Sub-quadratic Dependence of Visible Upconversion on Infra-red Direct Luminescence Decay Owing to Static Energy-transfer Upconversion

We investigate the influence of active-ion distributions on energy-transfer upconversion (ETU) in a static upconversion regime in which energy migration is inactive and the active local environment is important for the dynamics of ETU. Neodymium is used as the probe ion. In oxide and fluoride host materials, Nd3+ possesses only one metastable excited state (4F3/2) from which strong ETU occurs. The levels excited by ETU emit weak visible luminescence, possess short (multiphonon-quenched) lifetimes and, therefore, react almost instantaneously on the dynamics of the metastable level. The chosen host material lanthanum scandium borate [1] possesses large distances between the active-ion sites and ETU occurs in the static regime [2,3]. After excitation of the metastable level, we measure concentration-dependent (10, 25, 50, 100 at.%) infra-red (direct) and visible (upconversion) luminescence decay. The upconversion luminescence decays neither quadratically with respect to the direct luminescence as would be expected from a usual rate-equation model-even if two classes of isolated (non-ETU) and clustered (ETU) ions are assumed [4]-nor exponentially as would be expected from a dimer model [5]. The decay curves are described in a multimer model that takes into account the real structure of the host material and assumes centers with different numbers of active nearest neighbors. With decreasing excitation at longer decay times, its solution converges to the solution of a quasi-dimer model.