CONFIGURATIONAL RESONANCES IN OPTICAL NEAR-FIELD MICROSCOPY - A RIGOROUS POINT-DIPOLE APPROACH

A theoretical analysis of the framework for near-field microscopy based on a microscopic description of the interaction between the dielectric probe and the surface is presented. The probe tip is assumed to be a point-like sphere and the surface (selvedge) is represented by point-like spheres placed on a two-dimensional lattice. The bulk is treated as a homogeneous continuum. Using a Green's function formalism we have established a set of self-consistent algebraic equations to describe the local field at the sites of the probe tip and the selvedge. All contributions including bulk reflection and many-body interactions have been taken into account. By means of a point-dipole approach we have for N dipoles solved the 3N X 3N linear algebraic equations exactly. The results have been compared with approximate solutions obtained by a Born series expansion. We have found that the approximate solutions are very different from the exact solution in the case of strong interaction. The approximate solutions tend to infinity only when the tip-surface distance decreases to zero, and the results depend strongly on the number of Born iterations performed. However, for the exact solution it is shown that there are regions close to the surface where an enhanced field can be induced by the probe, while, when the tip-surface distance decreases to zero the self-consistent field tends to zero. Thus, we have found resonance interactions between the probe tip and the surface. These resonances are referred to as configurational ones, since, for any given dipole polarizabilities, the system can be adjusted to resonance by varying the distances between the dipoles. The resonance conditions for some simple systems are presented in an explicit form. It is demonstrated that the resonance coupling of the field component perpendicular to the surface occurs at a bigger distance of the tip dipole from the surface than that of the parallel components. The relation between the polarizability of the probe tip and the resonance positions is considered. It is shown that in the absence of retardation and damping the resolution of the system can be as close to infinity as the tip-surface distance is close to the resonance value. The self-consistent field at the site of the probe is calculated for different distances between the tip and the surface and as a function of the position of the tip along the surface.