Effect of the Euclidean dimensionality on the energy transfer up-conversion luminescence

Abstract

An analytical model to study the influence of the Euclidian spatial dimensionality of the medium on the transient luminescence produced exclusively by up-conversion energy transfer interaction among randomly distributed optical centers is developed. The model is intrinsically coherent in terms of the coordinated behavior of the relevant states luminescence and of the macroscopic energy transfer rate, and shows agreement with expected general trends. Its predictions indicate that, under comparable conditions, the rate of the up-conversion follows the 1D> 2D > 3D tendency at initial times, but that this conduct reverses at some (concentration and pump power independent) time point, resulting in a higher total up-conversion luminescence for larger dimensionalities. The model predicts that under continuous excitation regime higher up-conversion luminescence is expected for smaller Euclidean dimensions. Finally, the study also shows that up-conversion luminescence is very sensitive to the value of the minimum possible distance of optical centers mutual approach, Rm, especially in low-dimensional medium, and not considering it -as traditionally occurs in the analysis of other energy transfer processes- induces to inaccuracies in the observables description.