Abstract

The effect of Doppler broadening on degenerate four-wave mixing (DFWM) signal intensities in the regime of high pump and probe laser intensities is investigated theoretically. DFWM reflectivities are calculated by solving the time-dependent density-matrix equations for a two-level system interacting with three laser fields. The density-matrix equations are integrated directly in the time domain on a grid of spatial locations along the phase-matching axis; the DFWM signal level is then calculated by summation of the polarization contribution (with the appropriate phase factor) from each of the spatial grid points. For the case in which the Doppler and the collisional linewidths are comparable, the DFWM reflectivity is found to be inversely proportional to the factor 1 + (bΔωDωC)2, where ΔωD is the Doppler width, ΔωC is the collisional width, and b is weakly dependent on the pump and the probe laser powers. We developed an analytical expression for the reflectivity of a line that is both collision and Doppler broadened by dividing the widely used Abrams and Lind expression for homogeneous reflectivity Rhom by the factor 1 + (bΔωDωC)2. This modified reflectivity expression is found to give accurate results for the DFWM reflectivity over a wide range of values for the ratio of Doppler to collisional width. With this modified Abrams–Lind expression, strategies for quantitative DFWM concentration measurements in flames and plasmas are proposed and analyzed. We conclude that, by selection of the appropriate rotational transition, a DFWM reflectivity that is directly proportional to the square of the total species number density can be obtained over a wide range of temperature for constant-laser-intensity spatial profile mapping in flames.

© 1996 Optical Society of America

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  1. R. L. Farrow and D. J. Rakestraw, “Detection of trace molecular species using degenerate four-wave mixing,” Science 257, 1894–1900 (1992).
    [Crossref] [PubMed]
  2. K. Kohse-Höinghaus, “Laser techniques for the quantitative detection of reactive intermediates in combustion systems,” Prog. Energy Combust. Sci. 20, 203–279 (1994).
    [Crossref]
  3. S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. I. Weak-field limit,” J. Chem. Phys. 101, 1072–1092 (1994).
    [Crossref]
  4. S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. II. Strong-field limit,” J. Chem. Phys. 101, 1093–1107 (1994).
    [Crossref]
  5. R. L. Abrams and R. C. Lind, “Degenerate four-wave mixing in absorbing media,” Opt. Lett. 2, 94–96 (1978); erratum 3, 205 (1978).
    [Crossref] [PubMed]
  6. R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, and P. F. Liao, “Phase conjugation and high-resolution spectroscopy by resonant degenerate four-wave mixing,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 211–284.
    [Crossref]
  7. R. L. Farrow, D. J. Rakestraw, and T. Dreier, “Investigation of the dependence of degenerate four-wave mixing line intensities on transition dipole moment,” J. Opt. Soc. Am. B 9, 1770–1777 (1992).
    [Crossref]
  8. R. P. Lucht, R. L. Farrow, and D. J. Rakestraw, “Saturation effects in gas-phase degenerate four-wave mixing spectroscopy: nonperturbative calculations,” J. Opt. Soc. Am. B 10, 1508–1520 (1993).
    [Crossref]
  9. J. Nilsen and A. Yariv, “Nondegenerate four-wave mixing in a Doppler-broadened resonant medium,” J. Opt. Soc. Am. 71, 180–183 (1981).
    [Crossref]
  10. M. S. Brown, L. A. Rahn, and R. P. Lucht, “Degenerate four-wave mixing line shapes of hydroxyl at high pump intensities,” Appl. Opt. 34, 3274–3280 (1995).
    [Crossref] [PubMed]
  11. P. M. Danehy, E. J. Friedman-Hill, R. P. Lucht, and R. L. Farrow, “The effects of collisional quenching on degenerate four-wave mixing,” Appl. Phys. B 57, 243–248 (1993).
    [Crossref]
  12. R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992), p. 191.
    [Crossref]
  13. M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened systems. I. Angular dependence of intensity and lineshape of phase-conjugate emission,” J. Physique 42, 711–721 (1981).
    [Crossref]
  14. D. Bloch and M. Ducloy, “Theory of saturated line shapes in phase-conjugate emission by resonant degenerate four-wave mixing in Doppler-broadened three-level systems,” J. Opt. Soc. Am. 73, 635–646 (1983); errata 73, 1844–1845 (1983).
    [Crossref]
  15. M. Ducloy, F. A. M. de Oliveira, and D. Bloch, “Theory of resonant Doppler-broadened backward four-wave mixing in the pump saturation regime,” Phys. Rev. A 32, 1614–1623 (1985).
    [Crossref] [PubMed]
  16. S. Le Boiteaux, P. Simoneau, D. Bloch, F. A. M. de Oliveira, and M. Ducloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low pressure Ne discharge,” J. Quantum Electron. 22, 1229–1247 (1986).
    [Crossref]
  17. G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: the dressed atom approach,” Opt. Commun. 50, 261–264 (1984).
    [Crossref]
  18. G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: theory for a two-level atom,” J. Physique 47, 617–630 (1986).
    [Crossref]
  19. P. Verkerk, M. Pinard, and G. Grynberg, “Backward saturation in four-wave mixing in neon: case of cross-polarized pumps,” Phys. Rev. A 35, 4679–4695 (1987).
    [Crossref] [PubMed]
  20. J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
    [Crossref] [PubMed]
  21. D. S. Green, T. G. Owano, S. Williams, D. G. Goodwin, R. N. Zare, and C. H. Kruger, “Boundary layer profiles in plasma chemical vapor deposition,” Science 259, 1726–1729 (1993).
    [Crossref] [PubMed]
  22. S. Williams, D. S. Green, S. Sethuraman, and R. N. Zare, “Detection of trace species in hostile environments using degenerate four-wave mixing: CH in an atmospheric pressure flame,” J. Am. Chem. Soc. 114, 9122–9130 (1992).
    [Crossref]
  23. R. J. Cattolica, D. Stepowski, D. Puechberty, and M. Cottereau, “Laser-induced fluorescence of the CH molecule in a low-pressure flame,” J. Quant. Spectrosc. Radiat. Transfer 32, 363–370 (1984).
    [Crossref]
  24. D. E. Heard, J. B. Jeffries, and D. R. Crosley, “Collisional quenching of A2Σ+ NO and A2Δ CH in low pressure flames,” Chem. Phys. Lett. 178, 533–537 (1991).
    [Crossref]
  25. R. G. Joklik and J. W. Daily, “LIF study of CH A2Δ collision dynamics in a low pressure oxy-acetylene flame,” Combust. Flame 69, 211–219 (1987).
    [Crossref]
  26. T. Dreier and D. J. Rakestraw, “Measurement of OH rotational temperatures in a flame using degenerate four-wave mixing,” Opt. Lett. 15, 72–74 (1990).
    [Crossref] [PubMed]
  27. T. Dreier and D. J. Rakestraw, “Degenerate four-wave mixing diagnostics on OH and NH radicals in flames,” Appl. Phys. B 50, 479–485 (1990).
    [Crossref]
  28. M. Winter and P. P. Radi, “Nearly degenerate four-wave mixing using phase conjugate pump beams,” Opt. Lett. 17, 320–322 (1992).
    [Crossref] [PubMed]
  29. B. Yip, P. M. Danehy, and R. K. Hanson, “Degenerate four-wave mixing temperature measurements in a flame,” Opt. Lett. 17, 751–753 (1992).
    [Crossref] [PubMed]
  30. R. L. Vander Wal, R. L. Farrow, and D. J. Rakestraw, “High-resolution investigation of degenerate four-wave mixing in the γ(0, 0) band of nitric oxide,” in Twenty-Fourth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, Pa., 1993), pp. 1653–1659.
  31. D. A. Feikema, E. Domingues, and M.-J. Cottereau, “OH rotational temperature and number density measurements in high-pressure laminar flames using double phase-conjugate four-wave mixing,” Appl. Phys. B 55, 424–429 (1992).
    [Crossref]
  32. A. P. Smith and A. G. Astill, “Temperature measurement using degenerate four-wave mixing with non-saturating laser powers,” Appl. Phys. B 58, 459–466 (1994).
    [Crossref]
  33. H. Bervas, B. Attal-Tretout, S. Le Boiteaux, and J.-P. Taran, “OH detection and spectroscopy by DFWM in flames; comparison with CARS,” J. Phys. B 25, 949–969 (1992).
    [Crossref]
  34. D. R. Meacher, A. Charlton, P. Ewart, J. Cooper, and G. Alber, “Degenerate four-wave mixing with broad-bandwidth pulsed lasers,” Phys. Rev. A 42, 3018–3026 (1990).
    [Crossref] [PubMed]
  35. M. Kaczmarek, D. R. Meacher, and P. Ewart, “Time dependence of degenerate four-wave mixing with broad bandwidth pulsed lasers,” J. Mod. Opt. 37, 1561–1571 (1990).
    [Crossref]
  36. M. A. Linne and G. J. Fiechtner, “Picosecond degenerate four-wave mixing on potassium in a methane-air flame,” Opt. Lett. 19, 667–669 (1994).
    [Crossref] [PubMed]
  37. L. A. Rahn and M. S. Brown, “Polarization properties of degenerate four-wave mixing in flame OH,” Opt. Lett. 19, 1249–1251 (1994).
    [Crossref] [PubMed]
  38. S. Williams, L. A. Rahn, P. H. Paul, J. W. Forsman, and R. N. Zare, “Laser-induced thermal grating effects in flames,” Opt. Lett. 19, 1681–1683 (1994).
    [Crossref] [PubMed]
  39. P. H. Paul, R. L. Farrow, and P. M. Danehy, “Gas-phase thermal-grating contributions to four-wave mixing,” J. Opt. Soc. Am. B 12, 384–392 (1995).
    [Crossref]

