Abstract

We report high-resolution inverse Raman spectroscopy measurements of nitrogen Q-branch linewidths in pure nitrogen at temperatures up to 1500 K and at pressures from 20 to 760 Torr. Transitions from J = 0 to J = 30 have been measured with a resolution of 1.5 × 10−3 cm−1 and a Raman shift accuracy of 1 × 10−3 cm−1. Fits to the data using a Galatry line-shape model provide J-dependent collisional-broadening coefficients. A modified exponential-gap scaling law accurately describes the dependence of these coefficients on temperature and rotational quantum number.

© 1986 Optical Society of America

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  1. M. Péalat, P. Bouchardy, M. Lefebvre, J.-P. Taran, “Precision of multiplex CARS temperature measurements,” Appl. Opt. 24, 1012 (1985).
    [CrossRef] [PubMed]
  2. R. J. Hall, A. C. Eckbreth, “Coherent anti-Stokes Raman spectroscopy (CARS): application to combustion diagnostics,” in Laser Applications, J. F. Ready, R. K. Erf, eds. (Academic, New York, 1984), Vol. 5, pp. 213–309.
  3. S. A. J. Druet, J.-P. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1 (1981)
    [CrossRef]
  4. L. A. Rahn, P. L. Mattern, R. L. Farrow, “A comparison of coherent and spontaneous Raman combustion diagnostics,” in Eighteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1981), pp. 1533–1542.
    [CrossRef]
  5. L. A. Rahn, P. L. Mattern, R. L. Farrow, “A comparison of coherent and spontaneous Raman combustion diagnostics,” in Proceedings of the Seventh International Conference on Raman Spectroscopy, W. F. Murphy, ed. (North-Holland, Amsterdam, 1980), pp. 694–695; L. A. Rahn, R. L. Farrow, P. L. Mattern, “Nonlinear Raman spectroscopy in combustion research,” in Proceedings of the Eighth International Conference on Raman Spectroscopy, J. Lascombe, P. V. Huong, eds. (Wiley, New York, 1982), pp. 143–152.
  6. G. J. Rosasco, W. Lempert, W. S. Hurst, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435 (1983).
    [CrossRef]
  7. R. J. Hall, “Coherent anti-Stokes Raman spectroscopic modeling for combustion diagnostics,” Opt. Eng. 22, 322 (1983).
    [CrossRef]
  8. R. L. Farrow, L. A. Rahn, “Interpreting coherent anti-Stokes Raman spectra measured with multimode Nd:YAG pump lasers,” J. Opt. Soc. Am. B 2, 903 (1985).
    [CrossRef]
  9. G. J. Rosasco, W. S. Hurst, “Measurement of resonant and nonresonant third-order nonlinear susceptibilities by coherent Raman spectroscopy,” Phys. Rev. A 32, 281 (1985).
    [CrossRef] [PubMed]
  10. M. L. Koszykowski, L. A. Rahn, R. E. Palmer, M. E. Coltrin, “Theoretical and experimental studies of high-resolution inverse Raman spectra of N2at 1–10 atm,” J. Phys. Chem. (to be published, 1986).
  11. A. Owyoung, “High resolution coherent Raman spectroscopy of gases,” in Laser Spectroscopy IV, H. Walther, K. W. Rothe, eds. (Springer-Verlag, Berlin, 1979), pp. 175–187.
    [CrossRef]
  12. L. A. Rahn, P. L. Mattern, “Coherent Raman spectroscopy for combustion applications,” in Laser Spectroscopy, H. Schlossberg, ed., Proc. Soc. Photo-Opt. Instrum, Eng.158, 76 (1978).
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    [CrossRef] [PubMed]
  15. F. V. Kowalski, R. T. Hawkins, A. L. Schawlow, “Digital wavemeter for cw lasers,” J. Opt. Soc. Am. 66, 965 (1976).
    [CrossRef]
  16. J.-P. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szoke, F. Zernike, P. H. Lee, A. Javan, “Accurate laser wavelength measurement with a precision two-beam scanning Michelson interferometer,” Appl. Opt. 20, 736 (1981).
