  In this paper we consider the application of electromagnetic theory to the
analysis of the Scanning Near-field Optical Microscope (SNOM) in order to
predict experimentally observable quantities such as the transmission or
reflection coefficients for a particular tip-surface configuration. In
particular we present the first application of a transfer matrix based
calculation to this challenging problem by using an adaptive co-ordinate
transformation to accurately model the shape of the SNOM tip.
  We also investigate the possibility of increasing the transmitted light
through the SNOM tip by introducing a metal wire into the centre of the tip.
This converts the tip into a co-axial cable. We show that, in principle, this
can dramatically improve the transmission characteristics without having a
detrimental effect on the resolution.