1995 (2)

1994 (7)

M. A. Linne and G. J. Fiechtner, “Picosecond degenerate four-wave mixing on potassium in a methane-air flame,” Opt. Lett. 19, 667–669 (1994).
[Crossref] [PubMed]

L. A. Rahn and M. S. Brown, “Polarization properties of degenerate four-wave mixing in flame OH,” Opt. Lett. 19, 1249–1251 (1994).
[Crossref] [PubMed]

S. Williams, L. A. Rahn, P. H. Paul, J. W. Forsman, and R. N. Zare, “Laser-induced thermal grating effects in flames,” Opt. Lett. 19, 1681–1683 (1994).
[Crossref] [PubMed]

A. P. Smith and A. G. Astill, “Temperature measurement using degenerate four-wave mixing with non-saturating laser powers,” Appl. Phys. B 58, 459–466 (1994).
[Crossref]

K. Kohse-Höinghaus, “Laser techniques for the quantitative detection of reactive intermediates in combustion systems,” Prog. Energy Combust. Sci. 20, 203–279 (1994).
[Crossref]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. I. Weak-field limit,” J. Chem. Phys. 101, 1072–1092 (1994).
[Crossref]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. II. Strong-field limit,” J. Chem. Phys. 101, 1093–1107 (1994).
[Crossref]

1993 (3)

R. P. Lucht, R. L. Farrow, and D. J. Rakestraw, “Saturation effects in gas-phase degenerate four-wave mixing spectroscopy: nonperturbative calculations,” J. Opt. Soc. Am. B 10, 1508–1520 (1993).
[Crossref]

P. M. Danehy, E. J. Friedman-Hill, R. P. Lucht, and R. L. Farrow, “The effects of collisional quenching on degenerate four-wave mixing,” Appl. Phys. B 57, 243–248 (1993).
[Crossref]

D. S. Green, T. G. Owano, S. Williams, D. G. Goodwin, R. N. Zare, and C. H. Kruger, “Boundary layer profiles in plasma chemical vapor deposition,” Science 259, 1726–1729 (1993).
[Crossref] [PubMed]

1992 (7)

S. Williams, D. S. Green, S. Sethuraman, and R. N. Zare, “Detection of trace species in hostile environments using degenerate four-wave mixing: CH in an atmospheric pressure flame,” J. Am. Chem. Soc. 114, 9122–9130 (1992).
[Crossref]

M. Winter and P. P. Radi, “Nearly degenerate four-wave mixing using phase conjugate pump beams,” Opt. Lett. 17, 320–322 (1992).
[Crossref] [PubMed]

B. Yip, P. M. Danehy, and R. K. Hanson, “Degenerate four-wave mixing temperature measurements in a flame,” Opt. Lett. 17, 751–753 (1992).
[Crossref] [PubMed]