    [CrossRef] [PubMed]
  17. C. R. Pollock, D. A. Jennings, F. R. Petersen, J. S. Wells, R. E. Drullinger, E. C. Beaty, K. M. Evenson, “Direct frequency measurements of transitions at 520 THz (576 nm) in iodine and 260 THz (1.15 μ m) in neon,” Opt. Lett. 8, 133 (1983).
    [CrossRef] [PubMed]
  18. R. C. H. Tam, A. D. May, “Motional narrowing of the rotational Raman band of compressed CO, N2, and CO2,” Can. J. Phys. 61, 1558 (1983).
    [CrossRef]
  19. R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69 (1980).
    [CrossRef]
  20. M. L. Koszykowski, R. L. Farrow, R. E. Palmer, “Calculation of collisionally narrowed coherent anti-Stokes Raman spectra,” Opt. Lett. 10, 478 (1985). (The value for α based on the exponential-gap scaling law cited in this reference should be divided by 2.)
    [CrossRef] [PubMed]
  21. P. L. Varghese, R. K. Hanson, “Collisional narrowing effects on spectral line shapes measured at high resolution,” Appl. Opt. 23, 2376 (1984).
    [CrossRef] [PubMed]
  22. R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472 (1953).
    [CrossRef]
  23. L. Galatry, “Simultaneous effect of Doppler and foreign gas broadening on spectral lines,” Phys. Rev. 122, 1218 (1961).
    [CrossRef]
  24. P. L. Varghese, “Tunable infrared diode laser measurements of spectral parameters of carbon monoxide and hydrogen cyanide,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1983); also available as High Temperature Gasdynamics Laboratory (Stanford University)Rep. No. 6-83-T (March1983).
  25. J. Humlicek, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Transfer 21, 309 (1979).
    [CrossRef]
  26. J. O. Hirshfelder, C. F. Curtiss, R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1964), p. 539.
  27. T. A. Brunner, D. E. Pritchard, “Fitting laws for rotationally inelastic collisions,” in Dynamics of the Excited State, K. P. Lawley, ed. (Wiley, New York, 1982), pp. 589–641.
  28. D. A. Greenhalgh, F. M. Porter, “A polynomial energy-gap model for molecular linewidths,” J. Quant. Spectrosc. Radiat. Transfer 34, 95 (1985).
    [CrossRef]
  29. B. Lavoral, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, D. Robert, “Rotational collisional line broadening at high temperatures in the N2fundamental Q-branch studied with stimulated Raman spectroscopy,” J. Phys. (Paris) 47, 417 (1986).
    [CrossRef]
  30. J. C. Polanyi, K. B. Woodall, “Mechanism of rotational relaxation,” J. Chem. Phys. 56, 1563 (1972).
    [CrossRef]
  31. K. Akihama, T. Nomura, M. Hanabusa, S. Furuno, S. Iguchi, T. Inoue, “Temperature and pressure dependence of N2CARS spectra,” in Proceedings of the Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 334–335.
  32. Recently completed CARS measurements in nitrogen-filled tungsten lamps suggest that linewidths above 2000 K are better predicted by replacing the factor (T0/T)n in Eq. 1 by the functionf(T)=1−e−m1−e−mT/T0(T0T)0.5,where m = 0.1487, and the other parameters in Eq. 1 by the values α = 0.023, β = 1.67, and δ = 1.21. These changes also result in better overall agreement between the measured and calculated linewidths shown in Fig. 5, especially those for 1500 K. These improvements will be discussed in R. L. Farrow, R. Trebino, R. E. Palmer, “High-resolution CARS measurement of temperature profiles and pressure in a tungsten lamp,” to be submitted to Appl. Opt., 1986.

