Excitation back transfer in a statistical model for upconversion in Er-doped fibres

Abstract

We report a new analytical method to evaluate the accuracy of a statistical model of the migration assisted upconversion in Er-doped fibres. Unlike the mean-field approach to the excitation back transfer which was used in a previous statistical model, we use a new approximation accounting for the variance of population of the first excited level. Such an approach presents more realistic physical description of the excitation - emission processes in heavily-doped Er-based fibres. Implementing these results, we find that the accuracy of upconversion rate calculations is within 13% if the concentration of erbium ions is smaller than the critical one.