Intensity-dependent photon-echo relaxation in rare-earth-doped crystals

Photon-echo-relaxation measurements made on the ${}_{}{}^3{}_{}{}^{}\mathrm{H}_4^{}{}_{}{}^{}$ ${\mathrm{-}}^3$ ${\mathrm{P}}_0$ transition of 0.01 at. % ${\mathrm{Pr}}^{3+}$:YAG (where YAG represents yttrium aluminum garnet), ${}_{}{}^3{}_{}{}^{}\mathrm{H}_4^{}{}_{}{}^{}$ ${\mathrm{-}}^1$ ${\mathrm{D}}_2$ transition in 0.1 at. % ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_3$, and ${}_{}{}^7{}_{}{}^{}\mathrm{F}_0^{}{}_{}{}^{}$ ${\mathrm{-}}^5$ ${\mathrm{D}}_0$ transition in 0.25 at. % ${\mathrm{Eu}}^{3+}$:${\mathrm{YAlO}}_3$ show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in ${\mathrm{Pr}}^{3+}$:YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring ${\mathrm{Pr}}^{3+}$ ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.