Abstract

We examine theoretically the degenerate four-wave mixing (DFWM) signal intensities and line shapes obtained with the forward phase-matched geometry in which all beams propagate in the same direction and compare the results to those of the phase-conjugate geometry with counterpropagating pump beams. To examine the forward phase-matched geometry, we modify a theoretical approach used previously to calculate phase-conjugate DFWM signal intensities. This theoretical approach, which involves numerical integration of the time-dependent density-matrix equations, is validated for the forward phase-matched geometry by comparison of our calculated line shapes to both a perturbative solution and to experimental data. This methodology is then used to compare the signal intensities and line shapes obtained with the forward phase-matched geometry and the phase-conjugate geometry in the perturbative (low laser power) and saturated (high laser power) regimes. In the perturbative regime the forward phase-matched signal exhibits less sensitivity to the Doppler linewidth. At pump laser intensities approximately equal to the saturation intensity the signal for the forward phase-matched geometry is stronger than that for the phase-conjugate geometry for primarily Doppler-broadened resonances, assuming the same probe volume for both geometries. These advantages warrant further investigations employing the forward phase-matched configuration for DFWM measurements of gas-phase species.

© 1998 Optical Society of America

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  1. B. Attal-Trétout, H. Bervas, J. P. Taran, S. Le Boiteux, P. Kelley, and T. K. Gustafson, “Saturated FDFWM lineshapes and intensities: theory and application to quantitative measurements in flames,” J. Phys. B 30, 497–522 (1997).
    [CrossRef]
  2. 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]
  3. T. A. Reichardt and R. P. Lucht, “Effect of Doppler broadening on quantitative concentration measurements with degenerate four-wave mixing spectroscopy,” J. Opt. Soc. Am. B 13, 1107–1119 (1996).
    [CrossRef]
  4. 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.
  5. A. R. Bogdan, Y. Prior, and N. Bloembergen, “Pressure-induced degenerate frequency resonance in four-wave light mixing,” Opt. Lett. 6, 82–83 (1981).
    [CrossRef] [PubMed]
  6. Y. Prior, A. R. Bogdan, M. Dagenais, and N. Bloembergen, “Pressure-induced extra resonances in four-wave mixing,” Phys. Rev. Lett. 46, 111–114 (1981).
    [CrossRef]
  7. Y. Prior and E. Yarkoni, “Sub-Doppler resolution in strongly saturated copropagating degenerate four-wave mixing,” Phys. Rev. A 28, 3689–3691 (1983).
    [CrossRef]
  8. G. M. Carter, “Excited-state dynamics and temporally resolved nonresonant nonlinear-optical processes in polydiacetylenes,” J. Opt. Soc. Am. B 4, 1018–1024 (1987).
    [CrossRef]
  9. W. Du, X. Zhang, K. Chen, Z. Lu, Y. Zheng, and J. Wu, “Multiple forward phase conjugate waves by degenerate four-wave mixing in Langmuir–Blodgett films with BOXCARS geometry,” Opt. Commun. 84, 205–207 (1991).
    [CrossRef]
  10. G. Meijer and D. W. Chandler, “Degenerate four-wave mixing on weak transitions in the gas phase using a tunable excimer laser,” Chem. Phys. Lett. 192, 1–4 (1992).
    [CrossRef]
  11. H. Bervas, B. Attal-Trétout, L. Labrunie, and S. Le Boiteux, “Four-wave mixing in OH: comparison between CARS and DFWM,” Nuovo Cimento D 14, 1043–1050 (1992).
    [CrossRef]
  12. H. Bervas, S. Le Boiteux, L. Labrunie, and B. Attal-Trétout, “Rotational line strengths in degenerate four wave mixing,” Mol. Phys. 79, 911–941 (1993).
    [CrossRef]
  13. G. N. Robertson, K. Kohse-Höinghaus, S. Le Boiteux, F. Aguerre, and B. Attal-Trétout, “Observation of strong field effects and rotational line coupling in DFWM processes resonant with 2Σ–2Π electronic system,” J. Quant. Spectrosc. Radiat. Transf. 55, 71–101 (1996).
    [CrossRef]
  14. K. Nyholm, M. Kaivola, and C. G. Aminoff, “Detection of C2 and temperature measurement in a flame by using degenerate four-wave mixing in a forward geometry,” Opt. Commun. 107, 406–410 (1994).
    [CrossRef]
  15. 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]
  16. 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]
  17. P. Ewart, P. G. R. Smith, and R. B. Williams, “Imaging of trace species distributions by degenerate four-wave mixing: diffraction effects, spatial resolution, and image referencing,” Appl. Opt. 36, 5959–5968 (1997).
    [CrossRef] [PubMed]
  18. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Gordon and Breach, Amsterdam, The Netherlands, 1996).
  19. R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
  20. K. Kohse-Höinghaus, “Laser techniques for the quantitative detection of reactive intermediates in combustion systems,” Prog. Energy Combust. Sci. 20, 203–279 (1994).
    [CrossRef]
  21. R. L. Farrow and D. J. Rakestraw, “Detection of trace molecular species using degenerate four-wave mixing,” Science 257, 1894–1900 (1992).
    [CrossRef] [PubMed]
  22. P. M. Danehy, “Population- and thermal-grating contributions to degenerate four-wave mixing,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1995).
  23. J. Nilsen and A. Yariv, “Nondegenerate four-wave mixing in a Doppler-broadened resonant medium,” J. Opt. Soc. Am. 71, 180–183 (1981).
    [CrossRef]
  24. 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]
  25. 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. Phys. (France) 42, 711–721 (1981).
    [CrossRef]
  26. M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. (France) 43, 57–65 (1982).
    [CrossRef]
  27. J. F. Lam and R. L. Abrams, “Theory of nonlinear optical coherences in resonant degenerate four-wave mixing,” Phys. Rev. A 26, 1539–1548 (1982).
    [CrossRef]
  28. G. Grynberg, M. Pinard, and P. Verkerk, “Saturation in degenerate four-wave mixing: theory for a two-level atom,” J. Phys. (France) 47, 617–630 (1986).
    [CrossRef]
  29. 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]
  30. 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: Photophys. Laser Chem. 57, 243–248 (1993).
    [CrossRef]
  31. 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]
  32. 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]