1986 (2)

B. Lavoral, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, D. Robert, “Rotational collisional line broadening at high temperatures in the N2fundamental Q-branch studied with stimulated Raman spectroscopy,” J. Phys. (Paris) 47, 417 (1986).
[CrossRef]

R. L. Schmitt, L. A. Rahn, “Diode-laser-pumped Nd:YAG laser injection seeding system,” Appl. Opt. 25, 629 (1986).
[CrossRef] [PubMed]

1985 (5)

1984 (1)

1983 (4)

R. C. H. Tam, A. D. May, “Motional narrowing of the rotational Raman band of compressed CO, N2, and CO2,” Can. J. Phys. 61, 1558 (1983).
[CrossRef]

G. J. Rosasco, W. Lempert, W. S. Hurst, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435 (1983).
[CrossRef]

R. J. Hall, “Coherent anti-Stokes Raman spectroscopic modeling for combustion diagnostics,” Opt. Eng. 22, 322 (1983).
[CrossRef]

C. R. Pollock, D. A. Jennings, F. R. Petersen, J. S. Wells, R. E. Drullinger, E. C. Beaty, K. M. Evenson, “Direct frequency measurements of transitions at 520 THz (576 nm) in iodine and 260 THz (1.15 μ m) in neon,” Opt. Lett. 8, 133 (1983).
[CrossRef] [PubMed]

1981 (2)

1980 (1)

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69 (1980).
[CrossRef]

1979 (1)

J. Humlicek, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Transfer 21, 309 (1979).
[CrossRef]

1976 (1)

1972 (1)

J. C. Polanyi, K. B. Woodall, “Mechanism of rotational relaxation,” J. Chem. Phys. 56, 1563 (1972).
[CrossRef]

1961 (1)

L. Galatry, “Simultaneous effect of Doppler and foreign gas broadening on spectral lines,” Phys. Rev. 122, 1218 (1961).
[CrossRef]

1953 (1)

R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472 (1953).
[CrossRef]

Akihama, K.

K. Akihama, T. Nomura, M. Hanabusa, S. Furuno, S. Iguchi, T. Inoue, “Temperature and pressure dependence of N2CARS spectra,” in Proceedings of the Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 334–335.

Beaty, E. C.

Berger, H.

B. Lavoral, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, D. Robert, “Rotational collisional line broadening at high temperatures in the N2fundamental Q-branch studied with stimulated Raman spectroscopy,” J. Phys. (Paris) 47, 417 (1986).
[CrossRef]

Bird, R. B.

J. O. Hirshfelder, C. F. Curtiss, R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1964), p. 539.

Bonamy, J.

B. Lavoral, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, D. Robert, “Rotational collisional line broadening at high temperatures in the N2fundamental Q-branch studied with stimulated Raman spectroscopy,” J. Phys. (Paris) 47, 417 (1986).
[CrossRef]

Bouchardy, P.

Brunner, T. A.

T. A. Brunner, D. E. Pritchard, “Fitting laws for rotationally inelastic collisions,” in Dynamics of the Excited State, K. P. Lawley, ed. (Wiley, New York, 1982), pp. 589–641.

Coltrin, M. E.

M. L. Koszykowski, L. A. Rahn, R. E. Palmer, M. E. Coltrin, “Theoretical and experimental studies of high-resolution inverse Raman spectra of N2at 1–10 atm,” J. Phys. Chem. (to be published, 1986).

Curtiss, C. F.

J. O. Hirshfelder, C. F. Curtiss, R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1964), p. 539.

Dicke, R. H.

R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472 (1953).
[CrossRef]

Druet, S. A. J.

S. A. J. Druet, J.-P. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1 (1981)
[CrossRef]

Drullinger, R. E.

Eckbreth, A. C.

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69 (1980).
[CrossRef]

R. J. Hall, A. C. Eckbreth, “Coherent anti-Stokes Raman spectroscopy (CARS): application to combustion diagnostics,” in Laser Applications, J. F. Ready, R. K. Erf, eds. (Academic, New York, 1984), Vol. 5, pp. 213–309.

Evenson, K. M.

Farrow, R. L.

R. L. Farrow, L. A. Rahn, “Interpreting coherent anti-Stokes Raman spectra measured with multimode Nd:YAG pump lasers,” J. Opt. Soc. Am. B 2, 903 (1985).
[CrossRef]

M. L. Koszykowski, R. L. Farrow, R. E. Palmer, “Calculation of collisionally narrowed coherent anti-Stokes Raman spectra,” Opt. Lett. 10, 478 (1985). (The value for α based on the exponential-gap scaling law cited in this reference should be divided by 2.)
[CrossRef] [PubMed]

L. A. Rahn, P. L. Mattern, R. L. Farrow, “A comparison of coherent and spontaneous Raman combustion diagnostics,” in Proceedings of the Seventh International Conference on Raman Spectroscopy, W. F. Murphy, ed. (North-Holland, Amsterdam, 1980), pp. 694–695; L. A. Rahn, R. L. Farrow, P. L. Mattern, “Nonlinear Raman spectroscopy in combustion research,” in Proceedings of the Eighth International Conference on Raman Spectroscopy, J. Lascombe, P. V. Huong, eds. (Wiley, New York, 1982), pp. 143–152.

