Analytical modelling of Tm-doped tellurite glass including cross-relaxation process

In this paper, we present a comprehensive analytical model of Tm able to take into account direct cross-relaxation process. We show that by using an appropriate set of parameters the model is able to properly fit the first part of the fluorescence decay of Tm-doped tellurite glasses for different dopant concentration values. We also compare the model with a full numerical model to investigate its limitations. We assess the model is a valid tool to fit fluorescence properties but for precisely predicting population inversion is limited to doping level up to about 1%. In fact, we show the reverse cross-relaxation process becomes significant in case of higher doping level.