1997 (2)

B. Attal-Trétout, H. Bervas, J. P. Taran, S. Le Boiteux, P. Kelley, and T. K. Gustafson, “Saturated FDFWM lineshapes and intensities: theory and application to quantitative measurements in flames,” J. Phys. B 30, 497–522 (1997).
[CrossRef]

P. Ewart, P. G. R. Smith, and R. B. Williams, “Imaging of trace species distributions by degenerate four-wave mixing: diffraction effects, spatial resolution, and image referencing,” Appl. Opt. 36, 5959–5968 (1997).
[CrossRef] [PubMed]

1996 (2)

G. N. Robertson, K. Kohse-Höinghaus, S. Le Boiteux, F. Aguerre, and B. Attal-Trétout, “Observation of strong field effects and rotational line coupling in DFWM processes resonant with 2Σ–2Π electronic system,” J. Quant. Spectrosc. Radiat. Transf. 55, 71–101 (1996).
[CrossRef]

T. A. Reichardt and R. P. Lucht, “Effect of Doppler broadening on quantitative concentration measurements with degenerate four-wave mixing spectroscopy,” J. Opt. Soc. Am. B 13, 1107–1119 (1996).
[CrossRef]

1994 (4)

K. Nyholm, M. Kaivola, and C. G. Aminoff, “Detection of C2 and temperature measurement in a flame by using degenerate four-wave mixing in a forward geometry,” Opt. Commun. 107, 406–410 (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]

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]

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

H. Bervas, S. Le Boiteux, L. Labrunie, and B. Attal-Trétout, “Rotational line strengths in degenerate four wave mixing,” Mol. Phys. 79, 911–941 (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: Photophys. Laser Chem. 57, 243–248 (1993).
[CrossRef]

