Optical Homogeneous Linewidths of ${\mathrm{Pr}}^{+}$ in Be${\mathrm{F}}_2$ and Ge${\mathrm{O}}_2$ Glasses

Optical homogeneous linewidths of the ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}H_4^{}{}_{}{}^{}\mathrm{}\left(1\right)\mathrm{}$ transition of ${\mathrm{Pr}}^{3+}$ in Be${\mathrm{F}}_2$ and Ge${\mathrm{O}}_2$ glasses reveal an anomalously smooth quadratic dependence on temperature from 8 to 300 K. The low-temperature behavior is consistent with a recent model of Lyo and Orbach involving an interaction with a single two-level system but the smooth quadratic behavior at all temperatures has deep consequences for the relative roles played by the ordinary phonons and the two-level system in line broadening.