Abstract

Line shapes and intensities for coherent anti-Stokes Raman scattering (CARS) at saturation laser intensities are determined for nitrogen vibrational Q-branch lines by solving the time-dependent density-matrix equations numerically. We have previously performed measurements of saturated CARS line shapes in pure nitrogen by using nearly Fourier-transform-limited pump and Stokes lasers. The experimental laser pulse shapes, Stark effects, Doppler broadening, and the nonresonant background are incorporated in the numerical calculations. The numerical results show good agreement with the high-resolution measurements of saturated CARS line shapes. The lines show prominent saturation dips, and agreement between theory and experiment is excellent in terms of the depth and the width of the dips. The numerical results indicate that the Doppler effect tends to broaden and to deepen the dip in highly saturated lines, an effect that cannot be explained by a steady-state theory.

© 1988 Optical Society of America

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  1. S. A. J. Druet, J.-P. E. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1–72 (1981).
    [CrossRef]
  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, Orlando, Fla., 1984), Vol. 5, pp. 213–309.
  3. R. L. Farrow, R. P. Lucht, G. L. Clark, R. E. Palmer, “Species concentration measurements using CARS with non-resonant susceptibility normalization,” Appl. Opt. 24, 2241–2251 (1985).
    [CrossRef]
  4. R. L. Farrow, P. L. Mattern, L. A. Rahn, “Comparison between CARS and corrected thermocouple temperature measurements in a diffusion flame,” Appl. Opt. 21, 3119–3125 (1982).
    [CrossRef] [PubMed]
  5. G. L. Switzer, L. P. Goss, D. D. Trump, C. M. Reeves, J. S. Stutrud, R. P. Bradley, W. M. Roquemore, “CARS measurements in the near-wake region of an axisymmetric bluff-body combustor,” AIAA J. 24, 1155–1162 (1986).
    [CrossRef]
  6. A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Teller, “CARS temperature and species measurements in augmented jet engine exhausts,” Appl. Opt. 23, 1328–1339 (1984).
    [CrossRef] [PubMed]
  7. R. L. Farrow, “High-resolution coherent anti-Stokes Raman spectroscopy measurements of carbon monoxide in a flame,” in Twenty-First Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1987),p. 1703.
  8. M. Pealat, J.-P. E. Taran, J. Taillet, M. Bacal, A. M. Bruneteau, “Measurement of vibrational populations in low-pressure hydrogen plasmas by coherent anti-Stokes Raman scattering,” J. Appl. Phys. 52, 2687–2691 (1981).
    [CrossRef]
  9. L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an optical Stark effect on vibrational and rotational transitions,” Phys. Rev. Lett. 45, 620–623 (1980).
    [CrossRef]
  10. R. L. Farrow, L. A. Rahn, “Optical Stark splitting of rotational Raman transitions,” Phys. Rev. Lett. 48, 395–398 (1982).
    [CrossRef]
  11. M. D. Duncan, P. Oesterlin, F. König, R. L. Byer, “Observation of saturation broadening of the coherent anti-Stokes Raman spectrum (CARS) of acetylene in a pulsed molecular beam,” Chem. Phys. Lett. 80, 253–256 (1981).
    [CrossRef]
  12. A. D. Wilson-Gordon, H. Friedmann, “Comment on saturation effects in high-resolution coherent anti-Stokes Raman spectroscopy of a pulsed molecular beam,” Chem. Phys. Lett. 89, 273–278 (1982).
    [CrossRef]
  13. V. N. Zadkov, N. I. Koroteev, M. Y. Rychov, A. B. Feodorov, “Saturation spectroscopy of coherent Raman scattering in molecular gases,” Appl. Phys. B 34, 167–170 (1984).
    [CrossRef]
  14. V. N. Zadkov, N. I. Koroteev, “Saturation effects in CARS: collisionally narrowed Raman spectra of diatomic gases,” Chem. Phys. Lett. 105, 108–113 (1984).
    [CrossRef]
  15. A. D. Wilson-Gordon, R. Klimovsky-Barid, H. Friedmann, “Saturation effects in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 1580–1595 (1982).
    [CrossRef]
  16. G. S. Agarwal, S. Singh, “Effect of pump fluctuations on line shapes in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 3195–3205 (1982).
    [CrossRef]
  17. A. Owyoung, P. Esherick, “Sub-Doppler Raman saturation spectroscopy,” Opt. Lett. 5, 421–423 (1980).
    [CrossRef] [PubMed]
  18. A. M. Brodnikovskii, V. N. Zadkov, M. G. Karimov, N. I. Koroteev, “Effect of saturation of the two-photon rotational transition in the H2molecule: observation by photoacoustic and coherent active Raman spectroscopy,” Opt. Spectrosc. (USSR) 54, 227–228 (1983).
  19. I. L. Shumay, V. N. Zadkov, D. J. Heinzen, M. M. Kash, M. S. Feld, “Observation of the saturation effect in continuous-wave coherent anti-Stokes Raman spectroscopy of liquid nitrogen,” Opt. Lett. 11, 233–235 (1986).
    [CrossRef] [PubMed]
  20. R. L. Farrow, R. P. Lucht, “High-resolution measurements of saturated coherent anti-Stokes Raman spectroscopy line shapes,” Opt. Lett. 11, 374–376 (1986).
    [CrossRef] [PubMed]
  21. H. Weil, P. W. Schreiber, “Saturation and secondary Stokes effects in coherent anti-Stokes Raman spectroscopy,” Appl. Opt. 21, 941–948 (1982).
    [CrossRef] [PubMed]
  22. R. Miles, C. Cohen, J. Connors, P. Howard, S. Huang, E. Markovitz, G. Russell, “Velocity measurements by vibrational tagging and fluorescent probing of oxygen,” Opt. Lett. 12, 861–863 (1987).
    [CrossRef] [PubMed]
  23. D. W. Chandler, R. L. Farrow, “Measurement of rotational energy transfer rates for HD (υ = 1) in collisions with thermal HD,” J. Chem. Phys. 85, 810–816 (1986).
    [CrossRef]
  24. J. A. Giordmaine, W. Kaiser, “Light scattering by coherently driven lattice vibrations,” Phys. Rev. 144, 676–688 (1966).
    [CrossRef]
  25. A. Penzkofer, A. Laubereau, W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
    [CrossRef]
  26. R. P. Lucht, N. M. Laurendeau, D. W. Sweeney, “Balanced cross-rate model for saturated molecular fluorescence in flames using a nanosecond pulse length laser,” Appl. Opt. 19, 3295–3300 (1980).
    [CrossRef] [PubMed]
  27. M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982), pp. 29–65.
    [CrossRef]
  28. R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (1980).
    [CrossRef]
  29. M. L. Koszykowski, R. L. Farrow, R. E. Palmer, “Calculation of collisionally narrowed coherent anti-Stokes Raman spectroscopy spectra,” Opt. Lett. 10, 478–480 (1985).
    [CrossRef] [PubMed]
  30. M. A. Henesian, R. L. Byer, “High-resolution CARS line-shape function,” J. Opt. Soc. Am. 68, 648–649 (1978).
  31. G. J. Rosasco, W. Lempert, W. S. Hurst, A. Fein, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435–440 (1983).
    [CrossRef]
  32. L. A. Rahn, R. E. Palmer, “Studies of nitrogen self-broadening at high temperature with inverse Raman spectroscopy,” J. Opt. Soc. Am. B 3, 1164–1169 (1986).
    [CrossRef]