1992 (5)

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]

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]

G. Meijer and D. W. Chandler, “Degenerate four-wave mixing on weak transitions in the gas phase using a tunable excimer laser,” Chem. Phys. Lett. 192, 1–4 (1992).
[CrossRef]

H. Bervas, B. Attal-Trétout, L. Labrunie, and S. Le Boiteux, “Four-wave mixing in OH: comparison between CARS and DFWM,” Nuovo Cimento D 14, 1043–1050 (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]

1991 (1)

W. Du, X. Zhang, K. Chen, Z. Lu, Y. Zheng, and J. Wu, “Multiple forward phase conjugate waves by degenerate four-wave mixing in Langmuir–Blodgett films with BOXCARS geometry,” Opt. Commun. 84, 205–207 (1991).
[CrossRef]

1990 (1)

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]

1987 (1)

1986 (1)

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

1983 (1)

Y. Prior and E. Yarkoni, “Sub-Doppler resolution in strongly saturated copropagating degenerate four-wave mixing,” Phys. Rev. A 28, 3689–3691 (1983).
[CrossRef]

1982 (2)

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. (France) 43, 57–65 (1982).
[CrossRef]

J. F. Lam and R. L. Abrams, “Theory of nonlinear optical coherences in resonant degenerate four-wave mixing,” Phys. Rev. A 26, 1539–1548 (1982).
[CrossRef]

1981 (4)

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. Phys. (France) 42, 711–721 (1981).
[CrossRef]

A. R. Bogdan, Y. Prior, and N. Bloembergen, “Pressure-induced degenerate frequency resonance in four-wave light mixing,” Opt. Lett. 6, 82–83 (1981).
[CrossRef] [PubMed]

Y. Prior, A. R. Bogdan, M. Dagenais, and N. Bloembergen, “Pressure-induced extra resonances in four-wave mixing,” Phys. Rev. Lett. 46, 111–114 (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]

Abrams, R. L.

J. F. Lam and R. L. Abrams, “Theory of nonlinear optical coherences in resonant degenerate four-wave mixing,” Phys. Rev. A 26, 1539–1548 (1982).
[CrossRef]

Aguerre, F.

G. N. Robertson, K. Kohse-Höinghaus, S. Le Boiteux, F. Aguerre, and B. Attal-Trétout, “Observation of strong field effects and rotational line coupling in DFWM processes resonant with 2Σ–2Π electronic system,” J. Quant. Spectrosc. Radiat. Transf. 55, 71–101 (1996).
[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]

Aminoff, C. G.

K. Nyholm, M. Kaivola, and C. G. Aminoff, “Detection of C2 and temperature measurement in a flame by using degenerate four-wave mixing in a forward geometry,” Opt. Commun. 107, 406–410 (1994).
[CrossRef]

Attal-Trétout, B.

B. Attal-Trétout, H. Bervas, J. P. Taran, S. Le Boiteux, P. Kelley, and T. K. Gustafson, “Saturated FDFWM lineshapes and intensities: theory and application to quantitative measurements in flames,” J. Phys. B 30, 497–522 (1997).
[CrossRef]

G. N. Robertson, K. Kohse-Höinghaus, S. Le Boiteux, F. Aguerre, and B. Attal-Trétout, “Observation of strong field effects and rotational line coupling in DFWM processes resonant with 2Σ–2Π electronic system,” J. Quant. Spectrosc. Radiat. Transf. 55, 71–101 (1996).
[CrossRef]

H. Bervas, S. Le Boiteux, L. Labrunie, and B. Attal-Trétout, “Rotational line strengths in degenerate four wave mixing,” Mol. Phys. 79, 911–941 (1993).
[CrossRef]

H. Bervas, B. Attal-Trétout, L. Labrunie, and S. Le Boiteux, “Four-wave mixing in OH: comparison between CARS and DFWM,” Nuovo Cimento D 14, 1043–1050 (1992).
[CrossRef]

Bervas, H.

