Abstract
A self-similar system of recurrent equations was used for calculating the dynamics of the emission decays of rare-earth ion-doped photoluminescent nanoparticles. The proposed approach provides a smooth transition between different descriptions of all kinetic photoluminescence (PL) data and does not imply a solution through the convolution integral equation.The suggested method introduces a transition mechanism based on elementary mapping of the proposed hierarchical system. The main equation of the system contains two changeable parameters: one of these can be considered the decay value. The calculated dependence of the PL decay time is presented with a division into regions with different asymptotes.
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