Different mechanisms of nonlinear quenching of luminescence

An analytic solution for the kinetics of nonlinear (upconversion) luminescence quenching in solid-state laser materials and other luminophosphors is obtained under the assumptions of hopping character of migration-assisted energy transfer and finite excitation lifetime. It is shown how the observables of the luminescence experiment depend on microparameters of the energy transfer and ion concentrations. The critical ion concentrations separating different upconversion regimes are determined. The predictions of the theory are in agreement with experimental observations reported in the literature.