Two-photon excitation of ${\mathrm{Ho}}^{3+}$ in the Ca${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, and Cd${\mathrm{F}}_2$ lattices

The observation of two-photon absorption by a very efficient up-converted emission is reported for ${\mathrm{Ho}}^{3+}$ in Ca${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, and Cd${\mathrm{F}}_2$ with both cw- and pulse-laser excitations. The two-photon excitation spectra are found to be highly structured and consist of two bands: The band $A$ is excited by the dye-laser photons of frequencies 15 400-15 700 ${\mathrm{cm}}^{-1\mathrm{}}$: The band $B$ is excited by the dye-laser photons of frequencies 15 800-16 400 ${\mathrm{cm}}^{-1\mathrm{}}$. No one-photon absorption is observed for ${\mathrm{Ho}}^{3+}$ in the above lattices at twice these frequencies. Studies of concentration dependence, temperature dependence, and dependence on the pulse repetition rate are used for the assignment of the band. The investigation shows that the two bands $A$ and $B$ arise from two different modes of two-photon excitation. The band $A$ is assigned to arise from a sequential (stepwise) two-photon excitation ${}_{}{}^5{}_{}{}^{}I_8^{}{}_{}{}^{}\to {}_{}{}^5{}_{}{}^{}F_5^{}{}_{}{}^{}\to {}_{}{}^5{}_{}{}^{}D_2^{}{}_{}{}^{}$. The band $B$ is assigned to arise from the direct two-photon absorption ${}_{}{}^5{}_{}{}^{}I_8^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}L_8^{}{}_{}{}^{}$. Our results are in agreement with the prediction of the Judd-Ofelt theory of lanthanide transition intensities.