Theory of donor fluorescence governed by discrete energy transfers between rare-earth ions in glasses

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We have derived the macroscopic response theory of donor fluorescence in rare-earth glasses by calculating a statistical expectation of individual energy transfers from energy donors to energy acceptors. The distribution functions of energy acceptors were classified by their distances of the first-nearest neighbor through the fourth-nearest neighbor to donors. The role of the individual energy transfers was found to be important for the nonlinearity of the donor fluorescence. The experimental results of donor fluorescence of Tb3+ ions were well fitted both to the nonexponential decays caused by pulsed excitation and to the concentration quenching of fluorescence with a coupled parameter set of a critical transfer distance and an energy relaxation rate of the acceptor. The energy transfer depended closely on r-8 for the distance r from Tb3+ to Nd3+ ions or among Tb3+ ions in glasses. In this model the energy transfers from a donor to the first- and the second-nearest-neighbor acceptors was enough to explain the experimental results.