The two-photon resonances of atomic hydrogen (λ = 2×205.1 nm), atomic nitrogen (λ = 2×206.6 nm) and atomic oxygen (λ = 2×225.6 nm) are investigated together with two selected transitions in krypton (λ = 2×204.2 nm) and xenon (λ = 2×225.5 nm). The natural lifetimes of the excited states, quenching coefficients for the most important collisions partners, and the relevant ratios of the two-photon excitation cross sections are measured. These data can be applied to provide a calibration for two-photon laser-induced fluorescence measurements based on comparisons with spectrally neighbouring noble gas resonances.

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Absolute calibration of atomic density measurements by laser-induced fluorescence spectroscopy with two-photon excitation

The validity of the actinometry method applied to H-atom mole fraction measurements has been analyzed. First, a theoretical approach allowed us to determine boundary conditions for which the validity of actinometry may be critical. For these specific conditions, corresponding to an upper limit of electron temperature of 20 000 K and a lower limit of H-atom mole fraction of 2%–4%, spatial distributions of the ground state H-atom relative densities provided either by two photon allowed transition or by optical emission spectroscopy (OES) were compared and seen to be proportional. This proves that the H atoms excited in the level of quantum number n=3 (level used for OES experiments) are produced directly from the ground electronic state during collisions with electrons. Actinometry can then be applied under these experimental conditions. Second, the emission intensity ratio of two lines issued from excited states of argon was demonstrated to be indirectly related to the “electron temperature” of the hot ele...

Validation of actinometry for estimating relative hydrogen atom densities and electron energy evolution in plasma assisted diamond deposition reactors

QED theory of the spectral line profile and its applications to atoms and ions

We study the two-photon process for the transitions ns → 1s and nd → 1s in hydrogen up to large n .F orn ≤ 20 we provide simple analytic fitting formulae to describe the non-resonant part of the two-photon emission profiles. Combining these with the analytic form of the cascade-term yields a simple and accurate description of the full two-photon decay spectrum, which only involves a sum over a few intermediate states. We demonstrate that the cascade term naturally leads to a nearly Lorentzian shape of the two-photon profiles in the vicinity of the resonances. However, due to quantum-electrodynamical corrections, the two-photon emission spectra deviate significantly from the Lorentzian shape in the very distant wings of the resonances. We investigate up to which distance the two-photon profiles are close to a Lorentzian and discuss the role of the interference term. We then analyze how the deviation of the two-photon profiles from the Lorentzian shape affects the dynamics of cosmological hydrogen recombination. Since in this context the escape of photons from the Lyman-α resonance plays a crucial role, we concentrate on the two-photon corrections in the vicinity of the Lyman-α line. Our computations show that the changes in the ionization history due to the additional two-photon process from high shell (n > 2) likely do not reach the percent-level. For conservative assumptions we find a correction ∆Ne/Ne ∼− 0.4% at redshift z ∼ 1160. This is numerically similar to the result of another recent study; however, the physics leading to this conclusion is rather different. In particular, our calculations of the effective two-photon decay rates yield significantly different values, where the destructive interference of the resonant and non-resonant terms plays a crucial role in this context. We also show that the bulk of the corrections to the ionization history is only due to the 3s and 3d-states and that the higher states do not contribute significantly.

https://www.aanda.org/articles/aa/pdf/2008/12/aa7921-07.pdf

Two-photon transitions in hydrogen and cosmological recombination

Femtosecond, two-photon-absorption laser-induced fluorescence (fs-TALIF) is employed to measure space- and time-resolved distributions of atomic hydrogen and oxygen in moderate-pressure, non-equilibrium, nanosecond-duration pulsed-discharge plasmas. Temporally and spatially resolved hydrogen and oxygen TALIF images are obtained over a range of low-temperature plasmas in mixtures of helium and argon at 100 Torr total pressure. The high-peak-intensity, low-average-energy fs pulses combined with the increased spectral bandwidth compared to traditional ns-duration laser pulses provide a large number of photon pairs that are responsible for the two-photon excitation, which results in an enhanced TALIF signal. Krypton and xenon TALIF are used for quantitative calibration of the hydrogen and oxygen concentrations, respectively, with similar excitation schemes being employed. This enables 2D collection of atomic-hydrogen and -oxygen TALIF signals with absolute number densities ranging from 2 × 1012 cm−3 to 6 × 1015 cm−3 and 1 × 1013 cm−3 to 3 × 1016 cm−3, respectively. These 2D images are the first application of TALIF imaging in moderate-pressure plasma discharges. 1D self-consistent modeling predictions show agreement with experimental results within the estimated experimental error of 25%. The present results can be used to further the development of higher fidelity kinetic models while quantifying plasma-source characteristics.

https://iopscience.iop.org/article/10.1088/1361-6463/50/1/015204/pdf

Femtosecond, two-photon-absorption, laser-induced-fluorescence (fs-TALIF) imaging of atomic hydrogen and oxygen in non-equilibrium plasmas

Two-photon decay of hydrogenic atoms

Within the framework of nonrelativistic quantum mechanics, the analysis of the two-photon absorption by atomic hydrogen is generalized to the case of two incident beams with arbitrary direction and polarization (including circular polarization). In the dipole approximation, the second-order matrix elements responsible for two-photon absorption are transformed into a finite sum consisting of the product of a radial part and an angular part. Exact calculation of the angular part predicts that, for the s–s transition only, transparency is obtained regardless of the frequencies of the two beams with perpendicular polarizations. In addition, circularly polarized light is found to be more efficient (up to a factor of 1.5) for the s–d two-photon transition. The radial parts of the matrix elements are accurately evaluated by using the Coulomb Green’s function technique and an implicit technique of Dalgarno and Lewis. Their calculation indicates that “zeros” exist in the two-photon absorption spectrum, thereby predicting that absorption is not possible at certain frequencies. It should be noted that in the calculated spectrum, near or at resonance points, the linewidths of the intermediate levels must be included in order to obtain accurate results.

J. H. Tung

Papers

Two-photon decay of hydrogenic atoms

Two-Photon absorption of atomic hydrogen from two light beams