Super-quadratic upconversion luminescence among lanthanide ions

We explore the arguably most fundamental aspect of energy-transfer upconversion (ETU), namely the dependence of upconversion luminescence from a higher-energy level, following ETU excitation from a metastable lower-energy level, on direct luminescence from that metastable level. We investigate ETU among neighboring Nd³⁺ ions in single crystals of GdVO₄ and LaSc₃(BO₃)₄ with different doping concentrations by measuring, after short-pulse laser excitation with different pump energies, the infrared luminescence decay from the metastable ⁴F_3/2 level and the yellow upconversion luminescence decay from the ⁴G_7/2 level. We observe a highly super-quadratic dependence of upconversion on direct luminescence intensity. We conclude that the commonly assumed quadratic law of ETU, as proposed by Grant's model and frequently employed in rate-equation simulations, is inadequate to the description of ETU processes. Whereas Zubenko's model, which considers a finite migration rate, provides significantly better fits to the experimental luminescence-decay curves, also this model cannot accurately reproduce the measured decay curves, partly because it does not take the non-homogeneous distribution of active ions into account.

Statistical approaches to the transient populations and to the macroscopic energy transfer rate for the upconversion phenomenon in monodoped amorphous solid

In this article, statistical approaches to the first and the second excited state transient populations and to the temporal macroscopic energy transfer rate for the upconversion process in amorphous solid generic systems monodoped with trivalent lanthanide ions are reached. The plots of the expressions show general tendencies reported in the literature. The derivation and the analysis of the formalism allowed us to fulfill our main objective, that is, to make a theoretical study about the microscopic and statistical mechanisms present in the phenomenon and their relation with the classic kinetic analysis. The study shows that the inclusion of the minimum possible radius between two optical centers in a solid affects the initial slopes of the decay curves of the luminescence from the intermediate state. We also corroborate that the usual treatment of experimental data using direct equations for the dynamics of the populations in laser pulsed excitation experiments falls in the mistake of not considering the temporality of the macroscopic energy transfer rate. Finally, physical explanations are formulated about this temporal behavior and about the main factors that generate the characteristic simple exponential decay loss of the luminescence from the intermediate state.