B. Attal-Trétout, H. Bervas, J. P. Taran, S. Le Boiteux, P. Kelley, and T. K. Gustafson, “Saturated FDFWM lineshapes and intensities: theory and application to quantitative measurements in flames,” J. Phys. B 30, 497–522 (1997).
[CrossRef]

H. Bervas, S. Le Boiteux, L. Labrunie, and B. Attal-Trétout, “Rotational line strengths in degenerate four wave mixing,” Mol. Phys. 79, 911–941 (1993).
[CrossRef]

H. Bervas, B. Attal-Trétout, L. Labrunie, and S. Le Boiteux, “Four-wave mixing in OH: comparison between CARS and DFWM,” Nuovo Cimento D 14, 1043–1050 (1992).
[CrossRef]

Bloch, D.

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. (France) 43, 57–65 (1982).
[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. Phys. (France) 42, 711–721 (1981).
[CrossRef]

Bloembergen, N.

A. R. Bogdan, Y. Prior, and N. Bloembergen, “Pressure-induced degenerate frequency resonance in four-wave light mixing,” Opt. Lett. 6, 82–83 (1981).
[CrossRef] [PubMed]

Y. Prior, A. R. Bogdan, M. Dagenais, and N. Bloembergen, “Pressure-induced extra resonances in four-wave mixing,” Phys. Rev. Lett. 46, 111–114 (1981).
[CrossRef]

Bogdan, A. R.

Y. Prior, A. R. Bogdan, M. Dagenais, and N. Bloembergen, “Pressure-induced extra resonances in four-wave mixing,” Phys. Rev. Lett. 46, 111–114 (1981).
[CrossRef]

A. R. Bogdan, Y. Prior, and N. Bloembergen, “Pressure-induced degenerate frequency resonance in four-wave light mixing,” Opt. Lett. 6, 82–83 (1981).
[CrossRef] [PubMed]

Carter, G. M.

Chandler, D. W.

G. Meijer and D. W. Chandler, “Degenerate four-wave mixing on weak transitions in the gas phase using a tunable excimer laser,” Chem. Phys. Lett. 192, 1–4 (1992).
[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]

Chen, K.

W. Du, X. Zhang, K. Chen, Z. Lu, Y. Zheng, and J. Wu, “Multiple forward phase conjugate waves by degenerate four-wave mixing in Langmuir–Blodgett films with BOXCARS geometry,” Opt. Commun. 84, 205–207 (1991).
[CrossRef]

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]

Dagenais, M.

Y. Prior, A. R. Bogdan, M. Dagenais, and N. Bloembergen, “Pressure-induced extra resonances in four-wave mixing,” Phys. Rev. Lett. 46, 111–114 (1981).
[CrossRef]

Danehy, P. M.

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: Photophys. Laser Chem. 57, 243–248 (1993).
[CrossRef]

Dreier, T.

Du, W.

W. Du, X. Zhang, K. Chen, Z. Lu, Y. Zheng, and J. Wu, “Multiple forward phase conjugate waves by degenerate four-wave mixing in Langmuir–Blodgett films with BOXCARS geometry,” Opt. Commun. 84, 205–207 (1991).
[CrossRef]

Ducloy, M.

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. (France) 43, 57–65 (1982).
[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. Phys. (France) 42, 711–721 (1981).
[CrossRef]

Ewart, P.

Farrow, R. L.

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: Photophys. Laser Chem. 57, 243–248 (1993).
[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]

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]

Fiechtner, G. J.

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: Photophys. Laser Chem. 57, 243–248 (1993).
[CrossRef]

Green, D. 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]

Grynberg, G.

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

Gustafson, T. K.

B. Attal-Trétout, H. Bervas, J. P. Taran, S. Le Boiteux, P. Kelley, and T. K. Gustafson, “Saturated FDFWM lineshapes and intensities: theory and application to quantitative measurements in flames,” J. Phys. B 30, 497–522 (1997).
[CrossRef]

Kaivola, M.

