Four-wave-mixing spectroscopy of Cr-doped garnet crystals

The characteristics of the four-wave-mixing signal of ${\mathrm{Cr}}^{3+}$ ions were measured for host crystals of ${\mathrm{Gd}}_3$ ${\mathrm{Sc}}_2$ ${\mathrm{Ga}}_3$ ${\mathrm{O}}_{12}$, ${\mathrm{Gd}}_3$ ${\mathrm{Ga}}_5$ ${\mathrm{O}}_{12}$, (Gd,Ca${)}_5$(Ga,Mg,Zr${)}_2$ ${\mathrm{Ga}}_5$ ${\mathrm{O}}_{12}$, and ${\mathrm{La}}_3$ ${\mathrm{Lu}}_2$ ${\mathrm{Ga}}_3$ ${\mathrm{O}}_{12}$. Signal strengths and decay times were measured as functions of laser-beam crossing angles and temperature. The results are used to determine the properties of radiationless decay and energy-transfer processes in these samples. By comparing the characteristics of the ${}_{}{}^4{}_{}{}^{}$ ${\mathit{T}}_2$ ${\mathrm{-}}^2$E radiationless relaxation process among these and previously investigated ${\mathrm{Cr}}^{3+}$-doped laser crystals, it is shown that the ratio of the intersystem-crossing relaxation rate to the internal conversion relaxation rate decreases as the strength of the crystal field of the host material decreases. The properties of energy migration among the ${\mathrm{Cr}}^{3+}$ ions in the different host materials is found to depend on the average separation of the ${\mathrm{Cr}}^{3+}$ ions, the strength of the crystal field, and the electron-phonon interactions.