D. A. Feikema, E. Domingues, and M.-J. Cottereau, “OH rotational temperature and number density measurements in high-pressure laminar flames using double phase-conjugate four-wave mixing,” Appl. Phys. B 55, 424–429 (1992).
[Crossref]

H. Bervas, B. Attal-Tretout, S. Le Boiteaux, and J.-P. Taran, “OH detection and spectroscopy by DFWM in flames; comparison with CARS,” J. Phys. B 25, 949–969 (1992).
[Crossref]

R. L. Farrow and D. J. Rakestraw, “Detection of trace molecular species using degenerate four-wave mixing,” Science 257, 1894–1900 (1992).
[Crossref] [PubMed]

R. L. Farrow, D. J. Rakestraw, and T. Dreier, “Investigation of the dependence of degenerate four-wave mixing line intensities on transition dipole moment,” J. Opt. Soc. Am. B 9, 1770–1777 (1992).
[Crossref]

1991 (1)

D. E. Heard, J. B. Jeffries, and D. R. Crosley, “Collisional quenching of A2Σ+ NO and A2Δ CH in low pressure flames,” Chem. Phys. Lett. 178, 533–537 (1991).
[Crossref]

1990 (4)

T. Dreier and D. J. Rakestraw, “Measurement of OH rotational temperatures in a flame using degenerate four-wave mixing,” Opt. Lett. 15, 72–74 (1990).
[Crossref] [PubMed]

T. Dreier and D. J. Rakestraw, “Degenerate four-wave mixing diagnostics on OH and NH radicals in flames,” Appl. Phys. B 50, 479–485 (1990).
[Crossref]

D. R. Meacher, A. Charlton, P. Ewart, J. Cooper, and G. Alber, “Degenerate four-wave mixing with broad-bandwidth pulsed lasers,” Phys. Rev. A 42, 3018–3026 (1990).
[Crossref] [PubMed]

M. Kaczmarek, D. R. Meacher, and P. Ewart, “Time dependence of degenerate four-wave mixing with broad bandwidth pulsed lasers,” J. Mod. Opt. 37, 1561–1571 (1990).
[Crossref]

1989 (1)

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[Crossref] [PubMed]

1987 (2)

R. G. Joklik and J. W. Daily, “LIF study of CH A2Δ collision dynamics in a low pressure oxy-acetylene flame,” Combust. Flame 69, 211–219 (1987).
[Crossref]

P. Verkerk, M. Pinard, and G. Grynberg, “Backward saturation in four-wave mixing in neon: case of cross-polarized pumps,” Phys. Rev. A 35, 4679–4695 (1987).
[Crossref] [PubMed]

1986 (2)

G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: theory for a two-level atom,” J. Physique 47, 617–630 (1986).
[Crossref]

S. Le Boiteaux, P. Simoneau, D. Bloch, F. A. M. de Oliveira, and M. Ducloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low pressure Ne discharge,” J. Quantum Electron. 22, 1229–1247 (1986).
[Crossref]

1985 (1)

M. Ducloy, F. A. M. de Oliveira, and D. Bloch, “Theory of resonant Doppler-broadened backward four-wave mixing in the pump saturation regime,” Phys. Rev. A 32, 1614–1623 (1985).
[Crossref] [PubMed]

1984 (2)

G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: the dressed atom approach,” Opt. Commun. 50, 261–264 (1984).
[Crossref]

R. J. Cattolica, D. Stepowski, D. Puechberty, and M. Cottereau, “Laser-induced fluorescence of the CH molecule in a low-pressure flame,” J. Quant. Spectrosc. Radiat. Transfer 32, 363–370 (1984).
[Crossref]

1983 (1)

1981 (2)

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened systems. I. Angular dependence of intensity and lineshape of phase-conjugate emission,” J. Physique 42, 711–721 (1981).
[Crossref]

J. Nilsen and A. Yariv, “Nondegenerate four-wave mixing in a Doppler-broadened resonant medium,” J. Opt. Soc. Am. 71, 180–183 (1981).
[Crossref]

1978 (1)

Abrams, R. L.

R. L. Abrams and R. C. Lind, “Degenerate four-wave mixing in absorbing media,” Opt. Lett. 2, 94–96 (1978); erratum 3, 205 (1978).
[Crossref] [PubMed]

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, and P. F. Liao, “Phase conjugation and high-resolution spectroscopy by resonant degenerate four-wave mixing,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 211–284.
[Crossref]

Alber, G.

D. R. Meacher, A. Charlton, P. Ewart, J. Cooper, and G. Alber, “Degenerate four-wave mixing with broad-bandwidth pulsed lasers,” Phys. Rev. A 42, 3018–3026 (1990).
[Crossref] [PubMed]

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[Crossref] [PubMed]

Astill, A. G.

A. P. Smith and A. G. Astill, “Temperature measurement using degenerate four-wave mixing with non-saturating laser powers,” Appl. Phys. B 58, 459–466 (1994).
[Crossref]

Attal-Tretout, B.

H. Bervas, B. Attal-Tretout, S. Le Boiteaux, and J.-P. Taran, “OH detection and spectroscopy by DFWM in flames; comparison with CARS,” J. Phys. B 25, 949–969 (1992).
[Crossref]

Bervas, H.

H. Bervas, B. Attal-Tretout, S. Le Boiteaux, and J.-P. Taran, “OH detection and spectroscopy by DFWM in flames; comparison with CARS,” J. Phys. B 25, 949–969 (1992).
[Crossref]

Bloch, D.

S. Le Boiteaux, P. Simoneau, D. Bloch, F. A. M. de Oliveira, and M. Ducloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low pressure Ne discharge,” J. Quantum Electron. 22, 1229–1247 (1986).
[Crossref]

M. Ducloy, F. A. M. de Oliveira, and D. Bloch, “Theory of resonant Doppler-broadened backward four-wave mixing in the pump saturation regime,” Phys. Rev. A 32, 1614–1623 (1985).
[Crossref] [PubMed]

D. Bloch and M. Ducloy, “Theory of saturated line shapes in phase-conjugate emission by resonant degenerate four-wave mixing in Doppler-broadened three-level systems,” J. Opt. Soc. Am. 73, 635–646 (1983); errata 73, 1844–1845 (1983).
[Crossref]

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened systems. I. Angular dependence of intensity and lineshape of phase-conjugate emission,” J. Physique 42, 711–721 (1981).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992), p. 191.
[Crossref]

Brown, M. S.

