Hyperfine structures of praseodymium ions in solids using stimulated-photon-echo modulation

We report a systematic study of the stimulated-photon-echo relaxation on the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ ${\mathrm{-}}^3$ ${\mathit{H}}_4$ transition of ${\mathrm{Pr}}^{3+}$:${\mathrm{LaF}}_3$ and the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ ${\mathrm{-}}^3$ ${\mathit{H}}_4$ and ${}_{}{}^1{}_{}{}^{}$ ${\mathit{D}}_2$ ${\mathrm{-}}^3$ ${\mathit{H}}_4$ transitions of ${\mathrm{Pr}}^{3+}$:YAG (yttrium aluminum garnet). The stimulated-echo intensity is measured as a function of the delay between the first and the second pulses and the delay between the second and the third pulses. The stimulated-echo relaxation is modulated by the hyperfine interaction in the ground and the excited electronic states. We find that the modulation patterns can be quite distinct from those for two-pulse photon-echo relaxation and give complementary information about the hyperfine structures. We use the density-matrix theory of stimulated-photon-echo modulation, and the resulting simulation shows satisfactory agreement with the experimental data.