1987 (1)

1986 (5)

1985 (2)

1984 (3)

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Teller, “CARS temperature and species measurements in augmented jet engine exhausts,” Appl. Opt. 23, 1328–1339 (1984).
[CrossRef] [PubMed]

V. N. Zadkov, N. I. Koroteev, M. Y. Rychov, A. B. Feodorov, “Saturation spectroscopy of coherent Raman scattering in molecular gases,” Appl. Phys. B 34, 167–170 (1984).
[CrossRef]

V. N. Zadkov, N. I. Koroteev, “Saturation effects in CARS: collisionally narrowed Raman spectra of diatomic gases,” Chem. Phys. Lett. 105, 108–113 (1984).
[CrossRef]

1983 (2)

A. M. Brodnikovskii, V. N. Zadkov, M. G. Karimov, N. I. Koroteev, “Effect of saturation of the two-photon rotational transition in the H2molecule: observation by photoacoustic and coherent active Raman spectroscopy,” Opt. Spectrosc. (USSR) 54, 227–228 (1983).

G. J. Rosasco, W. Lempert, W. S. Hurst, A. Fein, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435–440 (1983).
[CrossRef]

1982 (6)

H. Weil, P. W. Schreiber, “Saturation and secondary Stokes effects in coherent anti-Stokes Raman spectroscopy,” Appl. Opt. 21, 941–948 (1982).
[CrossRef] [PubMed]

R. L. Farrow, P. L. Mattern, L. A. Rahn, “Comparison between CARS and corrected thermocouple temperature measurements in a diffusion flame,” Appl. Opt. 21, 3119–3125 (1982).
[CrossRef] [PubMed]

A. D. Wilson-Gordon, H. Friedmann, “Comment on saturation effects in high-resolution coherent anti-Stokes Raman spectroscopy of a pulsed molecular beam,” Chem. Phys. Lett. 89, 273–278 (1982).
[CrossRef]

A. D. Wilson-Gordon, R. Klimovsky-Barid, H. Friedmann, “Saturation effects in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 1580–1595 (1982).
[CrossRef]

G. S. Agarwal, S. Singh, “Effect of pump fluctuations on line shapes in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 3195–3205 (1982).
[CrossRef]

R. L. Farrow, L. A. Rahn, “Optical Stark splitting of rotational Raman transitions,” Phys. Rev. Lett. 48, 395–398 (1982).
[CrossRef]

1981 (3)

M. D. Duncan, P. Oesterlin, F. König, R. L. Byer, “Observation of saturation broadening of the coherent anti-Stokes Raman spectrum (CARS) of acetylene in a pulsed molecular beam,” Chem. Phys. Lett. 80, 253–256 (1981).
[CrossRef]

M. Pealat, J.-P. E. Taran, J. Taillet, M. Bacal, A. M. Bruneteau, “Measurement of vibrational populations in low-pressure hydrogen plasmas by coherent anti-Stokes Raman scattering,” J. Appl. Phys. 52, 2687–2691 (1981).
[CrossRef]

S. A. J. Druet, J.-P. E. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1–72 (1981).
[CrossRef]

1980 (4)

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an optical Stark effect on vibrational and rotational transitions,” Phys. Rev. Lett. 45, 620–623 (1980).
[CrossRef]

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (1980).
[CrossRef]

