Relaxation of 29-cm−1phonons in ruby

The relaxation of resonant 29-${\mathrm{cm}}^{\mathrm{-}1}$ phonons trapped in a laser-excited cylinder of submillimeter diameter is investigated under the conditions of modulated pumping in ruby of 130, 700, and 2500 at. ppm ${\mathrm{Cr}}^{3+}$ at 1.5 K. The decay time $T_{\mathrm{eff}}$ of the 2Ā${(\mathrm{}}^2$E) population, which is a measure of the phonon relaxation time, appears to depend on the metastable population $N^{\mathrm{*}}$ and the cylinder diameter L as the product $N^{\mathrm{*}}$L only, establishing boundary-limited phonon decay. At $N^{\mathrm{*}}$L below 5×${10}^{15}$ ${\mathrm{cm}}^{\mathrm{-}2}$, pure spatial diffusion prevails.