In scanning near-field optical microscopy, a tapered fibre tip scans above the sample surface at nanometric distances. The fibre tip can be used either as a detector to receive the near-field signal or as the light source to illuminate the sample or simultaneously for both purposes. When used as an emitter of light, the scanning near-field optical microscopy is said to function in emission mode. In such emission mode, the light emitted by the probe interacts with the microscopic features on the sample surface, and the result of this interaction is focussed by means of a conventional microscope. In our present work, we concentrate on how the light is emitted from the fibre tip. The power emitted by the probe is critical because it is directly related to the power that reaches the detector and in turn to the resolution of the instrument. A typical probe is made of a tapered optical fibre coated with metal. For probes fabricated by etching, the taper angle is high and the radii of the core and cladding are constant. Thus, the probe can be crudely approximated by a circular aperture on top of a metal-coated optical fibre end. It is interesting to study how the dielectric waveguide modes will couple into the metallic waveguide modes. In this work, a single mode excited in the dielectric waveguide is assumed, and calculations of the power transmitted through the aperture are carried out. A comparison between the power transmitted by different optical fibre modes and different optical fibre parameters is conducted, and the implications for the coupling efficiency of emission-mode fibre tips are discussed.