Mechanism of a population inversion between the ${}^4I_{11/2}$ and ${}^4I_{13/2}$ levels of the $Er^{3+}$ ion in $Y_3Al_5O_{12}$ crystals

Studies of the spectra of stimulated emission from $Y_3Al_5O_{12}-Er^{3+}$ crystals (${}^4I_{11/2}-{}^4I_{13/2}$) containing 20 wt.<i>%</i> activator ions, showed that, as the temperature decreased from 300 to 77K, a change was observed in the emission wavelength (at $T=300$K $\lambda_1=2,9364\mu m$, $\lambda_2=2,8310\mu m$, at $T=77$К $\lambda_1=2,6930\mu m$, $\lambda_2=2,8970\mu m$). This could not be attributed to a thermal redistribution of the populations of the Stark components of the ${}^4I_{11/2}$ and ${}^4I_{13/2}$ upper and lower active levels. An analysis of the results showed that the temperature shift of the stimulated emission spectrum was due to changes in the processes of relaxation of excitation from the upper levels of the $Er^{3+}$ ion which caused substantial changes in the populations of the ${}^4I_{11/2}$ and ${}^4I_{13/2}$ multiplets.