Dynamic modifications to the plasmon resonance of a metallic nanoparticle coupled to a planar waveguide: beyond the point-dipole limit

We show that the effects of a nearby surface on the plasmon resonance of a metallic nanoparticle of finite size can be modeled by expanding the secondary local field at the particle position in terms of an integral expansion of elementary waves that has the form of a Sommerfeld integral. In this way it is a straightforward matter to apply the Fresnel reflection coefficients of the surface to the secondary field and thus derive a corrected expression for the effective polarizability of the particle. We apply our theoretical result to particles near metal-clad and multilayer-dielectric waveguides and show that a substantial amount of the light scattered by a particle can propagate radially outward confined to the guided modes of the substrate.