Super-quadratic upconversion luminescence among lanthanide ions

The occurrence of energy-transfer upconversion (ETU) between two neighboring rare-earth ions depends on their excitation to the starting energy levels of the ETU process [1]. If both ions are of the same type and the two starting levels of the ETU process are the same, one expects the rate of ETU to be a quadratic function of the population density of this starting level. This quadratic dependency can be tested experimentally by measuring, upon the same pump conditions, the luminescence-decay curves of direct emission from the metastable electronic state, in which ETU originates, and of upconversion luminescence emitted from a higher-energy electronic state that is populated by the ETU process [2].