Homogeneous line width of rare-earth-doped glasses for levels in a Stark level ladder: A new simple rule

Concentrating on higher Stark states in multiplet ladders of lanthanide-doped glasses, we show that at 10 K, the homogeneous widths along Stark ladders vary quasi-linearly with the energy position in the ladder. Assuming that the mechanisms creating the homogeneous widths are first-order processes, either direct processes or two-phonon non-radiative transitions, the observed behavior is simply explained by the fact that energy separations between Stark levels for usual glasses are less, i.e., not far from kTD, the Debye energy. This in turn provides quasi-equal phonon transition probabilities between individual Stark states. A simple theoretical relationship is derived and compared with experiments.