K. Nyholm, M. Kaivola, and C. G. Aminoff, “Detection of C2 and temperature measurement in a flame by using degenerate four-wave mixing in a forward geometry,” Opt. Commun. 107, 406–410 (1994).
[CrossRef]

Kelley, P.

B. Attal-Trétout, H. Bervas, J. P. Taran, S. Le Boiteux, P. Kelley, and T. K. Gustafson, “Saturated FDFWM lineshapes and intensities: theory and application to quantitative measurements in flames,” J. Phys. B 30, 497–522 (1997).
[CrossRef]

Kohse-Höinghaus, K.

G. N. Robertson, K. Kohse-Höinghaus, S. Le Boiteux, F. Aguerre, and B. Attal-Trétout, “Observation of strong field effects and rotational line coupling in DFWM processes resonant with 2Σ–2Π electronic system,” J. Quant. Spectrosc. Radiat. Transf. 55, 71–101 (1996).
[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]

Labrunie, L.

H. Bervas, S. Le Boiteux, L. Labrunie, and B. Attal-Trétout, “Rotational line strengths in degenerate four wave mixing,” Mol. Phys. 79, 911–941 (1993).
[CrossRef]

H. Bervas, B. Attal-Trétout, L. Labrunie, and S. Le Boiteux, “Four-wave mixing in OH: comparison between CARS and DFWM,” Nuovo Cimento D 14, 1043–1050 (1992).
[CrossRef]

Lam, J. F.

J. F. Lam and R. L. Abrams, “Theory of nonlinear optical coherences in resonant degenerate four-wave mixing,” Phys. Rev. A 26, 1539–1548 (1982).
[CrossRef]

Le Boiteux, S.

B. Attal-Trétout, H. Bervas, J. P. Taran, S. Le Boiteux, P. Kelley, and T. K. Gustafson, “Saturated FDFWM lineshapes and intensities: theory and application to quantitative measurements in flames,” J. Phys. B 30, 497–522 (1997).
[CrossRef]

G. N. Robertson, K. Kohse-Höinghaus, S. Le Boiteux, F. Aguerre, and B. Attal-Trétout, “Observation of strong field effects and rotational line coupling in DFWM processes resonant with 2Σ–2Π electronic system,” J. Quant. Spectrosc. Radiat. Transf. 55, 71–101 (1996).
[CrossRef]

H. Bervas, S. Le Boiteux, L. Labrunie, and B. Attal-Trétout, “Rotational line strengths in degenerate four wave mixing,” Mol. Phys. 79, 911–941 (1993).
[CrossRef]

H. Bervas, B. Attal-Trétout, L. Labrunie, and S. Le Boiteux, “Four-wave mixing in OH: comparison between CARS and DFWM,” Nuovo Cimento D 14, 1043–1050 (1992).
[CrossRef]

Linne, M. A.

Lu, Z.

W. Du, X. Zhang, K. Chen, Z. Lu, Y. Zheng, and J. Wu, “Multiple forward phase conjugate waves by degenerate four-wave mixing in Langmuir–Blodgett films with BOXCARS geometry,” Opt. Commun. 84, 205–207 (1991).
[CrossRef]

Lucht, R. P.

Meacher, D. R.

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]

Meijer, G.

G. Meijer and D. W. Chandler, “Degenerate four-wave mixing on weak transitions in the gas phase using a tunable excimer laser,” Chem. Phys. Lett. 192, 1–4 (1992).
[CrossRef]

Nilsen, J.

Nyholm, K.

K. Nyholm, M. Kaivola, and C. G. Aminoff, “Detection of C2 and temperature measurement in a flame by using degenerate four-wave mixing in a forward geometry,” Opt. Commun. 107, 406–410 (1994).
[CrossRef]

Pinard, M.

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

Prior, Y.

Y. Prior and E. Yarkoni, “Sub-Doppler resolution in strongly saturated copropagating degenerate four-wave mixing,” Phys. Rev. A 28, 3689–3691 (1983).
[CrossRef]

A. R. Bogdan, Y. Prior, and N. Bloembergen, “Pressure-induced degenerate frequency resonance in four-wave light mixing,” Opt. Lett. 6, 82–83 (1981).
[CrossRef] [PubMed]

Y. Prior, A. R. Bogdan, M. Dagenais, and N. Bloembergen, “Pressure-induced extra resonances in four-wave mixing,” Phys. Rev. Lett. 46, 111–114 (1981).
[CrossRef]

Rahn, L. A.

