Branching ratios, cross sections, and radiative lifetimes of rare earth ions in solids: Application to Tm3+ and Ho3+ ions in LiYF4

The measurement of branching ratios, cross sections and radiative lifetimes for rare earth ions in solids is considered. The methods are applied to Tm and Ho in YLF as a test case. De-activation rates for electric dipole and magnetic dipole emission are calculated for many of the lower lying manifolds in Tm:YLF and Ho:YLF in the context of the Judd-Ofelt theory to determine radiative lifetimes. Measured values for the branching ratios as well as the absorption and emission cross sections are also presented for many of the excited state manifolds. From these measurements, a methodology is developed to extract measured values for the radiative lifetimes. These results are compared with the Judd-Ofelt theory as a guide for consistency and for determining the accuracy of the Judd-Ofelt theory in predicting branching ratios and radiative lifetimes. The parameters generated by the methods covered here have potential applications for more accurate modeling of Tm:Ho laser systems.