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Direct measurement of two-photon absorption in xenon and its impact on TALIF-measured atomic oxygen densities

Direct measurement of two-photon absorption in xenon confirms that the corresponding cross-section is twice smaller than what had been admitted via indirect estimates and suggests a downward revision of a large proportion of TALIF-measured atomic oxygen densities in low-temperature plasmas.

When two-photon absorption laser induced fluorescence (TALIF) is used to detect atomic species, or measure their density in low-temperature plasmas, one usually calibrates the process by a comparison with a similar fluorescence measurement carried out in a noble gas of known density, with a similar level scheme. One can then deduce the unknown density from the ratio of the measured fluorescence intensities, provided that the ratio of the excitation cross-sections can be known.
As a matter of fact, the density of atomic oxygen, in low-temperature plasmas or in flames, has been routinely determined by TALIF measurements following two-photon excitation of the 3p3P term at the wavelength 226 nm, with a calibration by similar measurements carried out in xenon, at similar wavelengths that make it possible to excite one of the 7p or 6p’ levels (the latter with a fine-structure excited core). However, while the two-photon excitation cross-section of oxygen has been known with reasonable accuracy (both experimentally and theoretically), the cross-section of xenon, in contradistinction, had been known only through an imprecise measurement of its ratio to that of oxygen. Previous experiments at LPP had already suggested that this “value of the ratio (...) may overestimate the O atom density by up to a factor of two” [1].
This has just been confirmed by Cyril Drag, Florian Marmuse et Christophe Blondel [2], who measured the two-photon excitation cross-section of xenon, not using the fluorescence intensity but measuring the absorption rate of the exciting light, after it has passed through a 51 cm-long xenon cell. This is a way to get rid of the unknown de-excitation branching ratios and fluorescence collection efficiency. On the other hand, inverting the observed absorption ratio into an experimental cross-section must rely on quantitative modelling of the absorption process, all along the absorption cell. Having a single-mode pulsed laser, i.e. with no mode beating, has definitely been an advantage for making the model reliable. A new analytical formula for the increment of the absorption rate has been proposed, as a function of the absorption length. After integration over the whole spectral width of the resonance (in angular frequency units), the cross-section appears to be 1,36+0,46-0,34×10-43 and 1,88+0,75-0,54×10-43 m4, for the 6p’[3/2]2 and 6p’[1/2]0 levels, respectively. The non-intuitive result of a larger cross-section for the lower final angular momentum, i.e. for the 6p’[1/2]0 level, suggests that it could be profitably used on a more current basis.

The reason why the cross-section is larger towards the final J’=0 level than towards the J’=2 one.
The two-photon excitation amplitude, either at the wavelength 224.3 or 222.6 nm, depending on whether one aims at the 6p’[3/2]2 or 6p’[1/2]0 level (these photons are symbolized by the wavy arrows), is the sum of all amplitudes built along paths that lead to the final level, through two successive virtual excitations, with a J=1 as the intermediate state (linear arrows). As the final levels considered correspond to identical 6p’ orbital states, they differ essentially by angular coefficients only. Whereas angular-determined amplitudes coming from the lower intermediate level 6s’[1/2]1 are of the same order of magnitude (and even slightly in favour of the J’=2 state), the amplitudes from the second intermediate level 5d’[3/2]1, appear very unbalanced, with a very weak dipole element to the 6p’[3/2]2 final level. This is a pure angular-momentum-algebra effect. It may thus be by a pure Racah-algebra whim (to be confirmed by examination of an infinity of other possible intermediate states) that the two-photon cross section finally appears larger for the 6p’[1/2]0 level than for the 6p’[3/2]2 one.

  1. Adriana Annušová, Daniil Marinov, Jean-Paul Booth, Nishant Sirse, Mário Lino da Silva, Bruno Lopez & Vasco Guerra, “Kinetics of highly vibrationally excited O2(X) molecules in inductively-coupled oxygen plasmas”, Plasma Sources Sci. Technol. 27 (2018) 045006
  2. Cyril Drag, Florian Marmuse & Christophe Blondel, “Measurement of the two-photon excitation cross-section of the 6p’[3/2]2 and 6p’[1/2]0 levels of Xe I at the wavelengths 224.3 and 222.6 nm”, Plasma Sources Sci. Technol. (2021) https://doi.org/10.1088/1361-6595/abfbeb

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