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

Abstract

The paper compares the mechanisms that enable the upconverted green emission ${(}^{5}{\stackrel{\ensuremath{\rightarrow}}{{S}_{2}}}^{5}{I}_{8})$ 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 ${\mathrm{BaY}}_{2}{\mathrm{F}}_{8}).$ 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.