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.

Reichardt, T. A.

Robertson, G. N.

G. N. Robertson, K. Kohse-Höinghaus, S. Le Boiteux, F. Aguerre, and B. Attal-Trétout, “Observation of strong field effects and rotational line coupling in DFWM processes resonant with 2Σ–2Π electronic system,” J. Quant. Spectrosc. Radiat. Transf. 55, 71–101 (1996).
[CrossRef]

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]

Smith, P. G. R.

Taran, J. P.

B. Attal-Trétout, H. Bervas, J. P. Taran, S. Le Boiteux, P. Kelley, and T. K. Gustafson, “Saturated FDFWM lineshapes and intensities: theory and application to quantitative measurements in flames,” J. Phys. B 30, 497–522 (1997).
[CrossRef]

Verkerk, P.

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

Williams, R. B.

Williams, S.

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, 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]

Wu, J.

W. Du, X. Zhang, K. Chen, Z. Lu, Y. Zheng, and J. Wu, “Multiple forward phase conjugate waves by degenerate four-wave mixing in Langmuir–Blodgett films with BOXCARS geometry,” Opt. Commun. 84, 205–207 (1991).
[CrossRef]

Yariv, A.

Yarkoni, E.

Y. Prior and E. Yarkoni, “Sub-Doppler resolution in strongly saturated copropagating degenerate four-wave mixing,” Phys. Rev. A 28, 3689–3691 (1983).
[CrossRef]

Zare, R. N.

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, 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]

Zhang, X.

W. Du, X. Zhang, K. Chen, Z. Lu, Y. Zheng, and J. Wu, “Multiple forward phase conjugate waves by degenerate four-wave mixing in Langmuir–Blodgett films with BOXCARS geometry,” Opt. Commun. 84, 205–207 (1991).
[CrossRef]

Zheng, Y.

W. Du, X. Zhang, K. Chen, Z. Lu, Y. Zheng, and J. Wu, “Multiple forward phase conjugate waves by degenerate four-wave mixing in Langmuir–Blodgett films with BOXCARS geometry,” Opt. Commun. 84, 205–207 (1991).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B: Photophys. Laser Chem. (1)

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: Photophys. Laser Chem. 57, 243–248 (1993).
[CrossRef]

Chem. Phys. Lett. (1)

G. Meijer and D. W. Chandler, “Degenerate four-wave mixing on weak transitions in the gas phase using a tunable excimer laser,” Chem. Phys. Lett. 192, 1–4 (1992).
[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. (1)

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]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (4)

J. Phys. (France) (3)

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. Phys. (France) 42, 711–721 (1981).
[CrossRef]

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. (France) 43, 57–65 (1982).
[CrossRef]

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

J. Phys. B (1)

B. Attal-Trétout, H. Bervas, J. P. Taran, S. Le Boiteux, P. Kelley, and T. K. Gustafson, “Saturated FDFWM lineshapes and intensities: theory and application to quantitative measurements in flames,” J. Phys. B 30, 497–522 (1997).
[CrossRef]

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

G. N. Robertson, K. Kohse-Höinghaus, S. Le Boiteux, F. Aguerre, and B. Attal-Trétout, “Observation of strong field effects and rotational line coupling in DFWM processes resonant with 2Σ–2Π electronic system,” J. Quant. Spectrosc. Radiat. Transf. 55, 71–101 (1996).
[CrossRef]

Mol. Phys. (1)

H. Bervas, S. Le Boiteux, L. Labrunie, and B. Attal-Trétout, “Rotational line strengths in degenerate four wave mixing,” Mol. Phys. 79, 911–941 (1993).
[CrossRef]

Nuovo Cimento D (1)