L. A. Rahn, P. L. Mattern, R. L. Farrow, “A comparison of coherent and spontaneous Raman combustion diagnostics,” in Eighteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1981), pp. 1533–1542.
[CrossRef]

Recently completed CARS measurements in nitrogen-filled tungsten lamps suggest that linewidths above 2000 K are better predicted by replacing the factor (T0/T)n in Eq. 1 by the functionf(T)=1−e−m1−e−mT/T0(T0T)0.5,where m = 0.1487, and the other parameters in Eq. 1 by the values α = 0.023, β = 1.67, and δ = 1.21. These changes also result in better overall agreement between the measured and calculated linewidths shown in Fig. 5, especially those for 1500 K. These improvements will be discussed in R. L. Farrow, R. Trebino, R. E. Palmer, “High-resolution CARS measurement of temperature profiles and pressure in a tungsten lamp,” to be submitted to Appl. Opt., 1986.

Furuno, S.

K. Akihama, T. Nomura, M. Hanabusa, S. Furuno, S. Iguchi, T. Inoue, “Temperature and pressure dependence of N2CARS spectra,” in Proceedings of the Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 334–335.

Galatry, L.

L. Galatry, “Simultaneous effect of Doppler and foreign gas broadening on spectral lines,” Phys. Rev. 122, 1218 (1961).
[CrossRef]

Greenhalgh, D. A.

D. A. Greenhalgh, F. M. Porter, “A polynomial energy-gap model for molecular linewidths,” J. Quant. Spectrosc. Radiat. Transfer 34, 95 (1985).
[CrossRef]

Hall, R. J.

R. J. Hall, “Coherent anti-Stokes Raman spectroscopic modeling for combustion diagnostics,” Opt. Eng. 22, 322 (1983).
[CrossRef]

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69 (1980).
[CrossRef]

R. J. Hall, A. C. Eckbreth, “Coherent anti-Stokes Raman spectroscopy (CARS): application to combustion diagnostics,” in Laser Applications, J. F. Ready, R. K. Erf, eds. (Academic, New York, 1984), Vol. 5, pp. 213–309.

Hanabusa, M.

K. Akihama, T. Nomura, M. Hanabusa, S. Furuno, S. Iguchi, T. Inoue, “Temperature and pressure dependence of N2CARS spectra,” in Proceedings of the Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 334–335.

Hanson, R. K.

Hawkins, R. T.

Hirshfelder, J. O.

J. O. Hirshfelder, C. F. Curtiss, R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1964), p. 539.

Humlicek, J.

J. Humlicek, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Transfer 21, 309 (1979).
[CrossRef]

Hurst, W. S.

G. J. Rosasco, W. S. Hurst, “Measurement of resonant and nonresonant third-order nonlinear susceptibilities by coherent Raman spectroscopy,” Phys. Rev. A 32, 281 (1985).
[CrossRef] [PubMed]

G. J. Rosasco, W. Lempert, W. S. Hurst, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435 (1983).
[CrossRef]

Iguchi, S.

K. Akihama, T. Nomura, M. Hanabusa, S. Furuno, S. Iguchi, T. Inoue, “Temperature and pressure dependence of N2CARS spectra,” in Proceedings of the Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 334–335.

Inoue, T.

K. Akihama, T. Nomura, M. Hanabusa, S. Furuno, S. Iguchi, T. Inoue, “Temperature and pressure dependence of N2CARS spectra,” in Proceedings of the Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 334–335.

Javan, A.

Jennings, D. A.

Kelly, M. J.

Koszykowski, M. L.

M. L. Koszykowski, R. L. Farrow, R. E. Palmer, “Calculation of collisionally narrowed coherent anti-Stokes Raman spectra,” Opt. Lett. 10, 478 (1985). (The value for α based on the exponential-gap scaling law cited in this reference should be divided by 2.)
[CrossRef] [PubMed]

M. L. Koszykowski, L. A. Rahn, R. E. Palmer, M. E. Coltrin, “Theoretical and experimental studies of high-resolution inverse Raman spectra of N2at 1–10 atm,” J. Phys. Chem. (to be published, 1986).

Kowalski, F. V.

Kurnit, N. A.