Cattolica, R. J.

R. J. Cattolica, D. Stepowski, D. Puechberty, and M. Cottereau, “Laser-induced fluorescence of the CH molecule in a low-pressure flame,” J. Quant. Spectrosc. Radiat. Transfer 32, 363–370 (1984).
[Crossref]

Charlton, A.

D. R. Meacher, A. Charlton, P. Ewart, J. Cooper, and G. Alber, “Degenerate four-wave mixing with broad-bandwidth pulsed lasers,” Phys. Rev. A 42, 3018–3026 (1990).
[Crossref] [PubMed]

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[Crossref] [PubMed]

Cooper, J.

D. R. Meacher, A. Charlton, P. Ewart, J. Cooper, and G. Alber, “Degenerate four-wave mixing with broad-bandwidth pulsed lasers,” Phys. Rev. A 42, 3018–3026 (1990).
[Crossref] [PubMed]

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[Crossref] [PubMed]

Cottereau, M.

R. J. Cattolica, D. Stepowski, D. Puechberty, and M. Cottereau, “Laser-induced fluorescence of the CH molecule in a low-pressure flame,” J. Quant. Spectrosc. Radiat. Transfer 32, 363–370 (1984).
[Crossref]

Cottereau, M.-J.

D. A. Feikema, E. Domingues, and M.-J. Cottereau, “OH rotational temperature and number density measurements in high-pressure laminar flames using double phase-conjugate four-wave mixing,” Appl. Phys. B 55, 424–429 (1992).
[Crossref]

Crosley, D. R.

D. E. Heard, J. B. Jeffries, and D. R. Crosley, “Collisional quenching of A2Σ+ NO and A2Δ CH in low pressure flames,” Chem. Phys. Lett. 178, 533–537 (1991).
[Crossref]

Daily, J. W.

R. G. Joklik and J. W. Daily, “LIF study of CH A2Δ collision dynamics in a low pressure oxy-acetylene flame,” Combust. Flame 69, 211–219 (1987).
[Crossref]

Danehy, P. M.

de Oliveira, F. A. M.

S. Le Boiteaux, P. Simoneau, D. Bloch, F. A. M. de Oliveira, and M. Ducloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low pressure Ne discharge,” J. Quantum Electron. 22, 1229–1247 (1986).
[Crossref]

M. Ducloy, F. A. M. de Oliveira, and D. Bloch, “Theory of resonant Doppler-broadened backward four-wave mixing in the pump saturation regime,” Phys. Rev. A 32, 1614–1623 (1985).
[Crossref] [PubMed]

Domingues, E.

D. A. Feikema, E. Domingues, and M.-J. Cottereau, “OH rotational temperature and number density measurements in high-pressure laminar flames using double phase-conjugate four-wave mixing,” Appl. Phys. B 55, 424–429 (1992).
[Crossref]

Dreier, T.

Ducloy, M.

S. Le Boiteaux, P. Simoneau, D. Bloch, F. A. M. de Oliveira, and M. Ducloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low pressure Ne discharge,” J. Quantum Electron. 22, 1229–1247 (1986).
[Crossref]

M. Ducloy, F. A. M. de Oliveira, and D. Bloch, “Theory of resonant Doppler-broadened backward four-wave mixing in the pump saturation regime,” Phys. Rev. A 32, 1614–1623 (1985).
[Crossref] [PubMed]

D. Bloch and M. Ducloy, “Theory of saturated line shapes in phase-conjugate emission by resonant degenerate four-wave mixing in Doppler-broadened three-level systems,” J. Opt. Soc. Am. 73, 635–646 (1983); errata 73, 1844–1845 (1983).
[Crossref]

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened systems. I. Angular dependence of intensity and lineshape of phase-conjugate emission,” J. Physique 42, 711–721 (1981).
[Crossref]

Ewart, P.

D. R. Meacher, A. Charlton, P. Ewart, J. Cooper, and G. Alber, “Degenerate four-wave mixing with broad-bandwidth pulsed lasers,” Phys. Rev. A 42, 3018–3026 (1990).
[Crossref] [PubMed]

M. Kaczmarek, D. R. Meacher, and P. Ewart, “Time dependence of degenerate four-wave mixing with broad bandwidth pulsed lasers,” J. Mod. Opt. 37, 1561–1571 (1990).
[Crossref]

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[Crossref] [PubMed]

Farrow, R. L.

P. H. Paul, R. L. Farrow, and P. M. Danehy, “Gas-phase thermal-grating contributions to four-wave mixing,” J. Opt. Soc. Am. B 12, 384–392 (1995).
[Crossref]

R. P. Lucht, R. L. Farrow, and D. J. Rakestraw, “Saturation effects in gas-phase degenerate four-wave mixing spectroscopy: nonperturbative calculations,” J. Opt. Soc. Am. B 10, 1508–1520 (1993).
[Crossref]

P. M. Danehy, E. J. Friedman-Hill, R. P. Lucht, and R. L. Farrow, “The effects of collisional quenching on degenerate four-wave mixing,” Appl. Phys. B 57, 243–248 (1993).
[Crossref]

R. L. Farrow, D. J. Rakestraw, and T. Dreier, “Investigation of the dependence of degenerate four-wave mixing line intensities on transition dipole moment,” J. Opt. Soc. Am. B 9, 1770–1777 (1992).
[Crossref]

R. L. Farrow and D. J. Rakestraw, “Detection of trace molecular species using degenerate four-wave mixing,” Science 257, 1894–1900 (1992).
[Crossref] [PubMed]

R. L. Vander Wal, R. L. Farrow, and D. J. Rakestraw, “High-resolution investigation of degenerate four-wave mixing in the γ(0, 0) band of nitric oxide,” in Twenty-Fourth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, Pa., 1993), pp. 1653–1659.

Feikema, D. A.

D. A. Feikema, E. Domingues, and M.-J. Cottereau, “OH rotational temperature and number density measurements in high-pressure laminar flames using double phase-conjugate four-wave mixing,” Appl. Phys. B 55, 424–429 (1992).
[Crossref]

Fiechtner, G. J.

Forsman, J. W.

Friedman-Hill, E. J.