A. Owyoung, P. Esherick, “Sub-Doppler Raman saturation spectroscopy,” Opt. Lett. 5, 421–423 (1980).
[CrossRef] [PubMed]

R. P. Lucht, N. M. Laurendeau, D. W. Sweeney, “Balanced cross-rate model for saturated molecular fluorescence in flames using a nanosecond pulse length laser,” Appl. Opt. 19, 3295–3300 (1980).
[CrossRef] [PubMed]

1979 (1)

A. Penzkofer, A. Laubereau, W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
[CrossRef]

1978 (1)

M. A. Henesian, R. L. Byer, “High-resolution CARS line-shape function,” J. Opt. Soc. Am. 68, 648–649 (1978).

1966 (1)

J. A. Giordmaine, W. Kaiser, “Light scattering by coherently driven lattice vibrations,” Phys. Rev. 144, 676–688 (1966).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, S. Singh, “Effect of pump fluctuations on line shapes in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 3195–3205 (1982).
[CrossRef]

Bacal, M.

M. Pealat, J.-P. E. Taran, J. Taillet, M. Bacal, A. M. Bruneteau, “Measurement of vibrational populations in low-pressure hydrogen plasmas by coherent anti-Stokes Raman scattering,” J. Appl. Phys. 52, 2687–2691 (1981).
[CrossRef]

Bradley, R. P.

G. L. Switzer, L. P. Goss, D. D. Trump, C. M. Reeves, J. S. Stutrud, R. P. Bradley, W. M. Roquemore, “CARS measurements in the near-wake region of an axisymmetric bluff-body combustor,” AIAA J. 24, 1155–1162 (1986).
[CrossRef]

Brodnikovskii, A. M.

A. M. Brodnikovskii, V. N. Zadkov, M. G. Karimov, N. I. Koroteev, “Effect of saturation of the two-photon rotational transition in the H2molecule: observation by photoacoustic and coherent active Raman spectroscopy,” Opt. Spectrosc. (USSR) 54, 227–228 (1983).

Bruneteau, A. M.

M. Pealat, J.-P. E. Taran, J. Taillet, M. Bacal, A. M. Bruneteau, “Measurement of vibrational populations in low-pressure hydrogen plasmas by coherent anti-Stokes Raman scattering,” J. Appl. Phys. 52, 2687–2691 (1981).
[CrossRef]

Byer, R. L.

M. D. Duncan, P. Oesterlin, F. König, R. L. Byer, “Observation of saturation broadening of the coherent anti-Stokes Raman spectrum (CARS) of acetylene in a pulsed molecular beam,” Chem. Phys. Lett. 80, 253–256 (1981).
[CrossRef]

M. A. Henesian, R. L. Byer, “High-resolution CARS line-shape function,” J. Opt. Soc. Am. 68, 648–649 (1978).

Chandler, D. W.

D. W. Chandler, R. L. Farrow, “Measurement of rotational energy transfer rates for HD (υ = 1) in collisions with thermal HD,” J. Chem. Phys. 85, 810–816 (1986).
[CrossRef]

Clark, G. L.

Cohen, C.

Connors, J.

Dobbs, G. M.

Druet, S. A. J.

S. A. J. Druet, J.-P. E. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1–72 (1981).
[CrossRef]

Duncan, M. D.

M. D. Duncan, P. Oesterlin, F. König, R. L. Byer, “Observation of saturation broadening of the coherent anti-Stokes Raman spectrum (CARS) of acetylene in a pulsed molecular beam,” Chem. Phys. Lett. 80, 253–256 (1981).
[CrossRef]

Eckbreth, A. C.

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Teller, “CARS temperature and species measurements in augmented jet engine exhausts,” Appl. Opt. 23, 1328–1339 (1984).
[CrossRef] [PubMed]

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (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, Orlando, Fla., 1984), Vol. 5, pp. 213–309.

Esherick, P.

Farrow, R. L.

D. W. Chandler, R. L. Farrow, “Measurement of rotational energy transfer rates for HD (υ = 1) in collisions with thermal HD,” J. Chem. Phys. 85, 810–816 (1986).
[CrossRef]

R. L. Farrow, R. P. Lucht, “High-resolution measurements of saturated coherent anti-Stokes Raman spectroscopy line shapes,” Opt. Lett. 11, 374–376 (1986).
[CrossRef] [PubMed]

R. L. Farrow, R. P. Lucht, G. L. Clark, R. E. Palmer, “Species concentration measurements using CARS with non-resonant susceptibility normalization,” Appl. Opt. 24, 2241–2251 (1985).
[CrossRef]

M. L. Koszykowski, R. L. Farrow, R. E. Palmer, “Calculation of collisionally narrowed coherent anti-Stokes Raman spectroscopy spectra,” Opt. Lett. 10, 478–480 (1985).
[CrossRef] [PubMed]

R. L. Farrow, L. A. Rahn, “Optical Stark splitting of rotational Raman transitions,” Phys. Rev. Lett. 48, 395–398 (1982).
[CrossRef]

R. L. Farrow, P. L. Mattern, L. A. Rahn, “Comparison between CARS and corrected thermocouple temperature measurements in a diffusion flame,” Appl. Opt. 21, 3119–3125 (1982).
[CrossRef] [PubMed]

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an optical Stark effect on vibrational and rotational transitions,” Phys. Rev. Lett. 45, 620–623 (1980).
[CrossRef]

R. L. Farrow, “High-resolution coherent anti-Stokes Raman spectroscopy measurements of carbon monoxide in a flame,” in Twenty-First Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1987),p. 1703.

