## 4 Conclusions  
We have conducted a detailed spectroscopic analysis on three new types of tellurite glass materials (Tm\({}_{2}\)O\({}_{3}\)-TeO\({}_{2}\)-ZnO (TeZnTm), Tm\({}_{2}\)O\({}_{3}\)-TeO\({}_{2}\)-Nb\({}_{2}\)O\({}_{5}\) (TeNbTm) and Tm\({}_{2}\)O\({}_{3}\)-TeO\({}_{2}\)-K\({}_{2}\)O-Nb\({}_{2}\)O\({}_{5}\) (TeNbKTm)) in order to investigate the effect of the host composition as well as Tm\({}^{3+}\) ion concentration on the cross sections and the luminescence quantum efficiencies. From the data, it can be concluded that J-O intensity parameters vary slightly among tellurite glasses with different compositions, as expected. Yet, our calculations showed that for the sample containing zinc as a glass modifier (TeZnTm), we obtained shorter radiative lifetimes for the transition corresponding to the 1860-nm  
Figure 4: Absorption and emission cross section of the 1.0% Tm\({}_{2}\)O\({}_{3}\)-doped TeNbKTm samples deduced by using the McCumber analysis. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{\(\Delta\Delta\) (FWHM, nm)} & \multicolumn{2}{c}{\(\sigma_{em}\) (10\({}^{-21}\) cm\({}^{2}\))} & \multicolumn{2}{c}{\(\sigma_{a}\) (10\({}^{-21}\) cm\({}^{2}\))} \\ \cline{2-7}  & **1460 nm** & **1860 nm** & **1460 nm** & **1860 nm** & **1860 nm** & **794 nm** \\ \hline
**TeNbKTm [(29)]** & \multicolumn{5}{c}{**Fucht-Laden.**} & **McCumber** \\ \hline
1.0 mol \% & 122 & 170 & 2.67 \(\pm\) 0.53 & 5.61 \(\pm\) 0.42 & 6.21 & 9.07 \\
0.5 mol \% & 116 & 231 & 2.74 \(\pm\) 0.54 & 6.12 \(\pm\) 0.45 & 6.04 & 8.33 \\
0.25 mol \% & 133 & 319 & 2.40 \(\pm\) 0.48 & 5.46 \(\pm\) 0.40 & 5.79 & 8.26 \\
0.125 mol \% & 128 & 240 & 3.00 \(\pm\) 0.59 & 6.85 \(\pm\) 0.51 & 6.10 & 7.07 \\ Average & & & 2.70 \(\pm\) 0.54 & 6.01 \(\pm\) 0.45 & 6.04 \(\pm\) 0.18 & 8.18 \\ \hline
**TeZnTm** & \multicolumn{5}{c}{**Fucht-Laden.**} & **McCumber** \\ \hline
1.0 mol \% & 106 & 192 & 2.74 \(\pm\) 0.40 & 5.48 \(\pm\) 0.30 & 6.00 & 8.08 \\
0.5 mol \% & 119 & 200 & 2.52 \(\pm\) 0.37 & 5.65 \(\pm\) 0.31 & 5.00 & 7.79 \\
0.25 mol \% & 111 & 172 & 2.91 \(\pm\) 0.37 & 6.85 \(\pm\) 0.33 & 4.98 & 7.65 \\
0.125 mol \% & 106 & 200 & 2.95 \(\pm\) 0.43 & 7.36 \(\pm\) 0.40 & 5,60 & 7.89 \\ Average & & & 2.78 \(\pm\) 0.39 & 6.33 \(\pm\) 0.34 & 5.40 \(\pm\) 0.5 & 7.85 \\ \hline
**TeNbTm** & \multicolumn{5}{c}{**Fucht-Laden.**} & **[PERSON]** \\ \hline
1.0 mol \% & 105 & 237 & 2.65 \(\pm\) 0.02 & 4.99 \(\pm\) 0.02 & 5.00 & 7.68 \\
0.25 mol \% & 100 & 103 & 2.60 \(\pm\) 0.02 & 6.28 \(\pm\) 0.02 & 6.20 & 6.90 \\ Average & & & 2.62 \(\pm\) 0.02 & 5.63 \(\pm\) 0.02 & 5.60 \(\pm\) 0.85 & 7.29 \\ \hline \end{tabular}
\end{table} 
Table 3: Emission cross sections and bandwidths at full-wave half maximum (FWHM) of the 1460-nm and 1860-nm bands, and absorption cross sections at 794 nm for the Tm\({}^{3+}\):TeO\({}_{2}\)-based glass hosts at different Tm\({}_{2}\)O\({}_{3}\) concentrations. band. We obtained average radiative lifetimes of 2.55 \(\pm\) 0.07 ms and 2.76 \(\pm\) 0.03 ms for the TeZnTm and TeNbTm samples for the \({}^{3}\)H\({}_{4}\) level. From the lifetime measurements and the radiative lifetime calculations based on the J-O theory, we determined the luminescence quantum efficiencies of the samples. The highest quantum efficiency for the sample TeZnTm was 32% for the 1860-nm emission band and 89% for the 1460-nm emission band. For the sample TeNbTm, we obtained the highest quantum yields as 32% and 76% for the 1860-nm and 1460-nm emission bands, respectively. For higher doping concentrations, we observed a cross-relaxation effect, which enhanced the 1860-nm emission band. Samples with low concentration provide higher quantum efficiencies that are favorable for lasing applications but on the other hand, exhibit weak absorption.