## 3 Results and Discussion
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multicolumn{1}{c}{**Physical Parameters \({}^{*}\) Units**} & \multicolumn{6}{c}{**Doping (mol\% Dy\({}_{2}\)O\({}_{3}\))**} \\ \cline{3-8}  & & **0.0** & **0.2** & **0.4** & **0.6** & **0.8** & **1** \\ \hline Density & (g.cm\({}^{-3}\)) & 2.144 & 2.162 & 2.182 & 2.210 & 2.238 & 2.260 \\ Molecular weight, M\({}_{\text{T}}\) & g & 62.903 & 63.509 & 64.116 & 64.723 & 65.330 & 65.937 \\ Molar volume \(V_{m}\) & (cm\({}^{3}\)/mol) & 29.339 & 29.375 & 29.384 & 29.286 & 29.191 & 29.175 \\ The volume of boron atoms per mole \(V_{m}^{b}\) & & 16.031 & 11.959 & 11.886 & 11.058 & 11.656 & 11.576 \\ Ion concentration (N) \(\times 10^{20}\) & (ions/cm\({}^{3}\)) & & 0.410 & 0.819 & 1.233 & 1.650 & 2.064 \\ Polaron radius & & & 11.687 & 9.279 & 8.096 & 7.347 & 6.819 \\ \((r_{p})\times 10^{-8}\) & & & 29.0004 & 23.027 & 20.091 & 18.232 & 16.921 \\ Field strength (F) \(\times 10^{16}\) & (cm\({}^{-2}\)) & & 1.189 & 1.887 & 2.479 & 3.010 & 3.494 \\ Average of boron-boron distance \(\cdot\)d\({}_{\text{B-B}^{\prime}}\) & nm & 0.298 & 0.270 & 0.270 & 0.263 & 0.268 & 0.267 \\ \hline \hline \end{tabular} \({}^{*}\) With consideration of \(\pm\) 0.01% error.  
\end{table} 
Table 3: Physical properties for all series of glasses. Figure 4: Polaron radius, inter-nuclear distance and field strength as functions of Dy\({}_{2}\)O\({}_{3}\) content of prepared glasses. The spectra show ten inhomogeneous of absorption bands existing at the wavelengths 352, 393, 458, 669, 802, 841, 904, 1095, 1271 and 1703 nm due to the transitions of Dy\({}^{3+}\) at the ground state (\({}^{6}\)H\({}_{15\gamma 2}\)) into different excited states (\({}^{6}\)P\({}_{7/2}\)), (\({}^{4}\)F\({}_{7/2}\)), (\({}^{4}\)I\({}_{15/2}\)), (\({}^{4}\)F\({}_{9/2}\)), (\({}^{6}\)F\({}_{3/2}\)), (\({}^{6}\)F\({}_{7/2}\)), (\({}^{6}\)F\({}_{9/2}\) + \({}^{6}\)H\({}_{7/2}\)), (\({}^{6}\)F\({}_{11/2}\) + \({}^{6}\)H\({}_{9/2}\)) and (\({}^{6}\)H\({}_{11/2}\)), respectively [17]. Due to the strong absorption of LAB host glass, some of the absorption bands have disappeared in ultraviolet (UV) regions and are very sparse at 352 nm (\({}^{6}\)H\({}_{15/2}\)\(\rightarrow\)\({}^{6}\)P\({}_{7/2}\)), 393 nm (\({}^{6}\)H\({}_{15/2}\)\(\rightarrow\)\({}^{4}\)F\({}_{7/2}\)) and 456 nm (\({}^{6}\)H\({}_{15/2}\)\(\rightarrow\)\({}^{4}\)I\({}_{15/2}\)), and also they have very low intensity [32]. Besides, the current samples showed a hypersensitive transition at 1270 nm (\({}^{6}\)H\({}_{15/2}\)\(\rightarrow\)\({}^{6}\)H\({}_{11/2}\)) with high intensity and were subjected to the rule of selection \(|\Delta S|=0\), \(|\Delta L|\leq 2\), and \(|\Delta J|\leq 2\), where these transitions are more sensitive than others [33]. The variation between transition levels and their respective oscillator of strength for the glass samples are tabulated in Table 4. Noting that, the influence of Dy\({}^{3+}\) ion on difference absorption bands led to their appropriate wavelengths, energies and oscillator strengths [34]. Figure 5 illustrate the optical energy band gaps for direct and indirect based on the curves of the UV-absorption spectrum. Figure 6a and 6b show the indirect and direct bandgap, respectively. The energy band gap value can be obtained by using Equation (9) to plot (\(\alpha\)hv)\({}^{n}\) against photon energy (_lvv_). Then, the linear extrapolating region of the curves extending to the \(X\)-axis gives the energy bandgap (\(E_{g}\)) reading. In the recent glass system, the values of the direct \(E_{g}\) exhibit from 3.650  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Absorption Transition** & \begin{tabular}{c} **Wavelength** \\ **(nm)** \\ \end{tabular}  & \ \begin{tabular}{c} **Energy** \\ **(\(\times 10^{-3}\)cm\({}^{-1}\))** \\ \end{tabular}  & \begin{tabular}{c} **Oscillator Strength \(\mathbf{f_{exp}}\) (\(\times 10^{-6}\))** \\ \end{tabular}