Fein, A.

G. J. Rosasco, W. Lempert, W. S. Hurst, A. Fein, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435–440 (1983).
[CrossRef]

Feld, M. S.

Feodorov, A. B.

V. N. Zadkov, N. I. Koroteev, M. Y. Rychov, A. B. Feodorov, “Saturation spectroscopy of coherent Raman scattering in molecular gases,” Appl. Phys. B 34, 167–170 (1984).
[CrossRef]

Friedmann, H.

A. D. Wilson-Gordon, H. Friedmann, “Comment on saturation effects in high-resolution coherent anti-Stokes Raman spectroscopy of a pulsed molecular beam,” Chem. Phys. Lett. 89, 273–278 (1982).
[CrossRef]

A. D. Wilson-Gordon, R. Klimovsky-Barid, H. Friedmann, “Saturation effects in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 1580–1595 (1982).
[CrossRef]

Giordmaine, J. A.

J. A. Giordmaine, W. Kaiser, “Light scattering by coherently driven lattice vibrations,” Phys. Rev. 144, 676–688 (1966).
[CrossRef]

Goss, L. P.

G. L. Switzer, L. P. Goss, D. D. Trump, C. M. Reeves, J. S. Stutrud, R. P. Bradley, W. M. Roquemore, “CARS measurements in the near-wake region of an axisymmetric bluff-body combustor,” AIAA J. 24, 1155–1162 (1986).
[CrossRef]

Hall, R. J.

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (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, Orlando, Fla., 1984), Vol. 5, pp. 213–309.

Heinzen, D. J.

Henesian, M. A.

M. A. Henesian, R. L. Byer, “High-resolution CARS line-shape function,” J. Opt. Soc. Am. 68, 648–649 (1978).

Howard, P.

Huang, S.

Hurst, W. S.

G. J. Rosasco, W. Lempert, W. S. Hurst, A. Fein, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435–440 (1983).
[CrossRef]

Kaiser, W.

A. Penzkofer, A. Laubereau, W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
[CrossRef]

J. A. Giordmaine, W. Kaiser, “Light scattering by coherently driven lattice vibrations,” Phys. Rev. 144, 676–688 (1966).
[CrossRef]

Karimov, M. G.

A. M. Brodnikovskii, V. N. Zadkov, M. G. Karimov, N. I. Koroteev, “Effect of saturation of the two-photon rotational transition in the H2molecule: observation by photoacoustic and coherent active Raman spectroscopy,” Opt. Spectrosc. (USSR) 54, 227–228 (1983).

Kash, M. M.

Klimovsky-Barid, R.

A. D. Wilson-Gordon, R. Klimovsky-Barid, H. Friedmann, “Saturation effects in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 1580–1595 (1982).
[CrossRef]

König, F.

M. D. Duncan, P. Oesterlin, F. König, R. L. Byer, “Observation of saturation broadening of the coherent anti-Stokes Raman spectrum (CARS) of acetylene in a pulsed molecular beam,” Chem. Phys. Lett. 80, 253–256 (1981).
[CrossRef]

Koroteev, N. I.

V. N. Zadkov, N. I. Koroteev, “Saturation effects in CARS: collisionally narrowed Raman spectra of diatomic gases,” Chem. Phys. Lett. 105, 108–113 (1984).
[CrossRef]

V. N. Zadkov, N. I. Koroteev, M. Y. Rychov, A. B. Feodorov, “Saturation spectroscopy of coherent Raman scattering in molecular gases,” Appl. Phys. B 34, 167–170 (1984).
[CrossRef]

A. M. Brodnikovskii, V. N. Zadkov, M. G. Karimov, N. I. Koroteev, “Effect of saturation of the two-photon rotational transition in the H2molecule: observation by photoacoustic and coherent active Raman spectroscopy,” Opt. Spectrosc. (USSR) 54, 227–228 (1983).

Koszykowski, M. L.

M. L. Koszykowski, R. L. Farrow, R. E. Palmer, “Calculation of collisionally narrowed coherent anti-Stokes Raman spectroscopy spectra,” Opt. Lett. 10, 478–480 (1985).
[CrossRef] [PubMed]

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an optical Stark effect on vibrational and rotational transitions,” Phys. Rev. Lett. 45, 620–623 (1980).
[CrossRef]

Laubereau, A.

A. Penzkofer, A. Laubereau, W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
[CrossRef]

Laurendeau, N. M.

Lempert, W.

G. J. Rosasco, W. Lempert, W. S. Hurst, A. Fein, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435–440 (1983).
[CrossRef]

Levenson, M. D.

M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982), pp. 29–65.
[CrossRef]

Lucht, R. P.

Markovitz, E.

Mattern, P. L.

R. L. Farrow, P. L. Mattern, L. A. Rahn, “Comparison between CARS and corrected thermocouple temperature measurements in a diffusion flame,” Appl. Opt. 21, 3119–3125 (1982).
[CrossRef] [PubMed]

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an optical Stark effect on vibrational and rotational transitions,” Phys. Rev. Lett. 45, 620–623 (1980).
[CrossRef]

Miles, R.

Oesterlin, P.

M. D. Duncan, P. Oesterlin, F. König, R. L. Byer, “Observation of saturation broadening of the coherent anti-Stokes Raman spectrum (CARS) of acetylene in a pulsed molecular beam,” Chem. Phys. Lett. 80, 253–256 (1981).
[CrossRef]

Owyoung, A.

