Plasmonic enhancement of Förster energy transfer between two molecules in the vicinity of a metallic nanoparticle: Nonlocal optical effects

Abstract

The problem of F\"orster resonance energy transfer (FRET) between two molecules in the vicinity of a metallic nanoparticle such as a nanoshell is studied within a phenomenological model which takes into account the nonlocal optical response of the metal. This model allows for arbitrary locations and orientations of the two molecular dipoles with respect to the metal particle which can be of ultrasmall sizes $(<10\text{ }\text{nm})$ and for which nonlocal effects are of high significance. In particular, for the nanoshell case, the molecules can be located both outside, both inside, or one inside and one outside the shell. Also, the case with a metallic spherical particle studied mostly in the literature can be obtained in the limit of zero inner radius for the nanoshell. Particular focus will be on the enhancement of this FRET process due mainly to the surface plasmon excitation of the free metallic electrons, and the nonlocal effects on this will be studied with reference to a number of factors including the molecular locations and orientations, the transition frequency of the donor and acceptor;\dots{}etc. Numerical results show that the resonances in the enhanced FRET rate will be dominated by the multipolar bonding and antibonding cross-coupled plasmonic modes of the nanoshell; and that the nonlocal effects will generally lead to blueshifted resonances, as well as diminution of the enhancement for the low-frequency portions of both modes. Such information will be useful for future application of plasmonic enhanced FRET using metallic particles of ultrasmall sizes.