Anomalous power dependence of sensitized upconversion luminescence

The expected excitation power dependencies for any upconversion emission band of an acceptor ion is investigated theoretically when the excitation takes place on a sensitizer ion and subsequent energy transfer upconversion from the sensitizer to the acceptor ion is exclusively responsible for the excitation of the acceptor ion. Under these limitations it is shown that emission from a state that requires $k$ energy transfer upconversion steps will have a slope of $k$ in the low-power regime when the luminescence intensity is plotted in a double-logarithmic representation versus absorbed pump intensity. In the high-power regime, any emission band will show a slope of 1, irrespective of the number of energy transfer steps from the sensitizer to the acceptor ions that are involved. The theoretical results are verified experimentally by data on three different inorganic systems with different types of sensitizer and acceptor ions: rare earth (RE) ions as well as transition metal (TM) ions. The active ions in the systems that are studied experimentally are RE/RE, RE/TM, and TM/TM, where the first dopant indicates the sensitizer ion and the second dopant indicates the upconverting ion. These different classes of sensitizer and upconverter ions all agree with the theoretical predictions put forward by the model. Thus providing confidence in the applicability (within the boundary conditions put forward here) of the model described.