1997
DOI: 10.1088/0953-4075/30/3/008
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Saturated FDFWM lineshapes and intensities: theory and application to quantitative measurements in flames

Abstract: The present paper deals with a three-level model of interaction with three crosspolarized and co-propagating fields having the same frequency. The two pump waves have arbitrary intensities and the third one (the probe wave) is assumed to be non-saturating. Using the radiative renormalization method, density matrix equations are solved analytically. The forward degenerate four-wave mixing (FDFWM) signal is calculated under thermodynamic conditions where collisional and Doppler broadenings are comparable. The ca… Show more

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Cited by 31 publications
(10 citation statements)
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“…This value is approximately a factor of 60 larger than the line center saturation intensity determined by Williams et al 32 of 0.32 MW/cm 2 for the Q 1 (4) transition of CH excited in the A 2 ⌬ -X 2 ⌸ ͑0,0͒ band in an atmospheric pressure flame. For OH a similar value was obtained by Brown et al 33 for the R 1 (9) transition (I sat ϭ0.72 MW/cm 2 ), whereas Attal et al 2 experimentally determined an effective saturation intensity of 1.8 MW/cm 2 for the Q 1 (6.5) line ͑the line strength ratio, Q 1 :R 1 , for these two branches is ϳ1.5͒, approximately a factor of 10 smaller than our value. In all cited experiments ns-laser pulses were used.…”
Section: A Saturation Of the Pumped Transitionsupporting
confidence: 79%
“…This value is approximately a factor of 60 larger than the line center saturation intensity determined by Williams et al 32 of 0.32 MW/cm 2 for the Q 1 (4) transition of CH excited in the A 2 ⌬ -X 2 ⌸ ͑0,0͒ band in an atmospheric pressure flame. For OH a similar value was obtained by Brown et al 33 for the R 1 (9) transition (I sat ϭ0.72 MW/cm 2 ), whereas Attal et al 2 experimentally determined an effective saturation intensity of 1.8 MW/cm 2 for the Q 1 (6.5) line ͑the line strength ratio, Q 1 :R 1 , for these two branches is ϳ1.5͒, approximately a factor of 10 smaller than our value. In all cited experiments ns-laser pulses were used.…”
Section: A Saturation Of the Pumped Transitionsupporting
confidence: 79%
“…[3,4,6] Most theoretical studies concerning DFWM assume a monochromatic laser and isolated transitions. [4,16,17] However, a molecular spectrum is often much more complicated, with several closely spaced transitions 'merging' into one absorption line, and these situations are harder to simulate. [9] There have been studies of this theoretical problem of closely spaced absorption lines in DFWM; [18] however, they usually assume the phase conjugate geometry, using UV lasers, and requiring large direct numerical simulation computations.…”
Section: Simulationsmentioning
confidence: 99%
“…Attal-Tretout and co-workers who used a non-perturbative approach to treat pump saturation and atomic motion effects in the FPG which led to modification of the signal lineshapes [60,61]. Their analytical result however was found to work only for unsaturating probes and provided the pumps were not strongly saturating.…”
Section: Analysis Of Dfwm Signals: Practical Considerationsmentioning
confidence: 99%