Lavoral, B.

B. Lavoral, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, D. Robert, “Rotational collisional line broadening at high temperatures in the N2fundamental Q-branch studied with stimulated Raman spectroscopy,” J. Phys. (Paris) 47, 417 (1986).
[CrossRef]

Lee, P. H.

Lefebvre, M.

Lempert, W.

G. J. Rosasco, W. Lempert, W. S. Hurst, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435 (1983).
[CrossRef]

Mattern, P. L.

L. A. Rahn, P. L. Mattern, R. L. Farrow, “A comparison of coherent and spontaneous Raman combustion diagnostics,” in Eighteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1981), pp. 1533–1542.
[CrossRef]

L. A. Rahn, P. L. Mattern, R. L. Farrow, “A comparison of coherent and spontaneous Raman combustion diagnostics,” in Proceedings of the Seventh International Conference on Raman Spectroscopy, W. F. Murphy, ed. (North-Holland, Amsterdam, 1980), pp. 694–695; L. A. Rahn, R. L. Farrow, P. L. Mattern, “Nonlinear Raman spectroscopy in combustion research,” in Proceedings of the Eighth International Conference on Raman Spectroscopy, J. Lascombe, P. V. Huong, eds. (Wiley, New York, 1982), pp. 143–152.

L. A. Rahn, P. L. Mattern, “Coherent Raman spectroscopy for combustion applications,” in Laser Spectroscopy, H. Schlossberg, ed., Proc. Soc. Photo-Opt. Instrum, Eng.158, 76 (1978).

May, A. D.

R. C. H. Tam, A. D. May, “Motional narrowing of the rotational Raman band of compressed CO, N2, and CO2,” Can. J. Phys. 61, 1558 (1983).
[CrossRef]

Millot, G.

B. Lavoral, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, D. Robert, “Rotational collisional line broadening at high temperatures in the N2fundamental Q-branch studied with stimulated Raman spectroscopy,” J. Phys. (Paris) 47, 417 (1986).
[CrossRef]

Monchalin, J.-P.

Nomura, T.

K. Akihama, T. Nomura, M. Hanabusa, S. Furuno, S. Iguchi, T. Inoue, “Temperature and pressure dependence of N2CARS spectra,” in Proceedings of the Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 334–335.

Owyoung, A.

A. Owyoung, “High resolution coherent Raman spectroscopy of gases,” in Laser Spectroscopy IV, H. Walther, K. W. Rothe, eds. (Springer-Verlag, Berlin, 1979), pp. 175–187.
[CrossRef]

Palmer, R. E.

M. L. Koszykowski, R. L. Farrow, R. E. Palmer, “Calculation of collisionally narrowed coherent anti-Stokes Raman spectra,” Opt. Lett. 10, 478 (1985). (The value for α based on the exponential-gap scaling law cited in this reference should be divided by 2.)
[CrossRef] [PubMed]

Recently completed CARS measurements in nitrogen-filled tungsten lamps suggest that linewidths above 2000 K are better predicted by replacing the factor (T0/T)n in Eq. 1 by the functionf(T)=1−e−m1−e−mT/T0(T0T)0.5,where m = 0.1487, and the other parameters in Eq. 1 by the values α = 0.023, β = 1.67, and δ = 1.21. These changes also result in better overall agreement between the measured and calculated linewidths shown in Fig. 5, especially those for 1500 K. These improvements will be discussed in R. L. Farrow, R. Trebino, R. E. Palmer, “High-resolution CARS measurement of temperature profiles and pressure in a tungsten lamp,” to be submitted to Appl. Opt., 1986.

M. L. Koszykowski, L. A. Rahn, R. E. Palmer, M. E. Coltrin, “Theoretical and experimental studies of high-resolution inverse Raman spectra of N2at 1–10 atm,” J. Phys. Chem. (to be published, 1986).

Péalat, M.

Petersen, F. R.

Polanyi, J. C.

J. C. Polanyi, K. B. Woodall, “Mechanism of rotational relaxation,” J. Chem. Phys. 56, 1563 (1972).
[CrossRef]

Pollock, C. R.

Porter, F. M.

D. A. Greenhalgh, F. M. Porter, “A polynomial energy-gap model for molecular linewidths,” J. Quant. Spectrosc. Radiat. Transfer 34, 95 (1985).
[CrossRef]

Pritchard, D. E.

