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We report a new analytical approach 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 previous statistical model, we use a new approximation accounting for the variance of population of the first excited level. 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.

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