Mathematical model of fluorescence processes accounting for the quantum effect of non-local screening

On the basis of the Discrete Sources Method, a mathematical model has been developed that enables to consider the fluorescence process in the presence of a plasmonic structure accounting for the nonlocal screening effect. It has been shown that the fluorescence quantum yield can be represented analytically. The influence of the effect on the quantum yield and the enhancement factor of fluorescence were investigated depending on the geometry of the plasmonic structure. It has been demonstrated that accounting for the non-local screening effect leads to a blue shift in the position of the maximum and a decrease in the amplitude of a fluorescence enhancement factor.