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Journal de physique

Three-photon absorption : selection rules and line intensities

G. Grynberg

Published Jan 1, 1979• 10 citations
Publisher

Abstract

We present in this paper several theoretical results about three-photon absorption using an expansion of the transition operator on an irreducible tensorial set basis. We deduce the selection fules and some results about the calculation of the line intensities.
DOI
10.1051/jphys:019790040010096500

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The expression for the absorption coefficient in two-photon resonance transitions is deduced under general conditions. No particular restrictions are imposed on the level system or on the frequencies and intensities of the fields. The following cases are considered: (i) a two-level system (with and without singularities) irradiated by a single wave and (ii) a three-level system irradiated by two waves. Some theoretical and experimental disagreements reported by authors of previous papers are examined and clarified by the present theory.
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Two-photon transitions have provided the basis for numerous useful nonlinear interactions with radiation. In this paper we calculate the absorption and coupling coefficients for one-, two-, and three-wave mixing in two-photon homogeneously broadened media. The resulting field equations form the basis for understanding saturation spectroscopy, phase conjugation,1 and single-mode instabilities2 in lasers and optical bistability in two-photon media. We assume that the wave frequencies are not resonant with any intermediate state j and that the probe and conjugate waves cannot saturate the two-photon transition. This allows us to use the two-photon two-level model and to transfer much of our knowledge of the one-photon two-level systems to the two-photon case. Two major differences occur between the two models. First, dynamic Stark shifts of the active levels play an important role in generating asymmetric spectra and nonzero dispersion (≃ω s T1) at line center. Second, high pump intensities do not bleach the absorption coefficient at the Rabi sidebands.
We report in this paper the principle of the calculation of the hyperfine components of a two-photon absorption line and we compare the results of the calculation with some of our expérimental results. In the first part of the paper, the two-photon transition operator is expanded on a tensorial irreductible set basis. That operator is generally the sum of two operators, one scalar and the other one quadrupolar. We deduce from it the selection rules for two-photon absorption and the formulae which permit one to calculate the intensities of the hyperfine components of a two-photon absorption line. We also report the density matrix in the excited state obtained after the two-photon excitation process, which permits one to calculate the fluorescence lines. At last we present the atomic quantities involved in the collision broadening of a two-photon absorption line. In the second part, we present the experimental hyperfine spectra obtained on the neon 21 atom for the transitions between the 3s[3/2] 2 metastable level and the 4d'[5/2] 2, 4d'[3/2] 2 and 4d[3/2] 2 excited levels. We show that the expérimental ratios between the scalar and the quadrupolar parts are very different from one transition to another. At last we compare these ratios with theoretical values obtained using the formulae of the first part. We find a good agreement between expérimental and theoretical values.