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 tran
smission or reflection coefficients for a particular tip-surface confi
guration. In particular we present the first application of a transfer
matrix based calculation to this challenging problem by using an adap
tive coordinate transformation to accurately model the shape of the SN
OM tip. We also investigate the possibility of increasing the transmit
ted light through the SNOM tip by introducing a metal wire into the ce
ntre of the tip. This converts the tip into a coaxial cable. We show t
hat, in principle, this can dramatically improve the transmission char
acteristics without having a detrimental effect on the resolution.