Interaction of molecules with localized surface plasmons in metallic nanoparticles

Abstract

A theory is developed to model the interaction of molecules with the localized surface plasmon resonances in metallic nanoparticles that are used for single-molecule sensing. Each molecule is represented by a simple point-like dipole based on a dielectric sphere, taken in the limit of a small radius. The surface-charge and surface-dipole eigenfunctions of a small spherical particle are represented analytically and it is shown that these are natural extensions of the electrostatic coupling theory of Davis [Phys. Rev. B 79, 155423 (2009)]. The effect of a molecule on the surface plasmon resonances is described in terms of an effective background permittivity and formulas for the frequency and ..