Palmer, R. E.

Pealat, M.

M. Pealat, J.-P. E. Taran, J. Taillet, M. Bacal, A. M. Bruneteau, “Measurement of vibrational populations in low-pressure hydrogen plasmas by coherent anti-Stokes Raman scattering,” J. Appl. Phys. 52, 2687–2691 (1981).
[CrossRef]

Penzkofer, A.

A. Penzkofer, A. Laubereau, W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
[CrossRef]

Rahn, L. A.

L. A. Rahn, R. E. Palmer, “Studies of nitrogen self-broadening at high temperature with inverse Raman spectroscopy,” J. Opt. Soc. Am. B 3, 1164–1169 (1986).
[CrossRef]

R. L. Farrow, L. A. Rahn, “Optical Stark splitting of rotational Raman transitions,” Phys. Rev. Lett. 48, 395–398 (1982).
[CrossRef]

R. L. Farrow, P. L. Mattern, L. A. Rahn, “Comparison between CARS and corrected thermocouple temperature measurements in a diffusion flame,” Appl. Opt. 21, 3119–3125 (1982).
[CrossRef] [PubMed]

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an optical Stark effect on vibrational and rotational transitions,” Phys. Rev. Lett. 45, 620–623 (1980).
[CrossRef]

Reeves, C. M.

G. L. Switzer, L. P. Goss, D. D. Trump, C. M. Reeves, J. S. Stutrud, R. P. Bradley, W. M. Roquemore, “CARS measurements in the near-wake region of an axisymmetric bluff-body combustor,” AIAA J. 24, 1155–1162 (1986).
[CrossRef]

Roquemore, W. M.

G. L. Switzer, L. P. Goss, D. D. Trump, C. M. Reeves, J. S. Stutrud, R. P. Bradley, W. M. Roquemore, “CARS measurements in the near-wake region of an axisymmetric bluff-body combustor,” AIAA J. 24, 1155–1162 (1986).
[CrossRef]

Rosasco, G. J.

G. J. Rosasco, W. Lempert, W. S. Hurst, A. Fein, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435–440 (1983).
[CrossRef]

Russell, G.

Rychov, M. Y.

V. N. Zadkov, N. I. Koroteev, M. Y. Rychov, A. B. Feodorov, “Saturation spectroscopy of coherent Raman scattering in molecular gases,” Appl. Phys. B 34, 167–170 (1984).
[CrossRef]

Schreiber, P. W.

Shumay, I. L.

Singh, S.

G. S. Agarwal, S. Singh, “Effect of pump fluctuations on line shapes in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 3195–3205 (1982).
[CrossRef]

Stufflebeam, J. H.

Stutrud, J. S.

G. L. Switzer, L. P. Goss, D. D. Trump, C. M. Reeves, J. S. Stutrud, R. P. Bradley, W. M. Roquemore, “CARS measurements in the near-wake region of an axisymmetric bluff-body combustor,” AIAA J. 24, 1155–1162 (1986).
[CrossRef]

Sweeney, D. W.

Switzer, G. L.

G. L. Switzer, L. P. Goss, D. D. Trump, C. M. Reeves, J. S. Stutrud, R. P. Bradley, W. M. Roquemore, “CARS measurements in the near-wake region of an axisymmetric bluff-body combustor,” AIAA J. 24, 1155–1162 (1986).
[CrossRef]

Taillet, J.

M. Pealat, J.-P. E. Taran, J. Taillet, M. Bacal, A. M. Bruneteau, “Measurement of vibrational populations in low-pressure hydrogen plasmas by coherent anti-Stokes Raman scattering,” J. Appl. Phys. 52, 2687–2691 (1981).
[CrossRef]

Taran, J.-P. E.

M. Pealat, J.-P. E. Taran, J. Taillet, M. Bacal, A. M. Bruneteau, “Measurement of vibrational populations in low-pressure hydrogen plasmas by coherent anti-Stokes Raman scattering,” J. Appl. Phys. 52, 2687–2691 (1981).
[CrossRef]

S. A. J. Druet, J.-P. E. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1–72 (1981).
[CrossRef]

Teller, P. A.

Trump, D. D.

G. L. Switzer, L. P. Goss, D. D. Trump, C. M. Reeves, J. S. Stutrud, R. P. Bradley, W. M. Roquemore, “CARS measurements in the near-wake region of an axisymmetric bluff-body combustor,” AIAA J. 24, 1155–1162 (1986).
[CrossRef]

Verdieck, J. F.

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (1980).
[CrossRef]

Weil, H.

Wilson-Gordon, A. D.

A. D. Wilson-Gordon, R. Klimovsky-Barid, H. Friedmann, “Saturation effects in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 1580–1595 (1982).
[CrossRef]

A. D. Wilson-Gordon, H. Friedmann, “Comment on saturation effects in high-resolution coherent anti-Stokes Raman spectroscopy of a pulsed molecular beam,” Chem. Phys. Lett. 89, 273–278 (1982).
[CrossRef]

Zadkov, V. N.

