Analytical results for enhancement factor (EF) of surface enhanced Raman spectroscopy (SERS) for two metallic spheres and nano-shells

Interactions between symmetric two metallic spheres and an electromagnetic (EM) field polarized in the axis are described. Spherical symmetries of present systems exploited by use bi-spherical coordinates. Boundary conditions applied, which assume a very large negative value for dielectric constant special metals. The EM small gaps (in hotspots) is amplified many orders magnitude relative to external field. Analytical results maximal enhancement factor surface enhanced Raman spectroscopy nano-shells obtained as function various parameters. calculations based on potentials derived using electrostatic model, valid particles.