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Physical Review

Two-Photon Processes in Complex Atoms

John D. Axe

Published Oct 5, 1964• 180 citations
Publisher

Abstract

The off-diagonal matrix elements of the polarizability operator when operating within an ${l}^{N}$ configuration of a complex atom can be approximately written in simple tensor-operator form. The resulting expressions are discussed in terms of two-photon absorption and the recently observed electronic Raman scattering in the trivalent rare-earth ions.

DOI
10.1103/physrev.136.a42

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The Journal of Chemical Physics•Aug 15, 1988•83 citations
The off-diagonal matrix elements of the polarizability operator when operating within an lN{l}^{N}lN configuration of a complex atom can be approximately written in simple tensor-operator form. The resulting expressions are discussed in terms of two-photon absorption and the recently observed electronic Raman scattering in the trivalent rare-earth ions.
To study the role of stepwise and relaxation processes under effective excitation of anti-Stokes luminescence of rare-earth (RE) ions in crystals the time-shifted pulse method is used. It is shown that direct comparison of measured single- and two-photon luminescence excitation spectra often enables one to make immediate conclusions on the position and classification of electron levels of RE ions. The Tb3+ and Eu3− level structures (crystal CaF2) in the near ultraviolet are considered as an example. The peculiarities connected with the polarization characteristics of the two-photon absorption of radiation by the trivalent RE ions in a crystal matrix are discussed. To obtain the two-photon spectra a frequency-tunable organic dye solution laser (ODSL) is used.
We have calculated the cross section for Raman scattering of light from a hydrogenic atom, for a wide range of photon energies. The calculation assumes the photon encounters the atom in its ground state and excites it to the 2s2s2s state. Since various contributions to the matrix element may be isolated in the computation, the calculation allows one to obtain a notion of the relative importance of various classes of intermediate states in a given frequency range. We also point out that the Raman efficiency SSS may be expressed in terms of the derivative of the electronic polarizability tensor with respect to a parameter that measures the degree of excitation of the atom. Thus, the formal expression for SSS assumes an appearance identical to the expression encountered in the phenomenological theory of the first-order Raman effect in solids.
Quantitative calculations show that numerous spin-forbidden linear optical transitions observed in trivalent rare earth ions acquire a major fraction of their intensity from hitherto neglected contributions involving spin–orbit linkages within excited configurations. Motivated by the importance of analogous linkages previously demonstrated in two-photon absorption, we derive a general expression applicable for all lN→lN transitions which can be incorporated into a revised Judd–Ofelt analysis of observed intensities. Presenting this revised analysis of observed linear absorption intensities for Gd3+ and Eu3+, we show that the new contribution is often comparable to standard contributions. With substantial modification of previously fitted phenomenological parameters, an improved fit to observed intensities is achieved, suggesting that reanalysis of linear intensity data for all trivalent rare earths is warranted.