Four-wave-mixing measurements of energy migration and radiationless relaxation processes in alexandrite crystals

Four-wave-mixing techniques were used to establish and probe population gratings of ${\mathrm{Cr}}^{3+}$ ions in both mirror and inversion sites in ${\mathrm{BeAl}}_2$ ${\mathrm{O}}_4$:${\mathrm{Cr}}^{3+}$ crystals as a function of temperature between about 6 and 300 K. The four-wave-mixing signal intensity and decay rate were monitored as a function of the crossing angle of the laser ‘‘write’’ beams. The variation of the signal intensity with crossing angle is explained theoretically with use of a model based on the interaction between the laser and a two-level atomic system. Theoretical fits to the results provide information concerning the relative importance of the absorption and dispersion contributions to the signal, and the dephasing time of the atomic system. The latter is found to be 2.2 psec for the mirror site ions and 80 psec for the inversion site ions. The signal decay rate of the inversion site ions was found to be independent of crossing angle at all temperatures, while the signal decay rate for ions in the mirror site increased with increasing crossing angle at temperatures below about 150 K. This indicates the presence of long-range energy migration, and the diffusion coefficient describing this process was found to increase to about 4.2×${10}^{\mathrm{-}7}$ ${\mathrm{cm}}^2$?${\mathrm{c}}^{\mathrm{-}1}$ at 6 K.