Stimulated-photon-echo spectroscopy. II. Echo modulation inPr3+:YAlO3

Stimulated-photon-echo measurements as a function of both the first-to-second (τ) and the second-to-third (T) pulse separations were conducted to study the echo-modulation behavior for the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{H}}_4$ ${\mathrm{-}}^1$ ${\mathit{D}}_2$ transition of a cryogenic ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_3$ sample. When T is shorter than the excited-state lifetime ${\mathit{T}}_1$, deep echo modulations along both the τ and T axes are observed, the frequencies of which correspond to the excited-state sublevel splittings. When T exceeds ${\mathit{T}}_1$, the modulation is still observed, although only along the τ axis. A density-matrix theory is developed in a perturbative manner to explain these coherent dynamical properties. The numerically simulated three-dimensional plots of the echo intensity versus τ and T are presented, predicting quite satisfactorily the seemingly complicated experimental modulation patterns.