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In this study, we systematically investigate the decay characteristics of upconversion luminescence (UCL) under anti-Stokes excitation through numerical simulations based on rate-equation models. We find that a UCL decay profile generally involves contributions from the sensitizer’s excited-state lifetime, energy transfer and cross-relaxation processes. It should thus be regarded as the overall temporal response of the whole upconversion system to the excitation function rather than the intrinsic lifetime of the luminescence emitting state. Only under certain conditions, such as when the effective lifetime of the sensitizer’s excited state is significantly shorter than that of the UCL emitting state and of the absence of cross-relaxation processes involving the emitting energy level, the UCL decay time approaches the intrinsic lifetime of the emitting state. Subsequently, Stokes excitation is generally preferred in order to accurately quantify the intrinsic lifetime of the emitting state. However, possible cross-relaxation between doped ions at high doping levels can complicate the decay characteristics of the luminescence and even make the Stokesexcitation approach fail. A strong cross-relaxation process can also account for the power dependence of the decay characteristics of UCL.
The frequency-domain (FD) method provides an alternative to the commonly used time-domain (TD) approach in characterizing the luminescence kinetics of luminophores, with its own strengths, e.g., the capability to decouple multiple lifetime components with higher reliability and accuracy. While extensively explored for characterizing luminophores with down-shifted emission, this method has not been investigated for studying nonlinear luminescent materials such as lanthanide-doped upconversion nanoparticles (UCNPs), featuring more complicated kinetics. In this work, employing a simplified rate-equation model representing a standard two-photon energy-transfer upconversion process, we thoroughly analyzed the response of the luminescence of UCNPs in the FD method. We found that the FD method can potentially obtain from a single experiment the effective decay rates of three critical energy states of the sensitizer/activator ions involved in the upconversion process. The validity of the FD method is demonstrated by experimental data, agreeing reasonably well with the results obtained by TD methods.