  Light diffraction through a subwavelength aperture located at the apex of a
metallic screen with conical geometry is investigated theoretically. A method
based on a multipole field expansion is developed to solve Maxwell's equations
analytically using boundary conditions adapted both for the conical geometry
and for the finite conductivity of a real metal. The topological properties of
the diffracted field are discussed in detail and compared to those of the field
diffracted through a small aperture in a flat screen, i. e. the Bethe problem.
The model is applied to coated, conically tapered optical fiber tips that are
used in Near-Field Scanning Optical Microscopy. It is demonstrated that such
tips behave over a large portion of space like a simple combination of two
effective dipoles located in the apex plane (an electric dipole and a magnetic
dipole parallel to the incident fields at the apex) whose exact expressions are
determined. However, the large "backward" emission in the P plane - a salient
experimental fact that remained unexplained so far - is recovered in our
analysis which goes beyond the two-dipole approximation.
