Characterization of clusters in rare earth-doped fibers by transmission measurements

We show theoretically that the absorption saturation behavior of clustered rare earth-doped fibers depends strongly on the percentage and/or the size of the clusters, which can form the basis for a simple diagnostic tool. When applied to published transmission measurements in Er-Al-P-doped fibers, this technique indicates low percentages of clusters in fibers co-doped with P and/or Al. In Nd-doped fibers with no co-dopants, it shows the presence of a high percentage of large clusters. Estimates of the time constant and strength of the cross relaxation process in Nd and Er clusters are inferred from these measurements