Fluorophore-metallic surface theory

Gersten, J. (2005] Theory of fluorophore-metallic surface interaction, in Topics in Fiuorescence Spectroscopy, Volume 8 Radiative Decay Engineering (ed. by Geddes, C. D., and Lakowicz, J. R., Springer), New-York. 

The preceding chapter showed that many different processes have to be considered if one would like to fully understand the interactions between a fluorophore and a nanostructured metallic template. Depending on the distance regime, classical image theory, electrodynamic theory, nonlocal effects or even wave functions of conduction band electrons leaking out of the metal surface have to be considered. Furthermore, each of the theories gives different results for fluorophores oriented perpendicular or tangential to the metallic surface. Different situations are also expected when either the absorption spectrum or the emission spectrum of the fluorophore overlaps with the plasmon... 

The two above features which modify the simplest theory extend the range of distances z between the fluorophore and the surface over which the results remain valid, from a minimum of several hundred nanometers without the modifications to less than ten nanometers with them. Those two features are incorporated into the results displayed here. Other refinements, not included here, involve consideration of energy transfer to electron-hole pairs (for metals only at z < 10 nm) and nonhomogeneous atomic field effects (z<0.25 nm). We first assume that the intrinsic quantum yield is 100% then we will modify that assumption. 

It should be pointed out that both, the reflectivity curve R(0), as well as, the angular distribution of the optical field intensity Is(9) are described by Fresnel s equations, i.e., can be calculated based on Maxwell s theory of such a layered architecture. Once R(6) is calculated by using the dielectric functions and the thicknesses of the involved materials (prism, metal layer, functional interfacial binding matrix, dielectric superstrate) the optical intensity and its angular dependence ls(0) can be calculated without any additional free parameter. It is important to keep in mind that for fluorescence spectroscopy with surface plasmon excitation it is the optical intensity Ij (and its angular dependence) that controls the excitation process of the fluorophores. 

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