P. M. Danehy, E. J. Friedman-Hill, R. P. Lucht, and R. L. Farrow, “The effects of collisional quenching on degenerate four-wave mixing,” Appl. Phys. B 57, 243–248 (1993).
[Crossref]

Goodwin, D. G.

D. S. Green, T. G. Owano, S. Williams, D. G. Goodwin, R. N. Zare, and C. H. Kruger, “Boundary layer profiles in plasma chemical vapor deposition,” Science 259, 1726–1729 (1993).
[Crossref] [PubMed]

Green, D. S.

D. S. Green, T. G. Owano, S. Williams, D. G. Goodwin, R. N. Zare, and C. H. Kruger, “Boundary layer profiles in plasma chemical vapor deposition,” Science 259, 1726–1729 (1993).
[Crossref] [PubMed]

S. Williams, D. S. Green, S. Sethuraman, and R. N. Zare, “Detection of trace species in hostile environments using degenerate four-wave mixing: CH in an atmospheric pressure flame,” J. Am. Chem. Soc. 114, 9122–9130 (1992).
[Crossref]

Grynberg, G.

P. Verkerk, M. Pinard, and G. Grynberg, “Backward saturation in four-wave mixing in neon: case of cross-polarized pumps,” Phys. Rev. A 35, 4679–4695 (1987).
[Crossref] [PubMed]

G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: theory for a two-level atom,” J. Physique 47, 617–630 (1986).
[Crossref]

G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: the dressed atom approach,” Opt. Commun. 50, 261–264 (1984).
[Crossref]

Hanson, R. K.

Heard, D. E.

D. E. Heard, J. B. Jeffries, and D. R. Crosley, “Collisional quenching of A2Σ+ NO and A2Δ CH in low pressure flames,” Chem. Phys. Lett. 178, 533–537 (1991).
[Crossref]

Jeffries, J. B.

D. E. Heard, J. B. Jeffries, and D. R. Crosley, “Collisional quenching of A2Σ+ NO and A2Δ CH in low pressure flames,” Chem. Phys. Lett. 178, 533–537 (1991).
[Crossref]

Joklik, R. G.

R. G. Joklik and J. W. Daily, “LIF study of CH A2Δ collision dynamics in a low pressure oxy-acetylene flame,” Combust. Flame 69, 211–219 (1987).
[Crossref]

Kaczmarek, M.

M. Kaczmarek, D. R. Meacher, and P. Ewart, “Time dependence of degenerate four-wave mixing with broad bandwidth pulsed lasers,” J. Mod. Opt. 37, 1561–1571 (1990).
[Crossref]

Kohse-Höinghaus, K.

K. Kohse-Höinghaus, “Laser techniques for the quantitative detection of reactive intermediates in combustion systems,” Prog. Energy Combust. Sci. 20, 203–279 (1994).
[Crossref]

Kruger, C. H.

D. S. Green, T. G. Owano, S. Williams, D. G. Goodwin, R. N. Zare, and C. H. Kruger, “Boundary layer profiles in plasma chemical vapor deposition,” Science 259, 1726–1729 (1993).
[Crossref] [PubMed]

Lam, J. F.

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, and P. F. Liao, “Phase conjugation and high-resolution spectroscopy by resonant degenerate four-wave mixing,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 211–284.
[Crossref]

Le Boiteaux, S.

H. Bervas, B. Attal-Tretout, S. Le Boiteaux, and J.-P. Taran, “OH detection and spectroscopy by DFWM in flames; comparison with CARS,” J. Phys. B 25, 949–969 (1992).
[Crossref]

S. Le Boiteaux, P. Simoneau, D. Bloch, F. A. M. de Oliveira, and M. Ducloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low pressure Ne discharge,” J. Quantum Electron. 22, 1229–1247 (1986).
[Crossref]

Liao, P. F.

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, and P. F. Liao, “Phase conjugation and high-resolution spectroscopy by resonant degenerate four-wave mixing,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 211–284.
[Crossref]

Lind, R. C.

R. L. Abrams and R. C. Lind, “Degenerate four-wave mixing in absorbing media,” Opt. Lett. 2, 94–96 (1978); erratum 3, 205 (1978).
[Crossref] [PubMed]

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, and P. F. Liao, “Phase conjugation and high-resolution spectroscopy by resonant degenerate four-wave mixing,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 211–284.
[Crossref]

Linne, M. A.

Lucht, R. P.

Meacher, D. R.

M. Kaczmarek, D. R. Meacher, and P. Ewart, “Time dependence of degenerate four-wave mixing with broad bandwidth pulsed lasers,” J. Mod. Opt. 37, 1561–1571 (1990).
[Crossref]

D. R. Meacher, A. Charlton, P. Ewart, J. Cooper, and G. Alber, “Degenerate four-wave mixing with broad-bandwidth pulsed lasers,” Phys. Rev. A 42, 3018–3026 (1990).
[Crossref] [PubMed]

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[Crossref] [PubMed]

Nilsen, J.

Owano, T. G.

D. S. Green, T. G. Owano, S. Williams, D. G. Goodwin, R. N. Zare, and C. H. Kruger, “Boundary layer profiles in plasma chemical vapor deposition,” Science 259, 1726–1729 (1993).
[Crossref] [PubMed]

Paul, P. H.

Pinard, M.

P. Verkerk, M. Pinard, and G. Grynberg, “Backward saturation in four-wave mixing in neon: case of cross-polarized pumps,” Phys. Rev. A 35, 4679–4695 (1987).
[Crossref] [PubMed]

G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: theory for a two-level atom,” J. Physique 47, 617–630 (1986).
[Crossref]

G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: the dressed atom approach,” Opt. Commun. 50, 261–264 (1984).
[Crossref]

Puechberty, D.

R. J. Cattolica, D. Stepowski, D. Puechberty, and M. Cottereau, “Laser-induced fluorescence of the CH molecule in a low-pressure flame,” J. Quant. Spectrosc. Radiat. Transfer 32, 363–370 (1984).
[Crossref]

Radi, P. P.

Rahn, L. A.

