Energy-transfer processes in Yb:Tm-doped<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">KY</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">LiYF</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">BaY</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>8</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>single crystals for laser operation at 1.5 and 2.3 μm

Energy-transfer processes have been quantitatively studied in various Tm:Yb-doped fluoride crystals. A comparison between the three host crystals which have been examined $({\mathrm{KY}}_{3}{\mathrm{F}}_{10},$ ${\mathrm{LiYF}}_{4},$ and ${\mathrm{BaY}}_{2}{\mathrm{F}}_{8})$ shows clearly that the efficiency of the $\mathrm{Y}\stackrel{\ensuremath{\rightarrow}}{b}\mathrm{Tm}$ energy transfers is larger in ${\mathrm{KY}}_{3}{\mathrm{F}}_{10}$ than in ${\mathrm{LiYF}}_{4}$ or ${\mathrm{BaY}}_{2}{\mathrm{F}}_{8}.$ The dependence of the energy-transfer parameters upon the codopant concentrations has been experimentally measured and compared with the results calculated on the basis of migration-assisted energy-transfer models. Using these energy-transfer parameters and a rate equation model, we have performed a theoretical calculation of the laser thresholds for the ${}^{3}{\stackrel{\ensuremath{\rightarrow}}{{H}_{4}}}^{3}{F}_{4}$ and ${}^{3}{\stackrel{\ensuremath{\rightarrow}}{{H}_{4}}}^{3}{H}_{5}$ laser transitions of the Tm ion around 1.5 and 2.3 \ensuremath{\mu}m, respectively. Laser experiments performed at 1.5 \ensuremath{\mu}m in ${\mathrm{Y}\mathrm{b}:\mathrm{T}\mathrm{m}:\mathrm{L}\mathrm{i}\mathrm{Y}\mathrm{F}}_{4}$ then led to laser threshold values in good agreement with those derived theoretically. Based on these results, optimized values for the Yb and Tm dopant concentrations for typical values of laser cavity and pump modes were finally derived to minimize the threshold pump powers for the laser transitions around 1.5 and 2.3 \ensuremath{\mu}m.