A comparison between different methods of calculating the radiative lifetime of the 4I13/2 level of Er3+ in various glasses.

A comparison between the radiative lifetimes of the 4I13/2 level of Er3+ derived from the conventional Judd–Ofelt (J–O) method and from a simple formula, that corresponds to Einstein relation for the emission probability of a two-level system, has been carried out in some typical glasses, such as germanate, phosphate, silicate, and tellurite. The uncertainties of the radiative lifetimes are evaluated using standard error analysis; it comes out that uncertainties are much larger (some tens %) when using the J–O method than with the simple formula (error less than 1%). The same simple method can be used to calculate the radiative lifetimes of other rare earth ions, such as Ho3+, Tm3+ and Yb3+.