M. S. Brown, L. A. Rahn, and R. P. Lucht, “Degenerate four-wave mixing line shapes of hydroxyl at high pump intensities,” Appl. Opt. 34, 3274–3280 (1995).
[Crossref] [PubMed]

S. Williams, L. A. Rahn, P. H. Paul, J. W. Forsman, and R. N. Zare, “Laser-induced thermal grating effects in flames,” Opt. Lett. 19, 1681–1683 (1994).
[Crossref] [PubMed]

L. A. Rahn and M. S. Brown, “Polarization properties of degenerate four-wave mixing in flame OH,” Opt. Lett. 19, 1249–1251 (1994).
[Crossref] [PubMed]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. II. Strong-field limit,” J. Chem. Phys. 101, 1093–1107 (1994).
[Crossref]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. I. Weak-field limit,” J. Chem. Phys. 101, 1072–1092 (1994).
[Crossref]

Rakestraw, D. J.

R. P. Lucht, R. L. Farrow, and D. J. Rakestraw, “Saturation effects in gas-phase degenerate four-wave mixing spectroscopy: nonperturbative calculations,” J. Opt. Soc. Am. B 10, 1508–1520 (1993).
[Crossref]

R. L. Farrow, D. J. Rakestraw, and T. Dreier, “Investigation of the dependence of degenerate four-wave mixing line intensities on transition dipole moment,” J. Opt. Soc. Am. B 9, 1770–1777 (1992).
[Crossref]

R. L. Farrow and D. J. Rakestraw, “Detection of trace molecular species using degenerate four-wave mixing,” Science 257, 1894–1900 (1992).
[Crossref] [PubMed]

T. Dreier and D. J. Rakestraw, “Degenerate four-wave mixing diagnostics on OH and NH radicals in flames,” Appl. Phys. B 50, 479–485 (1990).
[Crossref]

T. Dreier and D. J. Rakestraw, “Measurement of OH rotational temperatures in a flame using degenerate four-wave mixing,” Opt. Lett. 15, 72–74 (1990).
[Crossref] [PubMed]

R. L. Vander Wal, R. L. Farrow, and D. J. Rakestraw, “High-resolution investigation of degenerate four-wave mixing in the γ(0, 0) band of nitric oxide,” in Twenty-Fourth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, Pa., 1993), pp. 1653–1659.

Sethuraman, S.

S. Williams, D. S. Green, S. Sethuraman, and R. N. Zare, “Detection of trace species in hostile environments using degenerate four-wave mixing: CH in an atmospheric pressure flame,” J. Am. Chem. Soc. 114, 9122–9130 (1992).
[Crossref]

Simoneau, P.

S. Le Boiteaux, P. Simoneau, D. Bloch, F. A. M. de Oliveira, and M. Ducloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low pressure Ne discharge,” J. Quantum Electron. 22, 1229–1247 (1986).
[Crossref]

Smith, A. P.

A. P. Smith and A. G. Astill, “Temperature measurement using degenerate four-wave mixing with non-saturating laser powers,” Appl. Phys. B 58, 459–466 (1994).
[Crossref]

Steel, D. G.

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, and P. F. Liao, “Phase conjugation and high-resolution spectroscopy by resonant degenerate four-wave mixing,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 211–284.
[Crossref]

Stepowski, D.

R. J. Cattolica, D. Stepowski, D. Puechberty, and M. Cottereau, “Laser-induced fluorescence of the CH molecule in a low-pressure flame,” J. Quant. Spectrosc. Radiat. Transfer 32, 363–370 (1984).
[Crossref]

Taran, J.-P.

H. Bervas, B. Attal-Tretout, S. Le Boiteaux, and J.-P. Taran, “OH detection and spectroscopy by DFWM in flames; comparison with CARS,” J. Phys. B 25, 949–969 (1992).
[Crossref]

Vander Wal, R. L.

R. L. Vander Wal, R. L. Farrow, and D. J. Rakestraw, “High-resolution investigation of degenerate four-wave mixing in the γ(0, 0) band of nitric oxide,” in Twenty-Fourth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, Pa., 1993), pp. 1653–1659.

Verkerk, P.

P. Verkerk, M. Pinard, and G. Grynberg, “Backward saturation in four-wave mixing in neon: case of cross-polarized pumps,” Phys. Rev. A 35, 4679–4695 (1987).
[Crossref] [PubMed]

G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: theory for a two-level atom,” J. Physique 47, 617–630 (1986).
[Crossref]

G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: the dressed atom approach,” Opt. Commun. 50, 261–264 (1984).
[Crossref]

Williams, S.

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. II. Strong-field limit,” J. Chem. Phys. 101, 1093–1107 (1994).
[Crossref]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. I. Weak-field limit,” J. Chem. Phys. 101, 1072–1092 (1994).
[Crossref]

S. Williams, L. A. Rahn, P. H. Paul, J. W. Forsman, and R. N. Zare, “Laser-induced thermal grating effects in flames,” Opt. Lett. 19, 1681–1683 (1994).
[Crossref] [PubMed]

D. S. Green, T. G. Owano, S. Williams, D. G. Goodwin, R. N. Zare, and C. H. Kruger, “Boundary layer profiles in plasma chemical vapor deposition,” Science 259, 1726–1729 (1993).
[Crossref] [PubMed]

S. Williams, D. S. Green, S. Sethuraman, and R. N. Zare, “Detection of trace species in hostile environments using degenerate four-wave mixing: CH in an atmospheric pressure flame,” J. Am. Chem. Soc. 114, 9122–9130 (1992).
[Crossref]

Winter, M.

Yariv, A.

Yip, B.

Zare, R. N.

S. Williams, L. A. Rahn, P. H. Paul, J. W. Forsman, and R. N. Zare, “Laser-induced thermal grating effects in flames,” Opt. Lett. 19, 1681–1683 (1994).
[Crossref] [PubMed]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. I. Weak-field limit,” J. Chem. Phys. 101, 1072–1092 (1994).
[Crossref]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. II. Strong-field limit,” J. Chem. Phys. 101, 1093–1107 (1994).
[Crossref]

D. S. Green, T. G. Owano, S. Williams, D. G. Goodwin, R. N. Zare, and C. H. Kruger, “Boundary layer profiles in plasma chemical vapor deposition,” Science 259, 1726–1729 (1993).
[Crossref] [PubMed]

S. Williams, D. S. Green, S. Sethuraman, and R. N. Zare, “Detection of trace species in hostile environments using degenerate four-wave mixing: CH in an atmospheric pressure flame,” J. Am. Chem. Soc. 114, 9122–9130 (1992).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (4)

