Modelization of lifetime measurement in the presence of radiation trapping in solid-state materials

Abstract

Radiation trapping causes significant lengthening of the measured fluorescence lifetimes in solid samples, which leads to overestimating them. Self-absorption inside solid-state samples is considerably enhanced by successive total internal reflections at the sample/air interface. A simple method for quantitative estimation of radiation trapping in solid-state materials within the frame of the Holstein-Biberman equations is presented. This method is based on the assumption that the radiation propagation follows paths with many total internal reflections; it can be applied to many resonant two-level systems such as ${\mathrm{Er}}^{3+}$-, ${\mathrm{Yb}}^{3+}$-, or ${\mathrm{Ho}}^{3+}$-doped materials. The equations are solved for a pulsed excitation localized in a finite volume inside the sample. In our modeling approach, we take into account the initial geometric population distribution and the imaging setup. We derive analytical expressions of the measured decays, which give the deformation of the measured curves compared with the ideal exponential decay. We investigate the effect of the fraction of self-trapped light on the decay modification. We then show that the ratio between the pumping volume, the collected volume, and the sample dimension changes the measured decay significantly.