T. A. Brunner, D. E. Pritchard, “Fitting laws for rotationally inelastic collisions,” in Dynamics of the Excited State, K. P. Lawley, ed. (Wiley, New York, 1982), pp. 589–641.

Rahn, L. A.

R. L. Schmitt, L. A. Rahn, “Diode-laser-pumped Nd:YAG laser injection seeding system,” Appl. Opt. 25, 629 (1986).
[CrossRef] [PubMed]

R. L. Farrow, L. A. Rahn, “Interpreting coherent anti-Stokes Raman spectra measured with multimode Nd:YAG pump lasers,” J. Opt. Soc. Am. B 2, 903 (1985).
[CrossRef]

M. L. Koszykowski, L. A. Rahn, R. E. Palmer, M. E. Coltrin, “Theoretical and experimental studies of high-resolution inverse Raman spectra of N2at 1–10 atm,” J. Phys. Chem. (to be published, 1986).

L. A. Rahn, P. L. Mattern, R. L. Farrow, “A comparison of coherent and spontaneous Raman combustion diagnostics,” in Eighteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1981), pp. 1533–1542.
[CrossRef]

L. A. Rahn, P. L. Mattern, “Coherent Raman spectroscopy for combustion applications,” in Laser Spectroscopy, H. Schlossberg, ed., Proc. Soc. Photo-Opt. Instrum, Eng.158, 76 (1978).

L. A. Rahn, P. L. Mattern, R. L. Farrow, “A comparison of coherent and spontaneous Raman combustion diagnostics,” in Proceedings of the Seventh International Conference on Raman Spectroscopy, W. F. Murphy, ed. (North-Holland, Amsterdam, 1980), pp. 694–695; L. A. Rahn, R. L. Farrow, P. L. Mattern, “Nonlinear Raman spectroscopy in combustion research,” in Proceedings of the Eighth International Conference on Raman Spectroscopy, J. Lascombe, P. V. Huong, eds. (Wiley, New York, 1982), pp. 143–152.

Robert, D.

B. Lavoral, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, D. Robert, “Rotational collisional line broadening at high temperatures in the N2fundamental Q-branch studied with stimulated Raman spectroscopy,” J. Phys. (Paris) 47, 417 (1986).
[CrossRef]

Rosasco, G. J.

G. J. Rosasco, W. S. Hurst, “Measurement of resonant and nonresonant third-order nonlinear susceptibilities by coherent Raman spectroscopy,” Phys. Rev. A 32, 281 (1985).
[CrossRef] [PubMed]

G. J. Rosasco, W. Lempert, W. S. Hurst, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435 (1983).
[CrossRef]

Saint-Loup, R.

B. Lavoral, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, D. Robert, “Rotational collisional line broadening at high temperatures in the N2fundamental Q-branch studied with stimulated Raman spectroscopy,” J. Phys. (Paris) 47, 417 (1986).
[CrossRef]

Sala, J. P.

B. Lavoral, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, D. Robert, “Rotational collisional line broadening at high temperatures in the N2fundamental Q-branch studied with stimulated Raman spectroscopy,” J. Phys. (Paris) 47, 417 (1986).
[CrossRef]

Schawlow, A. L.

Schmitt, R. L.

Szoke, A.

Tam, R. C. H.

R. C. H. Tam, A. D. May, “Motional narrowing of the rotational Raman band of compressed CO, N2, and CO2,” Can. J. Phys. 61, 1558 (1983).
[CrossRef]

Taran, J.-P.

Thomas, J. E.

Trebino, R.

Recently completed CARS measurements in nitrogen-filled tungsten lamps suggest that linewidths above 2000 K are better predicted by replacing the factor (T0/T)n in Eq. 1 by the functionf(T)=1−e−m1−e−mT/T0(T0T)0.5,where m = 0.1487, and the other parameters in Eq. 1 by the values α = 0.023, β = 1.67, and δ = 1.21. These changes also result in better overall agreement between the measured and calculated linewidths shown in Fig. 5, especially those for 1500 K. These improvements will be discussed in R. L. Farrow, R. Trebino, R. E. Palmer, “High-resolution CARS measurement of temperature profiles and pressure in a tungsten lamp,” to be submitted to Appl. Opt., 1986.

Varghese, P. L.

