Non-isolated pair model for upconversion energy transfer processes

Abstract

The description of the temporary evolution of upconversion energy transfer processes in solid samples including doped luminescent centers is revised using a simple but non-restrictive pair model. The formalism is related to upconversion processes between a collective of donor and acceptor optical centers, and leads to analytic expressions for the temporary behavior of the emission intensities from the intermediate excited states and the up converted excited state. From a microscopic viewpoint, the results of the model are compared with numerical solutions of the system of differential equations and with those obtained from kinetic type equations, showing the limits of directly using the latter in the analysis of upconversion processes. The proposed model makes it possible to obtain average macroscopic solutions, explicitly dependent on the concentration of dopant luminescent centers in the crystalline lattice, and permits an adequate prediction of the shapes of the decay curves. It would improve the determination of the upconversion energy transfer rates from experimental data.