Using a stochastic model, we calculate the temperature dependence of the homogeneous linewidth and the two-pulse photon-echo decay rate of optically active impurities in glasses. The theory applies to the low-temperature regime T\ensuremath{\lesssim}10 K, where it is assumed that the dephasing arises from an elastic dipole interaction of the impurity with an array of thermally excited tunneling systems. Averaging over the tunneling parameters and using relaxation rates appropriate to vitreous silica, we find that the photon-echo decay rate varies as
T1.1 and the homogeneous linewidth as
T1.2 for 0.1\ensuremath{\le}T\ensuremath{\le}1 K, assuming a constant density of states for the tunneling systems. Both the photon-echo amplitude and the optical dipole-moment correlation function decay exponentially in time. The rates, however, are different, with a ratio of photon-echo dephasing time to optical-absorption dephasing time of 6.9 at T=1 K, assuming a constant density of states. The relation of our results to various experimental studies is discussed.
The homogeneous optical dephasing times (T2) and the non-photochemical hole burning (NPHB) linewidths of resorufin in glycerol glass are reported from 1.1 to 25.5 K. At low temperature, the linewidths obtained from NPHB are substantially wider than the linewidths (1/πT2) obtained from photon echo measurements, but the two become equal at high temperatures. The extra broadening of the NPHB is found to increase as T0.8. A model of homogeneous dephasing including both two-level system and pseudolocal mode contributions is successful over the entire temperature range.