Numerical analyses of the population dynamics and determination of the upconversion coefficients in a new high erbium-doped tellurite glass

A model for the population dynamics of Er³⁺ in tellurite glasses with high erbium concentrations is proposed. Luminescence decay curves from transitions of ⁴I_13/2 → ⁴I _15/2 and ⁴S_3/2 → ⁴I _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 ⁴I_13/2 and ⁴S _3/2 levels. The upconversion coefficient for ⁴I _13/2 + ⁴I_13/2 → ⁴I _9/2 + ⁴I_15/2 is found to be 2.74 × 10^-18 cm³/s and for ⁴I_11/2 + ⁴I_11/2 → ⁴I_15/2 + ²F_7/2 is 1.09 × 10^-18 cm³/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 Er³⁺ ions in glass hosts, where various energy levels of Er³⁺ 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.