I. L. Shumay, V. N. Zadkov, D. J. Heinzen, M. M. Kash, M. S. Feld, “Observation of the saturation effect in continuous-wave coherent anti-Stokes Raman spectroscopy of liquid nitrogen,” Opt. Lett. 11, 233–235 (1986).
[CrossRef] [PubMed]

V. N. Zadkov, N. I. Koroteev, M. Y. Rychov, A. B. Feodorov, “Saturation spectroscopy of coherent Raman scattering in molecular gases,” Appl. Phys. B 34, 167–170 (1984).
[CrossRef]

V. N. Zadkov, N. I. Koroteev, “Saturation effects in CARS: collisionally narrowed Raman spectra of diatomic gases,” Chem. Phys. Lett. 105, 108–113 (1984).
[CrossRef]

A. M. Brodnikovskii, V. N. Zadkov, M. G. Karimov, N. I. Koroteev, “Effect of saturation of the two-photon rotational transition in the H2molecule: observation by photoacoustic and coherent active Raman spectroscopy,” Opt. Spectrosc. (USSR) 54, 227–228 (1983).

AIAA J. (1)

G. L. Switzer, L. P. Goss, D. D. Trump, C. M. Reeves, J. S. Stutrud, R. P. Bradley, W. M. Roquemore, “CARS measurements in the near-wake region of an axisymmetric bluff-body combustor,” AIAA J. 24, 1155–1162 (1986).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. B (1)

V. N. Zadkov, N. I. Koroteev, M. Y. Rychov, A. B. Feodorov, “Saturation spectroscopy of coherent Raman scattering in molecular gases,” Appl. Phys. B 34, 167–170 (1984).
[CrossRef]

Chem. Phys. Lett. (4)

V. N. Zadkov, N. I. Koroteev, “Saturation effects in CARS: collisionally narrowed Raman spectra of diatomic gases,” Chem. Phys. Lett. 105, 108–113 (1984).
[CrossRef]

M. D. Duncan, P. Oesterlin, F. König, R. L. Byer, “Observation of saturation broadening of the coherent anti-Stokes Raman spectrum (CARS) of acetylene in a pulsed molecular beam,” Chem. Phys. Lett. 80, 253–256 (1981).
[CrossRef]

A. D. Wilson-Gordon, H. Friedmann, “Comment on saturation effects in high-resolution coherent anti-Stokes Raman spectroscopy of a pulsed molecular beam,” Chem. Phys. Lett. 89, 273–278 (1982).
[CrossRef]

G. J. Rosasco, W. Lempert, W. S. Hurst, A. Fein, “Line interference effects in the vibrational Q-branch spectra of N2and CO,” Chem. Phys. Lett. 97, 435–440 (1983).
[CrossRef]

J. Appl. Phys. (1)

M. Pealat, J.-P. E. Taran, J. Taillet, M. Bacal, A. M. Bruneteau, “Measurement of vibrational populations in low-pressure hydrogen plasmas by coherent anti-Stokes Raman scattering,” J. Appl. Phys. 52, 2687–2691 (1981).
[CrossRef]

J. Chem. Phys. (1)

D. W. Chandler, R. L. Farrow, “Measurement of rotational energy transfer rates for HD (υ = 1) in collisions with thermal HD,” J. Chem. Phys. 85, 810–816 (1986).
[CrossRef]

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M. A. Henesian, R. L. Byer, “High-resolution CARS line-shape function,” J. Opt. Soc. Am. 68, 648–649 (1978).

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

Opt. Commun. (1)

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (1980).
[CrossRef]

Opt. Lett. (5)

Opt. Spectrosc. (USSR) (1)

A. M. Brodnikovskii, V. N. Zadkov, M. G. Karimov, N. I. Koroteev, “Effect of saturation of the two-photon rotational transition in the H2molecule: observation by photoacoustic and coherent active Raman spectroscopy,” Opt. Spectrosc. (USSR) 54, 227–228 (1983).

Phys. Rev. (1)

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[CrossRef]

Phys. Rev. A (2)

A. D. Wilson-Gordon, R. Klimovsky-Barid, H. Friedmann, “Saturation effects in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 1580–1595 (1982).
[CrossRef]

G. S. Agarwal, S. Singh, “Effect of pump fluctuations on line shapes in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 3195–3205 (1982).
[CrossRef]

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[CrossRef]

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[CrossRef]

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S. A. J. Druet, J.-P. E. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1–72 (1981).
[CrossRef]

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[CrossRef]

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M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982), pp. 29–65.
[CrossRef]

R. L. Farrow, “High-resolution coherent anti-Stokes Raman spectroscopy measurements of carbon monoxide in a flame,” in Twenty-First Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1987),p. 1703.

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, Orlando, Fla., 1984), Vol. 5, pp. 213–309.

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Figures (9)

Fig. 1
Fig. 1

Energy-level schematic for the Raman pumping process.

Fig. 2
Fig. 2

CARS line shapes at low-Stokes laser intensity. The solid lines are theoretical calculations of (a) the homogeneous line shape and (b) the line shape including Doppler effects and the nonresonant background. The experimental data in (b) are indicated by filled circles. The nitrogen pressure was 25 Torr, and the Q(12) line was probed. The peak intensity of the Stokes laser was 0.4 (experimental) and 0.04 (theoretical) GW/cm2. The Stokes pulse energy was 0.25 mJ. The peak intensity and pulse energy of each pump laser beam were 37 GW/cm2 and 9 mJ, respectively. The nonresonant background susceptibility was 1.2 × 10−18 cm3/erg at line center with a slope of +2.8 × 10−18 (cm3/erg)/cm−1 at line center. The Stark-shifting coefficient KStark was equal to −0.6 × 10−13 cm−1/W.

