Abstract

A model of an ${\rm{E}}{{\rm{r}}^{3 +}}/{\rm{Y}}{{\rm{b}}^{3 +}}$ co-doped glass gain medium is proposed. The system of rate equations taking into account a minimum set of processes required to describe experimental data was built. As a result, a moderate number of fitting parameters is used, and thereby the model reliability is increased. For the populations of the energy levels of ${\rm{E}}{{\rm{r}}^{3 +}}$ and ${\rm{Y}}{{\rm{b}}^{3 +}}\;{\rm{ions}}$, analytic expressions were obtained, as well as for the gain factor of the medium. The model was validated by a series of measurements of gain in ${\rm{E}}{{\rm{r}}^{3 +}}/{\rm{Y}}{{\rm{b}}^{3 +}}$ fiber amplifiers of different lengths at varying pump power. Such parameters of the model were found to fit the experimental data with an account of the spatial inhomogeneity of the pump power along the fiber. The maximum inversion of erbium ion population at high pump powers was analytically expressed, which describes the “bottleneck” effect. The power required to pump the fiber along the entire length was found.

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