## 3 Results and Discussion
### Emission Spectroscopy and Analysis
Figure 2(a) shows the emission spectra of the two transitions of Tm\({}^{3+}\) ion originating from \({}^{3}\)F\({}_{4}\) and \({}^{3}\)H\({}_{4}\) levels to the ground level for the TeZnTm glass host with Tm\({}_{2}\)O\({}_{3}\) concentrations of 1.0 and 0.25 mol %. The emission spectra clearly show the two emission bands centered around 1860 nm and 1460 nm and further verify the role of cross relaxation, which is quite common for the Tm\({}^{3+}\)-doped systems [33; 34]. Cross relaxation is a non-radiative energy transfer process, which becomes significant at high ion concentrations, leading to the quenching of the 1460-nm emission and enhancement of the 1860-nm emission band (Figure 2(a)). On the other hand, the quantum efficiency drops from 32 to 6% for TeO\({}_{2}\)-ZnO glass host. As the Tm\({}^{3+}\) concentration increased, similar enhancement behavior was observed for the other tellurite glass hosts. It is important to find an optimum concentration level here where quantum yield and pump absorption are not dramatically low and still cross-relaxation is significant. Regarding this fact, 0.25 or 0.5 mol % Tm\({}_{2}\)O\({}_{3}\)-doped samples are potential candidates as hosts in laser applications for bulk as well as fiber applications. Figure 2(b) shows the emission spectra of the glass hosts with different glass modifiers at 1.0 mol % dopant concentration. As can be seen, the 1460-nm emission band remains similar for different glass modifiers. On the other hand, glass modifier changes produce a notable change in the 1860-nm emission band. In particular, the TeNbKTm glass has the highest emission peak at 1860 nm, whereas the lowest peak of 1795 nm was observed in the TeNbTm host. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Fluorescence and Radiative Lifetimes and Quantum Yields** & \multicolumn{2}{c}{\(\mathbf{\tau_{F}}\) (\(\upmu\)s)} & \multicolumn{2}{c}{\(\mathbf{\eta}\) (\%)} & \multicolumn{2}{c}{\(\mathbf{\tau_{Raverengal}}\) (ms)} \\ \cline{2-7}
**TeNbKTm** [29] & **1860 nm** & **1460 nm** & **1860 nm** & **1460 nm** & **(ms)** & **(ms)** \\ \hline
0.125 mol \% & 814 & 258 & 32 & 74 & 2.57 & 0.35 \\
0.25 mol \% & 572 & 199 & 22 & 57 & - & - \\
0.5 mol \% & 545 & 148 & 21 & 43 & - & - \\
1.0 mol \% & 439 & 47 & 17 & 14 & - & - \\ \hline
**TeZnTm** & & & & & \(\mathbf{\tau_{R}}\) (1860 nm) & \(\mathbf{\tau_{R}}\) (1460 nm) \\ \hline
0.125 mol \% & 806 & 327 & 32 & 89 & 2.55 & 0.37 \\
0.25 mol \% & 722 & 250 & 28 & 68 & - & - \\
0.5 mol \% & 511 & 171 & 20 & 47 & - & - \\
1.0 mol.\% & 145 & 35 & 6 & 10 & - & - \\ \hline
**TeNbTm** & & & & & \(\mathbf{\tau_{R}}\) (1860 nm) & \(\mathbf{\tau_{R}}\) (1460 nm) \\ \hline
0.25 mol \% & 893 & 284 & 32 & 76 & 2.76 & 0.37 \\
1.0 mol \% & 382 & 76 & 14 & 20 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measured fluorescence lifetimes (\(\tau_{F}\)), calculated radiative lifetimes (\(\tau_{R}\)), and the corresponding luminescence quantum yields (\(\eta\)) for the two transitions at 1860 nm and 1460 nm. In order to obtain the emission cross section, we used both the Fuchtbauer-Ladenburg equation [35; 36],  
\[\sigma_{em}(\lambda)=\frac{\lambda^{5}I(\lambda)A(J,J^{\prime})}{8\pi n^{2}c \int I(\lambda)\lambda d\lambda}, \tag{4}\]  
and the McCumber formula [37],  
\[\sigma_{em}(\lambda)=\sigma_{a}(\lambda)\bigg{[}\frac{Z_{l}}{Z_{u}}\bigg{]}\exp \bigg{[}\frac{hc}{kT}\bigg{(}\frac{1}{\lambda_{ZP}}-\frac{1}{\lambda}\bigg{)} \bigg{]}, \tag{5}\]  
where \(\sigma_{a}(\lambda)\) is the absorption cross section, \(\bigg{[}\frac{Z_{l}}{Z_{u}}\bigg{]}\) represents the ratio of the parity functions of lower and upper states (13/9 for the Tm\({}^{3+}\) ion), \(h\) is the Planck constant, \(k\) is the Boltzmann constant, \(T\) is the absolute temperature, and \(\lambda_{ZP}\) is the wavelength of the zero phonon line. From the overlap of the absorption and emission bands, \(\lambda_{ZP}\) was estimated to be 1780 nm.