Fig. 3
Fig. 3

CARS line shapes at high Stokes laser intensity. The solid lines are theoretical calculations of (a) the homogeneous line shape and (b) the line shape including Doppler effects and the nonresonant background. The experimental data in (b) are indicated by filled circles. The nitrogen pressure was 25 Torr, and the Q(12) line was probed. The peak intensity of the Stokes laser was 8.3 (experimental) and 0.7 (theoretical) GW/cm2. The peak intensity of each pump laser beam was 37 GW/cm2. The Stokes pulse energy was 5.2 mJ. The pulse energy for each pump beam was 9 mJ. The nonresonant background susceptibility and Stark-shifting coefficient were the same as for Fig. 2.

Fig. 4
Fig. 4

The real and imaginary parts of the CARS amplitude for homogeneous detunings Δω (cm−1) of (a) 0.000, (b) −0.002, and (c) −0.004 cm−1. The ratio of the detuning to the Raman linewidth (HWHM), 2Δω/Γ, is (a) 0.0, (b) 1.48, and (c) 2.96. The parameters of the calculation are identical to those of Fig. 2(a) except that Stark shifting is neglected.

Fig. 5
Fig. 5

Resonant and nonresonant CARS intensities and the excited-state population fraction at homogeneous detunings Δω (cm−1) of (a) 0.000, (b) −0.002, and (c) −0.004 cm−1. The ratio of the detuning to the Raman linewidth (HWHM), 2Δω/Γ, is (a) 0.0, (b) 1.48, and (c) 2.96. The parameters of the calculation are identical to those of Fig. 2(a) except that Stark shifting is neglected.

Fig. 6
Fig. 6

Calculated homogeneous (dashed line) and Doppler-broadened (solid line) CARS line shapes at Stokes laser intensities of (a) 0.001 and (b) 0.7 GW/cm2. The pump laser intensity was 37 GW/ cm2, the nitrogen pressure was 25 Torr, and the calculations were performed for the Q(12) line. Stark shifting and the nonresonant background were neglected.

Fig. 7
Fig. 7

CARS line shapes for the Q(12) line of nitrogen at a pressure of 100 Torr. The experimental Stokes laser intensities were (a) 0.8, (b) 3.3, and (c) 10 GW/cm2, corresponding to pulse energies of (a) 0.5, (b) 2.0, and (c) 6.0 mJ. The theoretical Stokes laser intensities were (a) 0.12, (b) 0.55, and (c) 1.8 GW/cm2. The solid lines are theoretical calculations of the line shape, including Doppler effects, Stark shifting, and the nonresonant background. The experimental data are indicated by filled circles. The nitrogen pressure was 100 Torr, and the Q(12) line was probed. The peak intensity and pulse energy of each pump laser beam were 37 GW/cm2 and 9 mJ, respectively. The nonresonant background susceptibility was 5.4 × 10−18 cm3/erg at line center with a slope of +11 × 10−18 (cm3/erg)/cm−1 at line center. The Stark-shifting coefficient KStark was equal to −0.6 × 10−13 cm−1/W.

Fig. 8
Fig. 8

Resonant and nonresonant CARS intensities and the excited-state population fraction at a homogeneous detuning Δω (cm−1) of 0.000 cm−1. The parameters of the calculation are identical to those of Fig. 6(c) except that Stark shifting is neglected.

Fig. 9
Fig. 9

Calculated homogeneous line shapes assuming top-hat (solid line) and Gaussian (dashed line) intensity profiles. For the Gaussian intensity profile calculation, the FWHM’s of the pump and Stokes beams were 50 and 75 μm, respectively. The peak intensity of each pump beam was 75 GW/cm2 in both cases. The peak intensity of the Stokes beam was 0.64 GW/cm2 for the top-hat profile and 1.28 GW/cm2 for the Gaussian profile. The dephasing time T2 was 4 × 10−9 sec. The Doppler effect and Stark shifting were neglected.

Equations (54)

