Spectral and up-conversion dynamics and their relationship to the laser properties of ${\mathrm{BaYb}}_2$${\mathrm{F}}_8$:${\mathrm{Ho}}^{3+}$

The optical spectroscopic properties, energy transfer, up-conversion transitions, and lasing dynamics of ${\mathrm{BaYb}}_2$ ${\mathrm{F}}_8$:${\mathrm{Ho}}^{3+}$ crystals are reported here. The positions of the various Stark components of the different J manifolds of ${\mathrm{Ho}}^{3+}$ are identified, and the branching ratios and radiative decay rates were calculated for the ${\mathrm{Ho}}^{3+}$ levels from the Judd-Ofelt theory. The fluorescence-decay kinetics of the ${\mathrm{Ho}}^{3+}$ emission originating on the ${}_{}{}^5{}_{}{}^{}\mathrm{F}_5^{}{}_{}{}^{}$ and ${}_{}{}^5{}_{}{}^{}\mathrm{S}_2^{}{}_{}{}^{}$ ${,}^5$ ${\mathrm{F}}_4$ levels and of the ${\mathrm{Yb}}^{3+}$ emission were measured and analyzed with two energy-transfer theories. These calculations show that the ${\mathrm{Ho}}^{3+}$-${\mathrm{Yb}}^{3+}$ interaction is greater for ions initially in the ${}_{}{}^5{}_{}{}^{}\mathrm{F}_5^{}{}_{}{}^{}$ level and that the diffusion of excitation energy among ${\mathrm{Yb}}^{3+}$ ions is a thermally assisted incoherent hopping process with a diffusion constant of 1.1×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^2$/sec at 300 K. The kinetics of the up-conversion processes were modeled with rate equations. It was necessary to include the effects of stimulated emission at 551.5 nm and three successive energy transfers from ${\mathrm{Yb}}^{3+}$ to ${\mathrm{Ho}}^{3+}$ to adequately describe the spectral dynamics of the up-conversion. The efficiencies of the different laser transitions were found to be dependent upon the pump power used. The output of the shorter-wavelength transition (0.55 μm) increases at the expense of the longer-wavelength transition (2.9 μm) as the pump power is increased. The 2.9-μm laser action was found to have a 15% energy conversion efficiency and a slope efficiency of 4.5% when pumped at 1.047 μm.