P. M. Danehy, E. J. Friedman-Hill, R. P. Lucht, and R. L. Farrow, “The effects of collisional quenching on degenerate four-wave mixing,” Appl. Phys. B 57, 243–248 (1993).
[Crossref]

T. Dreier and D. J. Rakestraw, “Degenerate four-wave mixing diagnostics on OH and NH radicals in flames,” Appl. Phys. B 50, 479–485 (1990).
[Crossref]

D. A. Feikema, E. Domingues, and M.-J. Cottereau, “OH rotational temperature and number density measurements in high-pressure laminar flames using double phase-conjugate four-wave mixing,” Appl. Phys. B 55, 424–429 (1992).
[Crossref]

A. P. Smith and A. G. Astill, “Temperature measurement using degenerate four-wave mixing with non-saturating laser powers,” Appl. Phys. B 58, 459–466 (1994).
[Crossref]

Chem. Phys. Lett. (1)

D. E. Heard, J. B. Jeffries, and D. R. Crosley, “Collisional quenching of A2Σ+ NO and A2Δ CH in low pressure flames,” Chem. Phys. Lett. 178, 533–537 (1991).
[Crossref]

Combust. Flame (1)

R. G. Joklik and J. W. Daily, “LIF study of CH A2Δ collision dynamics in a low pressure oxy-acetylene flame,” Combust. Flame 69, 211–219 (1987).
[Crossref]

J. Am. Chem. Soc. (1)

S. Williams, D. S. Green, S. Sethuraman, and R. N. Zare, “Detection of trace species in hostile environments using degenerate four-wave mixing: CH in an atmospheric pressure flame,” J. Am. Chem. Soc. 114, 9122–9130 (1992).
[Crossref]

J. Chem. Phys. (2)

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. I. Weak-field limit,” J. Chem. Phys. 101, 1072–1092 (1994).
[Crossref]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations. II. Strong-field limit,” J. Chem. Phys. 101, 1093–1107 (1994).
[Crossref]

J. Mod. Opt. (1)

M. Kaczmarek, D. R. Meacher, and P. Ewart, “Time dependence of degenerate four-wave mixing with broad bandwidth pulsed lasers,” J. Mod. Opt. 37, 1561–1571 (1990).
[Crossref]

J. Opt. Soc. Am. (2)

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

J. Phys. B (1)

H. Bervas, B. Attal-Tretout, S. Le Boiteaux, and J.-P. Taran, “OH detection and spectroscopy by DFWM in flames; comparison with CARS,” J. Phys. B 25, 949–969 (1992).
[Crossref]

J. Physique (2)

G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: theory for a two-level atom,” J. Physique 47, 617–630 (1986).
[Crossref]

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened systems. I. Angular dependence of intensity and lineshape of phase-conjugate emission,” J. Physique 42, 711–721 (1981).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (1)

R. J. Cattolica, D. Stepowski, D. Puechberty, and M. Cottereau, “Laser-induced fluorescence of the CH molecule in a low-pressure flame,” J. Quant. Spectrosc. Radiat. Transfer 32, 363–370 (1984).
[Crossref]

J. Quantum Electron. (1)

S. Le Boiteaux, P. Simoneau, D. Bloch, F. A. M. de Oliveira, and M. Ducloy, “Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: experimental analysis on a low pressure Ne discharge,” J. Quantum Electron. 22, 1229–1247 (1986).
[Crossref]

Opt. Commun. (1)

G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: the dressed atom approach,” Opt. Commun. 50, 261–264 (1984).
[Crossref]

Opt. Lett. (7)

Phys. Rev. A (4)

D. R. Meacher, A. Charlton, P. Ewart, J. Cooper, and G. Alber, “Degenerate four-wave mixing with broad-bandwidth pulsed lasers,” Phys. Rev. A 42, 3018–3026 (1990).
[Crossref] [PubMed]

P. Verkerk, M. Pinard, and G. Grynberg, “Backward saturation in four-wave mixing in neon: case of cross-polarized pumps,” Phys. Rev. A 35, 4679–4695 (1987).
[Crossref] [PubMed]

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[Crossref] [PubMed]

M. Ducloy, F. A. M. de Oliveira, and D. Bloch, “Theory of resonant Doppler-broadened backward four-wave mixing in the pump saturation regime,” Phys. Rev. A 32, 1614–1623 (1985).
[Crossref] [PubMed]

Prog. Energy Combust. Sci. (1)

K. Kohse-Höinghaus, “Laser techniques for the quantitative detection of reactive intermediates in combustion systems,” Prog. Energy Combust. Sci. 20, 203–279 (1994).
[Crossref]

Science (2)

R. L. Farrow and D. J. Rakestraw, “Detection of trace molecular species using degenerate four-wave mixing,” Science 257, 1894–1900 (1992).
[Crossref] [PubMed]

D. S. Green, T. G. Owano, S. Williams, D. G. Goodwin, R. N. Zare, and C. H. Kruger, “Boundary layer profiles in plasma chemical vapor deposition,” Science 259, 1726–1729 (1993).
[Crossref] [PubMed]

Other (3)

R. L. Vander Wal, R. L. Farrow, and D. J. Rakestraw, “High-resolution investigation of degenerate four-wave mixing in the γ(0, 0) band of nitric oxide,” in Twenty-Fourth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, Pa., 1993), pp. 1653–1659.

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, and P. F. Liao, “Phase conjugation and high-resolution spectroscopy by resonant degenerate four-wave mixing,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 211–284.
[Crossref]

R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992), p. 191.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Geometry for the DFWM calculations. In the rest frame of a molecule moving along the z axis the frequencies of all three laser beams are Doppler shifted.

Fig. 2
Fig. 2

Comparison of DNI calculated reflectivities with the Abrams–Lind theory for two different pulse profiles. The results for the case of a weak probe (Ipr = 0.01 Isat) are displayed for both the 60-ns (filled circles) and the 3.5-ns (open circles) pulses. The DNI code results are in excellent agreement with the Abrams–Lind model (solid curve) for the limiting case of a homogeneously broadened system and a long laser pulse. The case of a saturating probe (Ipr = 0.25 Ipump) is also displayed for the 3.5-ns pulses (open triangles).

Fig. 3
Fig. 3

Dependence of the reflectivity on ΔωCωD for constant ΔωC = 0.053 cm−1: (a), (b), (c) the value of Ipr was held constant at 0.1 Isat; (d), (e), (f) the value of Ipr was set equal to 0.25 Ipump. The DNI results are displayed with the circles, while the curves are the least-square fits of the modified Abrams–Lind expression [Eq. (1)] to the DNI results.

