Optical absorption and fluorescence intensities of ${\mathrm{Nd}}^{3+}$ in the garnets Ca${\mathrm{Y}}_2$${\mathrm{Mg}}_2$${\mathrm{Ge}}_3$${\mathrm{O}}_{12}$ and ${\mathrm{Gd}}_3$${\mathrm{Ga}}_5$${\mathrm{O}}_{12}$ and the biaxial crystal ${\mathrm{La}}_2$${\mathrm{Be}}_2$${\mathrm{O}}_5$

The Judd-Ofelt (JO) theory was applied to interpret the optical-absorption intensities of trivalent neodymium (${\mathrm{Nd}}^{3+}$) in the garnets Ca${\mathrm{Y}}_2$ ${\mathrm{Mg}}_2$ ${\mathrm{Ge}}_3$ ${\mathrm{O}}_{12}$ and ${\mathrm{Gd}}_3$ ${\mathrm{Ga}}_5$ ${\mathrm{O}}_{12}$ and the biaxial crystal ${\mathrm{La}}_2$ ${\mathrm{Be}}_2$ ${\mathrm{O}}_5$ yielding the JO parameters ${\Omega }_2$, ${\Omega }_4$, and ${\Omega }_6$. The JO theory applied to the ${}_{}{}^4{}_{}{}^{}F_{\frac{3}{2}}^{}{}_{}{}^{}$ fluorescence transition in ${\mathrm{Nd}}^{3+}$ predicts a linear relation between the ratio $R$ of the 1.06- to 1.35-μm fluorescence band intensities and the ratio $\frac{{\Omega }_4}{{\Omega }_6}$ of JO intensity parameters. This linearity was verified by independent measurements of $R$ and $\frac{{\Omega }_4}{{\Omega }_6}$ for a series of ${\mathrm{Nd}}^{3+}$-doped crystals and was found to be dependent on the type of free-ion wave functions that were used in calculating the required transition-matrix elements.