## Abstract

A model for the population dynamics of ${\mathrm{Er}}^{3+}$ in tellurite glasses with high erbium concentrations is proposed. Luminescence decay curves from transitions of ${}^{4}{I}_{13/2}{\to}^{4}{I}_{15/2}$ and ${}^{4}{S}_{3/2}{\to}^{4}{I}_{15/2}$ were measured experimentally. Upconversion coefficients were obtained by numerically solving the rate equations of the model to fit the population dynamics of the ${}^{4}{I}_{13/2}$ and ${}^{4}{S}_{3/2}$ levels. The upconversion coefficient for ${}^{4}{I}_{13/2}{+}^{4}{I}_{13/2}{\to}^{4}{I}_{9/2}+{\hspace{0.5em}}^{4}{I}_{15/2}$ is found to be $2.74\times {10}^{-18}$ cm^{3}/s and for ${}^{4}{I}_{11/2}{+}^{4}{I}_{11/2}{\to}^{4}{I}_{15/2}{+}^{2}{F}_{7/2}$ is $1.09\times {10}^{-18}$ cm^{3}/s. The model provides a good basis for explaining the experiment data because it shows a high sensitivity to the input fitting parameters. This model can be used to analyze transition properties of ${\mathrm{Er}}^{3+}$ ions in glass hosts, where various energy levels of ${\mathrm{Er}}^{3+}$ and the transitions between them cannot be neglected. A discussion of upconversion coefficients in tellurite glass in comparison with those in silica, silicate, and phosphate glasses is presented with an explanation of the origin of the differences from the perspective of different glass structures.

© 2001 Optical Society of America

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