Generalised analytical model of the transition power densities of the upconversion luminescence and quantum yield

Beam-profile compensation for quantum yield characterisation of Yb-Tm codoped upconverting nanoparticles emitting at 474 nm, 650 nm and 804 nm

Upconverting nanoparticles (UCNPs) have found widespread applications in biophotonics and energy harvesting due to their unique non-linear optical properties arising from energy transfer upconversion (ETU) mechanisms. However, accurately characterising the power density-dependent efficiency of UCNPs using the internal quantum yield (iQY) is challenging due to the lack of methods that account for excitation beam-profile distortions. This limitation hinders the engineering of optimal UCNPs for diverse applications. To address this, this work present a novel beam profile compensation strategy based on a general analytical rate-equations model, enabling the evaluation of iQY for ETU processes of arbitrary order, such as ETU2, ETU3, and beyond. The method was applied to characterise the ETU2 and ETU3 processes corresponding to the main emission peaks (474 nm, 650 nm, and 804 nm) of a Yb-Tm codoped core-shell β-UCNP. Through this approach, the transition power density points (which delimit the distinct non-linear regimes of the upconversion luminescence (UCL)), and the saturation iQY values (which are reached at high excitation power densities above the transition points) were determined. The ETU2 process exhibits a single transition power density point, denoted as ρ2, while the ETU3 processes involve two transition points, ρ2 and ρ3. By compensating for the beam profile, we evaluate the iQY of individual lines across a wide dynamic range of excitation power densities (up to 105 W cm-2), encompassing both non-linear and linear regimes of UCL. This study introduces a valuable approach for accurately characterising the iQY of UCNPs, facilitating a deeper understanding of the upconversion and its performance. By addressing excitation beam-profile distortions, this method provides a comprehensive and reliable assessment of the power density-dependent iQY. The results highlight the applicability and effectiveness of this beam profile compensation strategy, which can be employed for a wide range of UCNPs. This advancement opens new avenues for the tailored design and application of UCNPs in various fields, especially for biophotonics.