Theoretical Modeling of a $\sim {2}~\mu{\rm m}~{\rm Tm}^{3+}$ -Doped Tellurite Fiber Laser: The Influence of Cross Relaxation

A rate equation approach is used to model an experimentally realized ~ 2 mum Tm³⁺-doped tellurite fiber laser utilizing an in-band pumping scheme (³H₆ rarr ³F4) . Excellent agreement between the theoretically predicted and experimentally measured slope efficiency is obtained. It is shown that in order to achieve agreement between the predicted and measured thresholds it is important to include cross-relaxation mechanisms with the ³H₄ level, even with the in-band pumping scheme. By fitting the results of the model with level lifetime measurements and the threshold pump powers we have extracted the cross-relaxation parameters of Tm-doped tellurite glass.