Energy-transfer processes in ${\mathrm{Y}}_3$${\mathrm{Al}}_5$${\mathrm{O}}_{12}$:Tm,Ho

The characteristics of energy transfer and migration processes important in the optical dynamics of ${\mathrm{Y}}_3$ ${\mathrm{Al}}_5$ ${\mathrm{O}}_{12}$:Tm,Ho and ${\mathrm{Y}}_3$ ${\mathrm{Al}}_5$ ${\mathrm{O}}_{12}$:Tm laser crystals were investigated. Laser-induced grating spectroscopy was used to study spatial migration of energy among the Tm ions as a function of both temperature and Tm ion concentration. The presence of energy migration was identified in the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{H}}_4$ level, and this was shown to enhance the cross-relaxation process from this level. Efficient long-range energy migration was found to take place in the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{F}}_4$ level, which enhances the energy transfer to ${\mathrm{Ho}}^{3+}$ ions. The parameters describing excitation migration were determined experimentally and used to calculate an overall Tm-Ho energy transfer rate. This was found to be in close agreement with the rate determined by the results of fluorescence spectral dynamics measurements. Theoretical estimates were made of the fundamental ion-ion interaction rates responsible for each of the physical processes investigated here and the results were all found to be in close agreement with the experimentally determined values.