Rate Equations for Clusters in Rare Earth-Doped Fibers

Abstract

We present two rate equation models describing the effects of clusters on rare earth-doped silica fibers. The first one, valid for my cluster size, describes the interaction between clustered ions (cross relaxation) as a nonradiative process. The second model, valid only for large clusters, describes it as a cooperative upconversion process. These models are applied to both Nd- and Er-doped fibers. In the limit of large clusters, the two models predict comparable behavior, which provides the heretofore missing relationship between these two formalisms. Increasing the cluster size is found to significantly reduce the steady-state population of the metastable level and to introduce an increasingly faster and stronger fast component in its relaxation. The model is used to quantify the effect of clusters on the gain of fiber amplifiers and the threshold of fiber lasers. These results can be directly applied to study the impact of clusters of any size on doped fiber devices, as well as cooperative upconversion in highly doped materials.