Near- and mid-infrared fibre lasers find many applications in areas such as remote and chemical sensing, lidar and
medicine, and tellurite fibres offer advantages over other common fibre glasses such a lower phonon energy and higher
rare-earth ion solubility than silicate glasses, and greater chemical and environmental stability than fluoride glasses. Rate
equation modelling is a very useful tool for the characterisation and performance prediction of new rare earth transitions
in these novel fibre materials. We present the numerical rate equation modelling results for a ~2 μm Tm3+-doped tellurite
fibre laser when pumped with a 1.6 μm Er3+/Yb3+-doped double-clad silica fibre laser. A maximum slope efficiency of
76% with respect to launched pump power was achieved in the experimental fibre laser set up with a 32 cm long fibre.
The high slope efficiency is very close to the Stokes efficiency limit of ~82% which is due to the in-band pumping
scheme employed and the lack of pump excited state absorption. The two-level rate equations involving absorption and
emission between the Tm3+: 3H6 and 3F4 levels have been solved iteratively using a fourth-order Runge-Kutta algorithm
and the results compared with the experimental results. For the 32 cm fibre with output coupler reflectivities of 12%,
50%, 70% and 90%, the respective theoretical slope efficiencies of 73%, 64%, 53% and 29% are in very good agreement
with the experimentally measured values of 76%, 60%, 48% and 33%.