Fig. 4
Fig. 4

Fitting coefficient b versus Ipump/Isat for Ipr = 0.1 Isat and Ipr = 0.25 Ipump.

Fig. 5
Fig. 5

Reflectivity versus ΔωCωD for three different collisional widths: ΔωC equal to 0.027, 0.053, and 0.106 cm−1. For each of the three curves, Ipump = Isat and Ipr = 0.25 Ipump.

Fig. 6
Fig. 6

Normalized reflectivity R/(n10)2 as a function of temperature. Both the DNI results (symbols) and the modified Abrams–Lind expression (curves) are displayed for B equal to 30, 10, 5, 2, and 1.

Fig. 7
Fig. 7

Competing factors affecting the variation of R/(n10)2. The values of Rhom/(n10)2 and 1/[1 + (bΔωDωC)2] are displayed as functions of temperature for B = 10 and B = 1.

Fig. 8
Fig. 8

Normalized reflectivity R/(nCH)2 as a function of temperature for DFWM excitation of a two-level transition with J = 15.5 [e.g., the R1dc(15) line]. For each of the curves shown, Ipump is constant and independent of temperature; Ipump = 4 Isat at 4000 K, and Ipump = Isat at 1000 K. The probe laser intensity is given by Ipr = 0.25 Ipump.

Fig. 9
Fig. 9

Normalized reflectivity R/(nCH)2 as a function of temperature for DFWM excitation of a two-level transition with J = 10.5 [e.g., the R1dc(10) line]. For each of the curves shown, Ipump is constant and independent of temperature; Ipump = 4 Isat at 4000 K, and Ipump = Isat at 1000 K. The probe laser intensity is given by Ipr = 0.25 Ipump.

Fig. 10
Fig. 10

Normalized reflectivity R/(nCH)2 as a function of temperature for DFWM excitation of a two-level transition with J = 5.5 [e.g., the R1dc(5) line]. For each of the curves shown, Ipump is constant and independent of temperature; Ipump = 4 Isat at 4000 K, and Ipump = Isat at 1000 K. The probe laser intensity is given by Ipr = 0.25 Ipump.

Fig. 11
Fig. 11

CH concentration profiles measured by DFWM in a diamond-forming plasma. Filled circles are the data measured by Green et al.,21 and open circles are the same data corrected for the variation in ΔωCωD with Eq. (1). The temperature profile measured by Green et al.21 is also shown.

Tables (2)

Tables Icon

Table 1 Parameters for Calculations of the Effect of Temperature Changes on the Degenerate Four-Wave Mixing Signal for the R1dc(15) Transition of the CH Radicala

Tables Icon

Table 2 Parameters for calculations of the Effect of Temperature Changes on the Degenerate Four-Wave Mixing Signal for the Q1(8) Transition of the OH Radicala

Equations (19)

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R = R hom 1 + ( b Δ ω D / Δ ω C ) 2 .
ρ 11 ( z , t ) t = i ћ ( V 12 ρ 21 ρ 12 V 21 ) + Γ 21 ρ 22 ,
ρ 21 ( z , t ) t = ρ 21 ( i ω 21 + γ 21 ) i ћ V 21 ( ρ 11 ρ 22 ) ,
V 21 = μ 21 · E ( z , t ) = μ 21 [ E 1 ( z , t ) + E 2 ( z , t ) + E 3 ( z , t ) ] ,
E n ( z , t ) = ½ A n ( t ) exp [ i ( k n z cos θ n ω n t ) ] + c . c . , n = 1 , 2 , 3 ,
α 21 ( z , t ) t = α 21 γ 21 β 21 ( ω 1 ω 21 ) ( ρ 11 ρ 22 ) W ( z , t ) ,
β 21 ( z , t ) t = β 21 γ 21 α 21 ( ω 1 ω 21 ) + ( ρ 11 ρ 22 ) U ( z , t ) ,
ρ 11 ( z , t ) t = 2 α 21 W ( z , t ) 2 β 21 U ( z , t ) + ρ 22 Γ 21 ,
U ( z , t ) = Ω 1 ( t ) cos ( Φ 1 z ) + Ω 2 ( t ) { cos ( Φ 2 z ) × cos [ ( ω 1 ω 2 ) t ] sin ( Φ 2 z ) sin [ ( ω 1 ω 2 ) t ] } + Ω 3 ( t ) { cos ( Φ 3 z ) cos [ ( ω 1 ω 3 ) t ] sin ( Φ 3 z ) sin [ ( ω 1 ω 3 ) t ] } ,
W ( z , t ) = Ω 1 ( t ) sin ( Φ 1 z ) + Ω 2 ( t ) { cos ( Φ 2 z ) × sin [ ( ω 1 ω 2 ) t ] sin ( Φ 2 z ) cos [ ( ω 1 ω 2 ) t ] } + Ω 3 ( t ) { cos ( Φ 3 z ) sin [ ( ω 1 ω 3 ) t ] + sin ( Φ 3 z ) cos [ ( ω 1 ω 3 ) t ] } .
Ω n ( t ) = μ 21 A n ( t ) 2 ћ
P ( z , t ) = μ 21 [ ρ 12 ( z , t ) + ρ 21 ( z , t ) ] = μ 21 [ σ 12 exp ( + i ω 1 t ) + σ 21 exp ( i ω 1 t ) ] ,
P ( z , t ) = P 4 ( z , t ) + P other ( z , t ) .
P 4 ( z , t ) = P 40 ( t ) exp [ + i ( k 4 z ω 4 t ) ] .
S 4 ( ω L ) = laser pulse { [ vel grps A 4 r ( t ) ] 2 + [ vel grps A 4 i ( t ) ] 2 } d t .
R hom = I sig I pr = α 0 2 L 2 1 1 + ( Δ x ) 2 4 ( I pump / I sat ) 2 [ 1 + 4 ( I pump / I sat ) ] 3 ,
I sat = 0 c ћ 2 γ 21 Γ 21 2 μ 21 2 ,
R = R hom 1 + ( b Δ ω D / Δ ω C ) 2 ,
b = c 1 exp ( c 2 β pump ) + c 3 exp ( c 4 β pr ) ,

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