Spectral Intensities of Transitions Between Stark Levels of Er$^{3+}$(4f$^{11})$ in Single Crystal, Ceramic, and Nanocrystalline Y$_{2}$O$_{3}$

Similarities and differences among the optical properties of Er$^{3+}$:Y$_{2}$O$_{3}$ in single crystal, polycrystalline (ceramic), and nanocrystalline forms are discussed based on spectra obtained between 400 nm and 1700 nm and temperatures between 8 K and 300K. The observed crystal-field splitting and the measured intensities of transitions between the $^{2S+1}$L$_{J}$ manifolds of Er$^{3+}$(4f$^{11})$ in both the C$_{2}$ and C$_{3i}$ sites are analyzed in terms of models that invoke the mixing of states of opposite parity through the odd terms in the crystal-field Hamiltonian. The inversion symmetry of C$_{3i}$ sites limits electronic transitions to magnetic dipole transitions between the $^{4}$I$_{13/2}$ and $^{4}$I$_{15/2}$ manifolds. For Er$^{3+}$ ions in C$_{2}$ sites, the forced electric-dipole transitions along with some magnetic dipole contribution in certain cases, are allowed between the J+1/2 Stark levels within all manifolds. Within the instrumental resolution, there are some important differences between intensities of transitions depending on particle size of the Er$^{3+:}$Y$_{2}$O$_{3}$.