P. L. Varghese, R. K. Hanson, “Collisional narrowing effects on spectral line shapes measured at high resolution,” Appl. Opt. 23, 2376 (1984).
[CrossRef] [PubMed]

P. L. Varghese, “Tunable infrared diode laser measurements of spectral parameters of carbon monoxide and hydrogen cyanide,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1983); also available as High Temperature Gasdynamics Laboratory (Stanford University)Rep. No. 6-83-T (March1983).

Verdieck, J. F.

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69 (1980).
[CrossRef]

Wells, J. S.

Wenger, C.

B. Lavoral, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, D. Robert, “Rotational collisional line broadening at high temperatures in the N2fundamental Q-branch studied with stimulated Raman spectroscopy,” J. Phys. (Paris) 47, 417 (1986).
[CrossRef]

Woodall, K. B.

J. C. Polanyi, K. B. Woodall, “Mechanism of rotational relaxation,” J. Chem. Phys. 56, 1563 (1972).
[CrossRef]

Zernike, F.

Appl. Opt. (4)

Can. J. Phys. (1)

R. C. H. Tam, A. D. May, “Motional narrowing of the rotational Raman band of compressed CO, N2, and CO2,” Can. J. Phys. 61, 1558 (1983).
[CrossRef]

Chem. Phys. Lett. (1)

G. J. Rosasco, W. Lempert, W. S. Hurst, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435 (1983).
[CrossRef]

J. Chem. Phys. (1)

J. C. Polanyi, K. B. Woodall, “Mechanism of rotational relaxation,” J. Chem. Phys. 56, 1563 (1972).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

J. Phys. (Paris) (1)

B. Lavoral, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, D. Robert, “Rotational collisional line broadening at high temperatures in the N2fundamental Q-branch studied with stimulated Raman spectroscopy,” J. Phys. (Paris) 47, 417 (1986).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

J. Humlicek, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Transfer 21, 309 (1979).
[CrossRef]

D. A. Greenhalgh, F. M. Porter, “A polynomial energy-gap model for molecular linewidths,” J. Quant. Spectrosc. Radiat. Transfer 34, 95 (1985).
[CrossRef]

Opt. Commun. (1)

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69 (1980).
[CrossRef]

Opt. Eng. (1)

R. J. Hall, “Coherent anti-Stokes Raman spectroscopic modeling for combustion diagnostics,” Opt. Eng. 22, 322 (1983).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (2)

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[CrossRef]

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[CrossRef]

Phys. Rev. A (1)

G. J. Rosasco, W. S. Hurst, “Measurement of resonant and nonresonant third-order nonlinear susceptibilities by coherent Raman spectroscopy,” Phys. Rev. A 32, 281 (1985).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

S. A. J. Druet, J.-P. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1 (1981)
[CrossRef]

Other (12)

L. A. Rahn, P. L. Mattern, R. L. Farrow, “A comparison of coherent and spontaneous Raman combustion diagnostics,” in Eighteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1981), pp. 1533–1542.
[CrossRef]

L. A. Rahn, P. L. Mattern, R. L. Farrow, “A comparison of coherent and spontaneous Raman combustion diagnostics,” in Proceedings of the Seventh International Conference on Raman Spectroscopy, W. F. Murphy, ed. (North-Holland, Amsterdam, 1980), pp. 694–695; L. A. Rahn, R. L. Farrow, P. L. Mattern, “Nonlinear Raman spectroscopy in combustion research,” in Proceedings of the Eighth International Conference on Raman Spectroscopy, J. Lascombe, P. V. Huong, eds. (Wiley, New York, 1982), pp. 143–152.

P. L. Varghese, “Tunable infrared diode laser measurements of spectral parameters of carbon monoxide and hydrogen cyanide,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1983); also available as High Temperature Gasdynamics Laboratory (Stanford University)Rep. No. 6-83-T (March1983).

M. L. Koszykowski, L. A. Rahn, R. E. Palmer, M. E. Coltrin, “Theoretical and experimental studies of high-resolution inverse Raman spectra of N2at 1–10 atm,” J. Phys. Chem. (to be published, 1986).