H. Bervas, B. Attal-Trétout, L. Labrunie, and S. Le Boiteux, “Four-wave mixing in OH: comparison between CARS and DFWM,” Nuovo Cimento D 14, 1043–1050 (1992).
[CrossRef]

Opt. Commun. (2)

K. Nyholm, M. Kaivola, and C. G. Aminoff, “Detection of C2 and temperature measurement in a flame by using degenerate four-wave mixing in a forward geometry,” Opt. Commun. 107, 406–410 (1994).
[CrossRef]

W. Du, X. Zhang, K. Chen, Z. Lu, Y. Zheng, and J. Wu, “Multiple forward phase conjugate waves by degenerate four-wave mixing in Langmuir–Blodgett films with BOXCARS geometry,” Opt. Commun. 84, 205–207 (1991).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (3)

Y. Prior and E. Yarkoni, “Sub-Doppler resolution in strongly saturated copropagating degenerate four-wave mixing,” Phys. Rev. A 28, 3689–3691 (1983).
[CrossRef]

J. F. Lam and R. L. Abrams, “Theory of nonlinear optical coherences in resonant degenerate four-wave mixing,” Phys. Rev. A 26, 1539–1548 (1982).
[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]

Phys. Rev. Lett. (1)

Y. Prior, A. R. Bogdan, M. Dagenais, and N. Bloembergen, “Pressure-induced extra resonances in four-wave mixing,” Phys. Rev. Lett. 46, 111–114 (1981).
[CrossRef]

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 (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]

Other (5)

P. M. Danehy, “Population- and thermal-grating contributions to degenerate four-wave mixing,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1995).

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.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Gordon and Breach, Amsterdam, The Netherlands, 1996).

R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).

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Figures (7)

Fig. 1
Fig. 1

Illustrations of (a) the phase-conjugate geometry and (b) the forward phase-matched geometry.

Fig. 2
Fig. 2

Comparison between perturbation theory and the DNI calculations for the forward phase-matched geometry. For this line-shape comparison, Δν˜C=0.05 cm-1 and Δν˜D=0.1 cm-1. These conditions correspond to excitation of a trace concentration of NO in a 100-Torr bath of He at 226 nm and room temperature. For the DNI calculations the pump laser intensity was set equal to 0.02Isat. The laser detuning is given as ν˜L-νν˜0, where ν˜L=ωL/2πc is the laser frequency (cm-1) and ν˜0=ω0/2πc is the resonance frequency (cm-1). Each line shape is normalized to a maximum value of unity.

Fig. 3
Fig. 3

Comparison between forward phase-matched experimental data and DNI calculations for the O12(2) line of NO. The collisional width Δν˜C was 0.025 cm-1, and the Doppler width Δν˜D was 0.1 cm-1.

Fig. 4
Fig. 4

Saturation curves for the phase-conjugate geometry. The line-center reflectivity is plotted versus normalized pump intensity. The results are normalized so that the reflectivity is unity for a homogeneously broadened resonance with Ipump/Isat=0.02.

Fig. 5
Fig. 5

Saturation curves for the forward phase-matched geometry. The line-center reflectivity is plotted versus normalized pump intensity. The results are normalized so that the reflectivity is unity for a homogeneously broadened resonance with Ipump/Isat=0.02.

Fig. 6
Fig. 6

Variation of the ratio of the phase-conjugate line-center reflectivity to the forward phase-matched line-center reflectivity as a function of laser power.

Fig. 7
Fig. 7

Effect of saturation on a resonance that is both collision and Doppler broadened. The line shapes are normalized to a maximum value of unity. For the figures on the left, ΔωD=ΔωC, while for the figures on the right, ΔωD=2ΔωC.

Equations (7)

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En(z, t)=12 An(t)exp[+i(knr-ωnt)]+c.c.,
n=1, 2, 3.
knr=kn(cos θn)z,
θ1=2 sin-1d2l,
θ2=2 sin-1h2l,
l=(h/2)2+(d/2)2+flens2.
θ3=2 sin-1d2+h22l.

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