Comprehensive Rate Equation Analysis of Upconversion Luminescence Enhancement Due to BaCl<sub>2</sub> Nanocrystals in Neodymium-Doped Fluorozirconate-Based Glass Ceramics

In neodymium-doped fluorozirconate-based glasses, a huge increase of up to a factor of 20 of the Nd<sup>3+</sup> photoemission is possible by the introduction of BaCl<sub>2</sub> nanocrystals. A rate equation system was developed to describe the excitation and relaxation dynamics of neodymium ions in such composite matrix to quantify the enhancement mechanism due to the embedded nanocrystals. The model is extended to include the previously unknown quantitative nanocrystal influences in an effective-medium model, considering the change in the phonon spectrum in particular. Having verified the coefficients with time-dependent photoluminescence experiments, it is used to predict the intensity dependence of steady-state upconversion. The good agreement with experimental data indicates that the rate equations enable the quantitative simulation of photon upconversion in glass and glass ceramics under a variety of excitation scenarios. In addition, the strong reduction of the phonon emission probability in the BaCl<sub>2</sub> nanocrystals is confirmed as the key reason for (upconversion) emission enhancement in the fluorozirconate-based glass ceramics.