Semi-Empirical Approach for Evaluating Cooling Performance of Ytterbium-Doped Crystals

The use of optical cooling in the process of radiation generation is one of the ways to control the thermal load of laser crystals. The cooling efficiency of ytterbium-doped crystals largely depends on the purity and geometry of the crystal, which are its individual characteristics. Here, we propose a semi-empirical approach for evaluating quantities associated with the purity and geometric crystal characteristics that are difficult to determine experimentally: fluorescence escape efficiency and parasitic impurity absorption coefficient. This approach is based on quantum mechanical calculations using spectroscopic data. The proposed approach is easily implemented experimentally and allows one to get an evaluation using the dependence of the laser crystal temperature on the pump radiation intensity. The approach efficiency is demonstrated for a YAl₃(BO₃)₄ crystal doped with 10 at.% Yb³⁺ ions. It is shown that the absorption coefficient of parasitic impurities has an exponential dependence on the crystal temperature.