Four-wave-mixing techniques were used to establish and probe population gratings of
Cr3+ 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
Cr3+ 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
Cr3+ 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
4T2 and
2E levels, but the effects of scattering from a grating of ions in inversion sites is much stronger for
4T2 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
4T2 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
2E level the dephasing is dominated by dephasing processes associated with the inhomogeneous linewidth of the transition.
Laser-induced grating measurements were made as a function of laser power and write beam crossing angle for various temperatures between 10 and 300 K on Cr3+ ions in Gd3Ga5O12 (GGG), Gd3Sc2Ga3O12 (GSGG), and GGG mixed with Ca, Mg, and Zr ions. Population gratings were produced in the Cr3+ ions, and the diffusion coefficient describing energy migration among the Cr3+ ions was determined from the grating decay rate. The energy migration was found to increase as the temperature was raised for GGG and to decrease with decreasing temperature for GSGG. This difference is attributed to the differences in the crystal field splittings of the excited states in the two hosts. Enhanced energy diffusion was observed in the multiply doped GGG sample. Contributions to the laser-induced gratings from absorption and dispersion changes were determined, and this was used to provide information on radiationless relaxation and excited state absorption processes. For long writing times, long-lived changes in the refractive index were observed and attributed to optically induced color centers.
Four-wave-mixing techniques were used to establish and probe population gratings of
Cr3+ ions in both mirror and inversion sites in
BeAl2O4:
Cr3+ 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\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$
cm2?${\mathrm{c}}^{\mathrm{\ensuremath{-}}1}$ at 6 K.
The influence of spatial migration of excitation among neighboring Er3+ ions on the dynamics of population grating formation in Er-doped optical fibers is reported. The effect manifests itself in an additional increment in the grating formation rate compared with the fluorescence growth rate observed for the same spatially uniform average light power. The experiments, performed at lambda=1549 nm in the configuration of transient two-wave mixing with two similar single-mode Er-doped fibers with significantly different erbium concentrations (approximately 640 and approximately 5600 parts in 10(6)), demonstrated the essential contribution of this effect to the grating formation rate in the latter fiber. The evaluated diffusion coefficient proved to be approximately 2.3 x 10(-9) cm2/s, which ensures effective migration of the excitation by approximately 48 nm, i.e., by approximately 18 average inter-ion distances in this fiber.