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Journal of Chongqing University of Posts and Telecommunications

Calculation of intensity for transitions within 4f~N configuration of rare-earth ions in crystals

Chang‐Kui Duan

Published Jan 1, 2005• 1 citation
OpenAlex

Abstract

Firstly,the crystal-field model is reviewedwith emphasis on the energy-splitting and the lift of parity-forbidden rule for d-d or f-f one-photon ED transition caused by it.Then based on our work the progressof transition intensity calculations for one-photon,two-photon transitions and electronic Raman scattering within the 4f~(N) configuration of rare earth ions are commented on and some suggestions on further directions in this field are proposed.

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Pavel A Apanasevich, R. I. Gintoft, V. S. Korol'kov +2 more

Abstract Theoretical and experimental investigations are made of two‐photon absorption spectra of trivalent rare‐earth ions in crystals. Effective cross‐sections, selection rules, and relative intensities of the components are found. The most intensive two‐photon transitions are established. Two‐photon excitation spectra of luminescence of Er3+ and Ho3+ ions in CaF2 are obtained and effective excitation cross‐sections are measured using a tunable dye laser (715 to 850 nm). It is shown that the spectra have a peculiar structure which differs considerably from that of the one‐photon absorption spectra. The experimental results agree with theory. It is established that one of the levels in Ho3+ is the level 5G6 rather than 3K7 usually assumed.

physica status solidi (b)•Aug 1, 1973•41 citations
Firstly,the crystal-field model is reviewedwith emphasis on the energy-splitting and the lift of parity-forbidden rule for d-d or f-f one-photon ED transition caused by it.Then based on our work the progressof transition intensity calculations for one-photon,two-photon transitions and electronic Raman scattering within the 4f~(N) configuration of rare earth ions are commented on and some suggestions on further directions in this field are proposed.
Rare-earth ions play an important role in modern technology as optically active elements in solid-state luminescent materials. In many of these materials, interactions between the electronic band states of the host crystal and the rare-earth ion's localized 4f N and 4f N−1 5d states influence the material's optical properties. The importance of these interactions is discussed for material applications in photon-gated hole burning, quantum information and phosphors. Material dependent trends in the relative binding energies of the 4f N states and the host bands have been observed and are summarized. An empirical model for the ion dependence of the 4f electron binding energies is formulated in terms of atomic number and compared with previous models. These models are extended to describe the 4f N−1 5d states with one additional parameter. Improved estimates for the free-ion ionization potentials used in the model are also presented and discussed.
The absorption of a single photon by the simultaneous excitation of two rare-earth ions was first reported by Varsanyi and Dieke in 1961.1 D. L. Dexter explained this unusual observation by including the electron-electron interactions (that also give rise to energy transfer) between the rare earth ions with perturbation theory.2 In the 70's Dexter became interested in electronic-vibrational coupling. A theory of two-center optical transitions was developed for a rare-earth ion weakly coupled to a high energy, internal vibrational mode of a near-lying ion.3 Using theoretical techniques that had been developed for rare-earth ion pairs, intensities and selection rules could be determined.
Symmetry adaptation techniques are applied to the determination of the intensity of two-photon absorption transitions, between Stark levels of configurations with opposite parities, for transition ions in finite symmetry environments. The equivalence between third-order mechanisms and second- plus first-order mechanisms is clearly established. A compact formula is derived for the intensity of a two-photon transition between two levels with well-defined symmetries. A set of (selection) rules which controls the number of intensity parameters for inter-configurational transitions is given. The formalism is illustrated with the case of an ion with 4f configuration in tetragonal symmetry.
A theoretical analysis of the lowest zero-phonon 4f\ensuremath{\rightarrow}5d two-photon absorption cross section in CaF2{\mathrm{CaF}}_{2}CaF2​:Ce3+{\mathrm{Ce}}^{3+}Ce3+ is presented. The transition is parity allowed because of an interaction of the rare-earth ion with the odd-parity components of the crystal field. This interaction takes two forms. The static contribution serves to mix the 4f and 5d orbitals, while a dynamic term couples the rare-earth orbitals to the nearby ligand states. A comparison of the predicted polarization anisotropy to the experimentally measured value allows an estimate of the relative strengths of the static and dynamic terms. The theoretical estimates of both the polarization anisotropy and the absolute magnitude of the cross section compare well with the experimental results.
Abstract Theoretical and experimental investigations are made of two‐photon absorption spectra of trivalent rare‐earth ions in crystals. Effective cross‐sections, selection rules, and relative intensities of the components are found. The most intensive two‐photon transitions are established. Two‐photon excitation spectra of luminescence of Er3+ and Ho3+ ions in CaF2 are obtained and effective excitation cross‐sections are measured using a tunable dye laser (715 to 850 nm). It is shown that the spectra have a peculiar structure which differs considerably from that of the one‐photon absorption spectra. The experimental results agree with theory. It is established that one of the levels in Ho3+ is the level 5G6 rather than 3K7 usually assumed.