Prediction of the Optical Polarization and High Field Hyperfine Structure Via a Parametrized Crystal-Field Model for the Low Symmetry Centers in Er$^{3+}$ Doped Y$_{2}$SiO$_{5}$

Abstract: We report on the development and application of a parametrized crystal-field model for both C${1}$ symmetry centers in trivalent erbium-doped Y${2}$SiO${5}$. High resolution Zeeman and temperature dependent absorption spectroscopy was performed to acquire the necessary experimental data. The obtained data, in addition to the ground ($^{4}$I${15/2}$Z${1}$) state and exited ($^{4}$I${13/2}$Y${1}$) state Zeeman and hyperfine structure, was simultaneously fitted in order to refine an existing crystal-field interpretation of the Er$^{3+}$:Y${2}$SiO${5}$ system. We demonstrate that it is possible to account for the electronic, magnetic and hyperfine structure of the full 4f$^{11}$ configuration of Er$^{3+}$:Y${2}$SiO$_{5}$ and further, that it is possible to predict both optical polarization behavior and high magnetic field hyperfine structure of transitions in the 1.5 $\mu$m telecommunications band.