Near-infrared emission ofCr4+-doped garnets: Lifetimes, quantum efficiencies, and emission cross sections

The lifetimes of the excited state of the tetrahedrally coordinated ${\mathrm{Cr}}^{4+}$ ion in several garnets were measured in the temperature range between 15 and 380 K. Both the nonradiative and radiative transition rates increase with temperature due to the coupling of phonons to the electronic states. This temperature dependence is described with the model of Struck and Fonger for the nonradiative decay rate and with the coth law for the radiative decay process. It is shown that even at low temperatures the nonradiative transition rate is larger than the radiative rate. With these data the quantum efficiencies are calculated to be between 8% and 33% at room temperature for the investigated crystals. The cross sections for the emission of the ${\mathrm{Cr}}^{4+}$ ion in the garnets are determined using the theory of McCumber. The ${\mathrm{\sigma }}_{\mathrm{em}}$τ product is highest for ${\mathrm{Cr}}^{4+}$:${\mathrm{Lu}}_3$ ${\mathrm{Al}}_5$ ${\mathrm{O}}_{12}$, ${\mathrm{Cr}}^{4+}$:${\mathrm{Y}}_3$ ${\mathrm{Al}}_5$ ${\mathrm{O}}_{12}$, and for ${\mathrm{Cr}}^{4+}$:${\mathrm{Y}}_3$ ${\mathrm{Sc}}_{\mathit{x}}$ ${\mathrm{Al}}_{5\mathrm{-}\mathit{x}}$ ${\mathrm{O}}_{12}$ crystals with low scandium content. Therefore, these crystals are most promising as tunable room-temperature lasers. A method for the calorimetric measurement of the quantum efficiency of the ${\mathrm{Cr}}^{4+}$ emission in yttrium aluminum garnet is also presented. DOI: http://dx.doi.org/10.1103/PhysRevB.51.17323 © 1995 The American Physical Society