Numerical rate equation modelling of a 1.6 μm pumped ∼2 μm Tm³⁺-doped tellurite fibre laser

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%.