Calculation of tip enhanced Raman scattering caused by nanoparticle plasmons acting on a molecule placed near a metallic film

Abstract

Light scattering in an axially symmetric composite system of a nanoparticle, an oscillating dipole and a metal film (covering a dielectric support) is considered. Nanoparticle and dipole are placed on the axis of symmetry. The axially oriented dipole is situated between film and nanoparticle. The field-enhancement factor at the position of the dipole and dipole radiation is calculated on the basis of Maxwell's equations, reduced by Green's functions to a system of boundary integral equations. The total enhancement of the light scattering, which is a product of the enhancement of the field intensity and the dipole radiation, depends on many parameters: the wavelength of light, the metal permittivity, film thickness, geometry of the nanoparticle, angle of incidence of the laser beam, but most strongly on the distance between the nanoparticle and film surface. According to our calculations, the total enhancement factor for Raman radiation can reach huge values in the order of ${10}^{10}--{10}^{11}$. The angular spectrum of the radiating dipole is derived and the accuracy of calculations is checked by the optical theorem of reciprocity.