Evanescent coupling between a Raman-active molecule and surface plasmons in ensembles of metallic nanoparticles

A theory of surface-enhanced Raman scattering (SERS) is developed based on the coupling between an ensemble of nanoparticles supporting localized surface-plasmon resonances (LSPRs) and a Raman-active molecule. The molecule is modeled by a dielectric particle supporting many different modes that represent its response to an applied electric field. It is shown that the modes can be modified to include the effects of the vibrational resonances of the molecule that lead to Raman scattering and the associated Stokes and anti-Stokes frequency shifts. The same theory can describe the LSPR in an ensemble of metallic nanoparticles of arbitrary shape which leads to a description of the coupling of the evanescent electric fields between the Raman-active molecule and the surface plasmons. The theory predicts the magnitudes of the SERS observed experimentally and can model many of the known Raman effects associated with the LSPR resonances in nanoparticles, including the dependence of the enhancement on the shape and geometry of the nanoparticles, and the effects of the polarization of the incident light. An analytical expression is derived for the enhancement associated with a nanoparticle ensemble that exhibits two degenerate modes and it includes an interference effect arising from the coupling between the modes and the Raman scattering from the molecule.