Unraveling Upconversion Dynamics Through Laplace Transforms

The study of upconversion dynamics at the nanoscale still presents some challenges. Characterization of such dynamics through rate equation models represents an invaluable tool, although affected, as any model, by some drawbacks. The resolution of a complete rate equation model can be computationally heavy, even more so if the rate equation parameters are calculated based on the actual ionic distribution of the dopant ions, rather than obtained as average macroscopic values. The obtained parameters, even if indicative of a certain mechanism, do not explain the effect of each excitation parameter on the excited‐state population. Considering the tunability of current lasers in terms of pulse width and repetition rate, a clear description of their effect on the upconversion mechanism is still missing, as the literature provides some differing explanations. Here, we prove the effect of these parameters on the dynamics of the Yb ³⁺ ions, the most employed sensitizer in upconversion luminescence, by comparing our results with literature data. The proposed approach provides a direct mathematical justification of the effect of the exciting source on the sensitizer's dynamics, extended to a sensitizer–activator system. The reported results have the potential to represent a lighter computational tool for a full understanding of upconversion dynamics at the nanoscale.