Laser-induced grating spectroscopy of alexandrite crystals

Four-wave-mixing techniques were used to establish and probe population gratings of ${\mathrm{Cr}}^{3+}$ ions in alexandrite crystals at temperatures between 10 and 300 K. The results were interpreted in terms of the interaction of the laser radiation with a two-level atomic system. They provide information about the characteristics of four-wave-mixing signals for this physical situation as well as being useful in characterizing the properties of energy transfer and dephasing within the ensemble of ${\mathrm{Cr}}^{3+}$ ions. The patterns of the transient four-wave-mixing signals are consistent with a model based on the pumping dynamics of ions in the mirror and inversion crystal-field sites. The variation of the signal intensity with laser power is strongly affected by beam depletion. The characteristics of exciton migration among ${\mathrm{Cr}}^{3+}$ ions in mirror sites were determined from the results of measuring the variation of the signal decay rate with grating spacing. The temperature dependences of the ion-ion interaction rate, the exciton-phonon scattering rate, and the diffusion coefficient were determined. These are found to be essentially the same for pumping into the ${}_{}{}^4{}_{}{}^{}\mathrm{T}_2^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{E}$ levels, but the effects of scattering from a grating of ions in inversion sites is much stronger for ${}_{}{}^4{}_{}{}^{}\mathrm{T}_2^{}{}_{}{}^{}$ pumping. The dephasing times for the atomic system were found from analyzing the variation of the signal intensity with grating spacing. For pumping into the ${}_{}{}^4{}_{}{}^{}\mathrm{T}_2^{}{}_{}{}^{}$ level the dephasing is dominated by radiationless decay processes. A model is presented for the decay channel that provides a theoretical explanation for the decay process which is consistent with the measured temperature and frequency dependences of the results as well as their variation with crystal-field strength. For pumping into the ${}_{}{}^2{}_{}{}^{}\mathrm{E}$ level the dephasing is dominated by dephasing processes associated with the inhomogeneous linewidth of the transition.