Effect of Host Glass on the Stimulated Emission Cross-section of Dy$^{3+}$ ions in bismuth borate glasses

Optical properties of Dy$^{3+}$ ions in bismuth borate glasses were analyzed using Judd-Ofelt theory as a function of the glass composition with Bi$_{2}$O$_{3\, }$content varying from 29.5 to 59.5mol{\%}. The intensity of an absorption band can be expressed in terms of the oscillator strength. Absorption coefficient at each wavelength was obtained from the optical absorption spectrum of a glass sample and number density of rare-earth ions was calculated from the measurement of the glass density. These two parameters were then used to calculate the oscillator strength of each transition using Judd-Ofelt theory. Using the oscillator strength for each transition, we obtained the intensity parameters which represent changes in the asymmetry of the ligand field at the rare-earth (\textit{RE}) site (due to structural changes) and to changes in \textit{RE}-O covalency. Radiative transition probabilities, the radiative lifetime of the excited states and the branching ratios are then obtained from these intensity parameters. The compositional dependence of stimulated emission cross-section ($\sigma _{p})$, is then evaluated using radiative transition probability, refractive index of the host glass, effective fluorescence linewidth, and position of the band. The $\sigma_{p} $values of the 574 nm band of Dy$^{3+}$ for bismuth borate glasses are found to be in the range 2.7 x 10$^{-21}$ cm$^{2}$ -- 3.8 x 10$^{-21}$ cm$^{2\, }$which is slightly higher than those obtained for other oxide glasses.