Calculation of the electric-field enhancement at nanoparticles of arbitrary shape in close proximity to a metallic surface

An axis-symmetrical problem of light diffraction on a nanometer-sized particle placed in arbitrary distance close to a surface is solved based on Maxwell's equations. Complex dielectric functions for the particle and the surface are taken into account. By applying the Green function method, the initial Maxwell equations are reduced to an equivalent system of integral equations. The boundary element method permits one to transform these to a linear system of equations and to solve it by the Gaussian method. In this paper metallic spheres, prolate ellipsoids, and conical bodies of arbitrary size, placed in vacuum and near a metallic surface are considered. Enhancement factors of the electric field of these bodies consisting of Na, Ag, Au, and Cu are calculated surface averaged and at the poles. Large field enhancement factors (up to several hundred times) were indeed observed for these metals. It is shown that the presence of the metallic surface results in an additional field enhancement which is strongly dependent on the apex shape of the bodies.