Evaluation of the upconversion mechanisms inHo3+-doped crystals: Experiment and theoretical modeling

The paper compares the mechanisms that enable the upconverted green emission ${(}^5{\overrightarrow{S_2}}^5{I}_8)$ of the ${\mathrm{Ho}}^{3+}$ ion under infrared excitation (700–920 nm) in several crystalline hosts $({\mathrm{YAlO}}_3,$ ${\mathrm{YLiF}}_4,$ ${\mathrm{Y}}_3{\mathrm{Sc}}_2{\mathrm{Ga}}_3{\mathrm{O}}_{12},$ and ${\mathrm{BaY}}_2{\mathrm{F}}_8).\mathrm{}$ Parameters involved in the upconversion such as excited-state absorption and cross-relaxation rates were determined from spectroscopic measurements. A system of differential equation (rate equations) was used to describe the upconversion mechanism and was numerically solved. The results were compared with experimental data. A reduction of this system to a three-level “simplified system” is presented, which includes only the ground level, the emitting level, and the intermediate level. The differences between the photon-avalanche mechanism and the looping mechanism are discussed and analyzed according to this simplified system.