Phonon spectroscopy. II. Spectral, spatial, and temporal evolution of a phonon pulse

A vibronic sideband spectrometer has been used to determine the spectral, spatial, and temporal evolution of a phonon distribution propagating in a crystal of Sr${\mathrm{F}}_2$:${\mathrm{Eu}}^{2+}$. Spectral and spatial evolution depends strongly on the frequency dependence of phonon scattering at the ${\mathrm{Eu}}^{2+}$ probe ions. The mean free path of phonons in the frequency range of 1-4 THz is found to vary from ${10}^{-3\mathrm{}}$ to ${10}^{-4\mathrm{}}$ mm. The temporal evolution is strongly influenced by anharmonic processes. The effective lifetime for phonons of frequency from 1 to 3 THz is found to be of the order of microseconds.