Determination of excited-state polarizabilities ofCr3+-doped materials by degenerate four-wave mixing

We have measured the degenerate four-wave-mixing signals from several ${\mathrm{Cr}}^{3+}$-doped oxide and fluoride laser crystals. The signals are predominantly generated by scattering of the input beams from a refractive index grating that is due to a spatially modulated excited-state population. From the measured reflectivity, the change in polarizability between the ground and excited states of ${\mathrm{Cr}}^{3+}$ is calculated. The polarizability change in the oxide hosts is accounted for by large-oscillator-strength charge-transfer transitions in the energy region of 50 000 ${\mathrm{cm}}^{\mathrm{-}1}$. The fluoride hosts, however, did not give measurable signal levels, and this is attributed to the lack of high-oscillator-strength transitions in this energy range. The polarizability changes in the oxide hosts are observed to depend on the relative thermal population of the ${}_{}{}^4{}_{}{}^{}\mathrm{T}_2^{}{}_{}{}^{}$ and the ${}_{}{}^2{}_{}{}^{}\mathrm{E}$ excited states. The polarizability change between the ${}_{}{}^4{}_{}{}^{}\mathrm{T}_2^{}{}_{}{}^{}$ excited state and the ${}_{}{}^4{}_{}{}^{}\mathrm{A}_2^{}{}_{}{}^{}$ ground state is found to be greater than that between the ${}_{}{}^2{}_{}{}^{}\mathrm{E}$ and the ${}_{}{}^4{}_{}{}^{}\mathrm{A}_2^{}{}_{}{}^{}$.