Dissolution of rare-earth clusters inSiO2by Al codoping: A microscopic model

Abstract

A microscopic model for the incorporation of Er 2 O 3 units in silica codoped with Al 2 O 3 is presented. The model assumes that Er clustering is counteracted by the formation of Er-Al complexes in which each Er ion provides valence compensation for three substitutional Al ions. These complexes are investigated by theoretical calculations within the framework of density functional theory. Bond lengths and coordination numbers for Er and Al are in good agreement with results from extended x-ray absorption fine structure spectroscopy. The total energy of the Er-Al complexes is slightly higher than that of the phase-separated state, but thermodynamic arguments show that they are favored by entropy considerations and will prevail for sufficiently high values of the Al/Er ratio and a fictitious temperature parameter controlling the entropy contribution to the free energy of the glass. An analysis of the Kohn-Sham eigenvalue spectrum and the electrostatic potential around the dissolved Er ion provides only limited support for the approximations commonly made in the discussion of ligand-field effects.

Molecular homogeneity in erbium-doped sol-gel waveguide amplifiers

“…Appropriate ratios when Yb and phosphorous are included are less clear. In any case, the analysis of [21] suggests that the resulting structure should be stable with further annealing at the given temperature, which is not what we find.…”

“…If we assume that the clusters have a common composition and structure, as suggested in [21], then and should remain approximately constant. If we further assume that, after the first three hours of annealing, the fractional cluster volume reaches an equilibrium, then according to (4) the scattering losses of the waveguide will increase in the third power of the cluster diameter.…”

“…Although the mechanisms are not well understood, a solvation shell model is frequently cited [20]. Aluminum co-doping has been the most studied, and recent thermodynamical analysis [21] has suggested that there is a critical value of aluminum to rare-earth ion ratio required to avoid aggregation, which depends on the rare earth concentration and moreover on the annealing temperature and time exposure. According to these observations, and the consolidation temperatures and erbium concentrations in this case, the required should be 8-10, similar to the Al:Er ratio used.…”

Multilayered Waveguides for Increasing the Gain Bandwidth of Integrated Amplifiers

“…This could be achieved by improving the performance of aluminosilicate compositions and by further optimizing the waveguide design in order to minimize the background losses, which, in this case, are high. This can be achieved by increasing the ratio of aluminum to rare earth ions in the composition, which has been known to improve the performance of Nd-doped waveguide amplifiers [13] but has also been theoretically predicted [28]. It should also be pointed out that the actual ratios of the individual layers of a laminated amplifier could act as an additional degree of freedom for tailoring the final amplifier characteristics.…”

“…This is probably due to low levels of homogeneity of the erbium ion environment. A potential increase of the aluminum content of aluminosilicate compositions to 5%-7.5% could, however, assist in the dissolution of clusters [13], [28] and result in similar homogeneity levels to those in TH4 composition. In this case, the levels of net gain that could be expected are on the order of 1.5-2 dB/cm, which are significantly higher than those so far observed for aluminophosphosilicate amplifiers.…”