Absolute quantum yield for understanding upconversion and downshift luminescence in PbF$_{2}$:Er$^{3+}$,Yb$^{3+}$ crystals

The search for new materials capable of efficient upconversion continues to attract attention. In this work, a comprehensive study of the upconversion luminescence in PbF$_{2}$:Er$^{3+}$,Yb$^{3+}$ crystals with different concentrations of Yb$^{3+}$ ions in the range of 2 to 7.5 mol% (Er$^{3+}$ concentration was fixed at 2 mol%) was carried out. The highest value of upconversion quantum yield (ϕ$_{UC}$) 5.9% (at 350 W cm$^{-2}$) was found in the PbF$_{2}$ crystal doped with 2 mol% Er$^{3+}$ and 3 mol% Yb$^{3+}$. Since it is not always easy to directly measure ϕ$_{UC}$ and estimate the related key figure of merit parameter, saturated photoluminescence quantum yield (ϕ$_{UCsat}$), a method to reliably predict ϕ$_{UCsat}$ can be useful. Judd–Ofelt theory provides a convenient way to determine the radiative lifetimes of the excited states of rare-earth ions based on absorption measurements. When the luminescence decay times after direct excitation of a level are also measured, ϕ$_{UCsat}$ for that level can be calculated. This approach is tested on a series of PbF$_{2}$:Er$^{3+}$,Yb$^{3+}$ crystals. Good agreement between the estimates obtained as above and the directly experimentally measured ϕ$_{UCsat}$ values is demonstrated. In addition, three methods of Judd–Ofelt calculations on powder samples were tested and the results were compared with Judd–Ofelt calculations on single crystals, which served as the source of the powder samples. Taken together, the results presented in our work for PbF$_{2}$:Er$^{3+}$,Yb$^{3+}$ crystals contribute to a better understanding of the UC phenomena and provide a reference data set for the use of UC materials in practical applications.