The far field radiated by a dipole above a substrate with a film

Abstract

Dipoles are all around us and the extent to which it is possible to distinguish two dipoles next to each other is a very important criterion for optical resolution. This report proposes that the resolution can be enhanced by placing a substrate with a film underneath the dipoles. This report specifically looks at the effect on the near and far field using a coupling of the field radiated by the dipole and a guided mode in the film. In an integral over reflected plane waves, in case a guided wave occurs, the integrand has a singularity which has to be dealt with using the Cauchy Principle value technique. Other singularities are dealt with using multiple first order Taylor expansions. With the singularities dealt with, a Matlab function has been constructed that can compute the reflected field of a single dipole. The substrate underneath the dipole has a significant effect on the total field, both in the near and far field areas. Due to the reflection, the polarizability is represented more in the intensity and can be determined more easily. Although the influence of the film on enhancing the resolution requires to investigate to what extent two dipoles can be distinguished better when a film is present, due to lack of time, this report considers the computation of the field of a single dipole only. The extension to the case of two dipoles is in principle easy however.