.0 cm. Distribution no. 3 for VR relaxation and Boltzmann pumping assumed. (a) VR energy exchange; (b) RR,T energy exchange.

Fig. 3
Fig. 3

Effect of kinetics on rotational lasing energy. Gas mixture: 0.02F:0.99F2:1 H2:20He, Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.7, L = 10.0 cm, l = 10.0 cm. Distribution no. 3 for VR relaxation and Boltzmann pumping assumed: (a) VR energy exchange; (b) RR,T energy exchange.

Tables (8)

Tables Icon

Table I Relative J Dependence of Rotational Relaxation

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Table II Relative Rotational Relaxation Efficiencies

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Table III Possible V–R Relaxation Distributions About Jmin for HF(v,J) + M ⇋ HF(v′,J′) + M

Tables Icon

Table IV Effect of V–R Mechanisms for Cases Without R-R Lasing

Tables Icon

Table V Comparison of Vibrational-to-Rotational Energy Exchange Model with Vibrational-to-Translational Energy Exchange Model

Tables Icon

Table VI Effect of Rotational Lasing

Tables Icon

Table VII Impact of Important Kinetics on Laser Performance b

Tables Icon

Table VIII Effect of Rotational Relaxation Rate on Laser Performance

Equations (15)

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

d d t [ N HF ( v , j ) ] = X i ( v , J ) + P ( v , J ) + R VRT + R RRT + α VR ( v , J ) f VR ( v , J ) - α VR ( v - 1 , J + 1 ) f VR ( v - 1 , J + 1 ) + α RR ( v , J ) f RR ( v , J ) - α RR ( v , J - 1 ) f RR ( v , J - 1 ) ,
α ( v , J ) = h N A 4 π ω ϕ B [ ( g L g u ) N u - N L ] ,
d f ( v , J ) d t = c [ α ( v , J ) - α thr ] f ( v , J ) L / l ,
α thr = - 1 / ( 2 L ) ln ( R O R L ) ,
i N i C v i d T d t = - P L - i d N i d t H i ,
P L v , J = h c N A α thr ω ( v , J ) f ( v , J ) .
E v J = 0 t c P L v J d t ,
E v = J E v , J .
P ( v , J ) = B ( v , J ) P ( v ) ,
HF ( v , J ) + M HF ( v , J - Δ J ) + M ,
HF ( v 1 , J 1 ) + HF ( v 2 , J 2 ) HF ( v 1 , J 1 - Δ J ) + HF ( v 2 , J 2 + Δ J ) .
k 0 , 10 10 + Δ J = 0.341 × 10 16 T - 0.805 exp ( - 2569 / RT ) ,
k 1 , 10 10 + Δ J = 0.113 × 10 17 T - 0.893 exp ( - 2436 / RT ) .
HF ( v , J ) + M HF ( v , J ) + M + Δ E ,
HF ( v 1 , J 1 ) + HF ( v 2 , J 2 ) HF ( v 1 - 1 , J 1 ) + HF ( v 2 + 1 , J 2 ) + Δ E ,

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