The diffracted field of a hollow-core optical fibre is studied and it is shown how the near field of a guided mode develops into the far field. We then describe our method of producing a diffracted output in the shape of a diverging dark hollow beam with a minimum dark spot of a few mu m, which is comparable to the hollow-core diameter, by superposing two LP11 modes which have node lines and polarizations orthogonal to each other. Its possible application to an efficient, novel atomic funnel which guides cold atoms into the hollow fibre is also discussed.