An approach based on the theory of McCumber is described to calculate the emission cross sections of a transition of the rare-earth ions in glass. It overcomes the drawback of the theory that the knowledge of the electronic structures of the rare-earth ions is usually demanded to determine the emission cross section. Instead, only the measurement of the absorption spectra of the ions is necessary. The Judd-Ofelt theory is used to determine the energy parameters. The emission cross sections of Tm3+, Er3+ and Yb3+ in fluoride glasses are calculated. The results are consistent with those reported before, which indicates the method is simple and quite effective.
"Evaluation of cross sections of rare-earth ions in glass", Proc. SPIE 3942, Rare-Earth-Doped Materials and Devices IV, (13 April 2000); doi: 10.1117/12.382866; https://doi.org/10.1117/12.382866