A. Owyoung, “High resolution coherent Raman spectroscopy of gases,” in Laser Spectroscopy IV, H. Walther, K. W. Rothe, eds. (Springer-Verlag, Berlin, 1979), pp. 175–187.
[CrossRef]

L. A. Rahn, P. L. Mattern, “Coherent Raman spectroscopy for combustion applications,” in Laser Spectroscopy, H. Schlossberg, ed., Proc. Soc. Photo-Opt. Instrum, Eng.158, 76 (1978).

Model 699-29, Coherent, Inc., Palo Alto, Calif.

K. Akihama, T. Nomura, M. Hanabusa, S. Furuno, S. Iguchi, T. Inoue, “Temperature and pressure dependence of N2CARS spectra,” in Proceedings of the Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 334–335.

Recently completed CARS measurements in nitrogen-filled tungsten lamps suggest that linewidths above 2000 K are better predicted by replacing the factor (T0/T)n in Eq. 1 by the functionf(T)=1−e−m1−e−mT/T0(T0T)0.5,where m = 0.1487, and the other parameters in Eq. 1 by the values α = 0.023, β = 1.67, and δ = 1.21. These changes also result in better overall agreement between the measured and calculated linewidths shown in Fig. 5, especially those for 1500 K. These improvements will be discussed in R. L. Farrow, R. Trebino, R. E. Palmer, “High-resolution CARS measurement of temperature profiles and pressure in a tungsten lamp,” to be submitted to Appl. Opt., 1986.

R. J. Hall, A. C. Eckbreth, “Coherent anti-Stokes Raman spectroscopy (CARS): application to combustion diagnostics,” in Laser Applications, J. F. Ready, R. K. Erf, eds. (Academic, New York, 1984), Vol. 5, pp. 213–309.

J. O. Hirshfelder, C. F. Curtiss, R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1964), p. 539.

T. A. Brunner, D. E. Pritchard, “Fitting laws for rotationally inelastic collisions,” in Dynamics of the Excited State, K. P. Lawley, ed. (Wiley, New York, 1982), pp. 589–641.

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Figures (6)

Fig. 1
Fig. 1

High-resolution IRS apparatus.

Fig. 2
Fig. 2

Typical inverse Raman spectra for the N2Q branch at 295 and 1500 K, both at 1 atm.

Fig. 3
Fig. 3

Collisional-broadening coefficients versus pressure for the N2Q(6) transition at 1300 K determined from Lorentzian, Voigt, and Galatry models. The optical diffusion coefficient has been chosen so that the Galatry model correctly predicts a broadening coefficient that is independent of pressure. The horizontal dashed line indicates the value for the collisional-broadening coefficient in the high-pressure limit. [Following the conventions in the references, 2γj refers to broadening coefficients (FWHM) and γij refers to S-matrix elements.]

Fig. 4
Fig. 4

N2Q(6) line shape at 1300 K and 172 Torr. The difference between the experimental line shape and Lorentzian, Voigt, and Galatry model predictions is shown below the spectrum. The Galatry model gives the best agreement.

Fig. 5
Fig. 5

N2–N2 collisional self-broadening coefficients as a function of temperature and rotational quantum number. The symbols represent experimental values (also listed in Table 1) determined by Galatry model fits to each line, including overlap from the wings of neighboring lines. The solid curves are predictions from the modified exponential-gap scaling law discussed in the text.

Fig. 6
Fig. 6

Nitrogen collisional-broadening coefficients (filled circles) in the postflame gases of a lean methane–air flame at 1730 K, taken from Ref. 5, compared with self-broadening scaling-law predictions for 1730 K (open circles). The self-broadening coefficients measured for lower temperatures, listed in Table 1, are also shown (dashed lines) to indicate their temperature dependence. Note that the broadening coefficients for the flame are slightly larger than those that would be expected at 1730 K from self-broadening alone, indicating that broadening due to other collision partners should be considered.

Tables (1)

Tables Icon

Table 1 Collisional Self-Broadening Coefficients (FWHM) for the N2Q Branch as a Function of Temperature and Rotational Quantum Number

Equations (4)

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γ j i = α p ( T 0 T ) n ( 1 + 1.5 E i / k T δ 1 + 1.5 E i / k T ) 2 exp ( β Δ E i j / k T )
γ i j = 2 J i + 1 2 J j + 1 γ j i exp ( Δ E i j / k T ) .
Γ j 2 = i j γ i j .
f(T)=1em1emT/T0(T0T)0.5,

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