Radiative, nonradiative, and mixed-decay transitions of rare-earth ions in dielectric media

Abstract

We present and discuss in a comprehensive, deductive, and simplified manner, issues of nonradiative transitions involvement in fluorescence of ions embedded in dielectric solid matrices. The semiclassical approach is favored over a full quantum description, and empiric quantities are introduced from the start. One issue is nonradiative single-phonon transitions when the energy gap between the adjacent electronic ion states is smaller than the cutoff matrix phonon energy. Another issue is transitions in a complex energy scheme, where some visible and near-visible transitions are radiative and others are nonradiative. A refined Füchtbauer-Ladenburg recipe for calculation of the stimulated emission spectrum on the basis of measurable absorption and fluorescence emission spectra is worked out. The last issue is multiphonon nonradiative transitions occurring when the energy gap between adjacent electronic ion states is larger than the cutoff matrix phonon energy. Transition probabilities were calculated on the basis of anharmonicity of the effective potential supporting the internal atomic basis vibrations. An expression in a closed form is obtained, similar to the empiric "energy gap" law, however, with parameters related to specific host material properties and the actual transition in the ion. Comparison to existing experimental evidence is presented and discussed in detail.