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ψ ( t ) = c 1 ( t ) ψ 1 + c 2 ( t ) ψ 2 .
d ρ d t = i [ ρ , H ] ,
ρ = [ ρ 11 ρ 12 ρ 21 ρ 22 ] = [ c 1 c 1 * c 1 c 2 * c 2 c 1 * c 2 c 2 * ] .
H int = 1 2 q ( α q ) i j E i ( t ) E j ( t ) ,
H = [ W 1 V 12 ( t ) V 12 ( t ) W 2 ] ,
V 12 ( t ) = 1 2 q 12 ( α q ) E ( t ) E ( t ) .
q 12 = 1 | q | 2 = 2 | q | 1 = ( / 2 m r ω 0 ) 1 / 2 ( n + 1 ) 1 / 2 ,
ρ 11 t = i ( ρ 12 ρ 21 ) V 12 ,
ρ 12 t = i [ ( ρ 11 ρ 22 ) V 12 + ρ 12 ( W 2 W 1 ) ] ,
ρ 21 t = i [ ( ρ 11 ρ 22 ) V 12 + ρ 21 ( W 2 W 1 ) ] ,
ρ 22 t = i ( ρ 12 ρ 21 ) V 12 .
ρ 11 t = i [ ( ρ 12 ρ 21 ) V 12 ] ρ 11 k rot + R 31 ,
ρ 12 t = i [ ( ρ 11 ρ 22 ) V 12 + ρ 12 ( W 2 W 1 ) ] ρ 12 / T 2 ,
ρ 21 t = i [ ( ρ 11 ρ 22 ) V 12 + ρ 21 ( W 2 W 1 ) ] ρ 21 / T 2 ,
ρ 22 t = i ( ρ 12 ρ 21 ) V 12 ρ 22 ( k rot + k vib ) + R 42 ,
T 1 = 1 / k rot ,
T 2 = [ 1 2 ( k rot ) 1 + 1 2 ( k rot ) 2 + ( 1 T 2 * ) ] 1 ,
P ( t ) = N ( α q ) q E ( t ) + P nres ( t ) ,
q = q 12 ( ρ 12 + ρ 21 ) ,
2 q t 2 + 2 T 2 q t + ω 0 2 q = ω 0 q 12 2 ( α q ) E ( t ) E ( t ) ( 1 2 n ) ,
n t + n T 1 = 1 2 ω 0 ( α q ) E ( t ) E ( t ) ( q t + q T 2 ) .
q = 1 / 2 { Q exp [ i k υ x i ω υ t ] + c . c . } ,
E ( x , t ) = 1 / 2 { A p ( x , t ) exp ( i k p x i ω p t ) + A s ( x , t ) exp ( i k s x i ω s t ) + A a ( x , t ) exp ( i k a x i ω a t ) + c . c . } ,
ω υ = ω p ω s , k υ = k p k s .
Q t + ( 1 T 2 + i ω 0 2 ω υ 2 2 ω υ ) Q = i 1 4 m r ω υ ( α q ) ( A p A s * ) ( 1 2 n ) ,
n t + n n eq T 1 = i ω υ 8 ω 0 ( α q ) ( A p A s * Q * A p * A s Q ) .
Q r t = Q r T 2 + δ Q i γ ( A p A s * ) i = Q r T 2 + δ Q i γ ( A p i A s r A p r A s i ) ,
Q i t = Q i T 2 δ Q r + γ ( A p A s * ) r = Q i T 2 δ Q r + γ ( A p r A s r + A p i A s i ) ,
δ = ω 0 2 ω υ 2 2 ω υ
γ = ( α / q ) 4 m r ω υ ( 1 2 n ) .
A a x + μ a c A a t = i π ω a μ a c exp ( i Δ k a x ) [ N ( α q ) A p Q + χ nres A p 2 A s * ] ,
A a x = i π ω a μ a c exp ( i Δ k a x ) [ N ( α q ) A p Q + χ nres A p 2 A s * ] .
A a ( l int , t ) = i π l int ω a μ a c [ N ( α q ) A p Q + χ nres A p 2 A s * ] .
A a 1 res = i Λ res A p 2 Q 1 = i Λ res ( A p r 2 + i A p i 2 ) ( Q r 1 + i Q i 1 ) ,
Λ res = π l int ω a μ a c N ( α q ) .
A a 2 res = i Λ res A p 1 Q 2 = i Λ res ( A p r 1 + i A p i 1 ) ( Q r 2 + i Q i 2 ) .
A a r 1 res = Λ res [ A p r 2 Q i 1 + A p i 2 Q r 1 ] ,
A a i 1 res = Λ res [ A p r 2 Q r 1 A p i 2 Q i 1 ] ,
A a r 2 res = Λ res [ A p r 1 Q i 2 + A p i 1 Q r 2 ] ,
A a i 2 res = Λ res [ A p r 1 Q r 2 A p i 1 Q i 2 ] .
n t + n T 1 = i ω υ 8 ω 0 ( α q ) [ ( A p 1 + A p 2 ) A s * ( Q 1 + Q 2 ) * ( A p 1 + A p 2 ) * A s ( Q 1 + Q 2 ) ] .
Δ ω 0 ( t ) = K Stark [ I p ( t ) + I s ( t ) ] .
Δ ω H = ω p ω s ω 0 .
A a res ( t , Δ ω L ) = A a ( t , Δ ω H ) f ( Δ ω L Δ ω H ) d Δ ω H ,
f ( Δ ω ) = 2 Δ ω D ( ln 2 π ) 1 / 2 exp [ 4 ln 2 ( Δ ω Δ ω D ) 2 ] ,
A a nres ( t , Δ ω L ) = i Λ nres ( Δ ω L ) ( A p 1 A p 2 A s * + A p 2 A p 1 A s * ) ,
Λ nres ( Δ ω L ) = 2 π l int ω a μ a c χ nres ( Δ ω L ) .
A a r nres = Λ nres ( A p i 2 A p i 1 A s i A p i 2 A p r 1 A s r A p r 2 A p i 1 A s r + A p r 2 A p r 1 A s i ) ,
A a i nres = Λ nres [ A p r 2 A p r 1 A s r + A p r 2 A p i 1 A s i + A p i 2 A p r 1 A s i A p i 2 A p i 1 A s r ] ,
A a ( t , Δ ω L ) = A a res + A a nres ,
I a ( t , Δ ω L ) = c μ a 8 π A a A a * .
I a ( Δ ω ) = [ 1 + ( Δ ω T 2 ) 2 ] I p 2 ( r ) I s ( r ) [ 1 / T 2 + Δ ω 2 T 2 + I p ( r ) I s ( r ) / ( I p I s ) sat ] 2 r d r ,
( I p I s ) sat = m r c 2 ω 0 8 π 2 ( α / q ) 2 T 1 T 2 .
T 1 = ( k vib + k rot R 42 n ) 1 .

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