A cutting method and apparatus are provided to cut a portion of an optical fibre or waveguide with a laser beam. The proposed cutting action takes advantage of the sharp cutting edge of a laser beam generated so as to have a predetermined asymmetric intensity distribution. In operation, a prescribed amount of the beam distribution is impinged on the fibre or waveguide portion and causes the portion to ablate or vaporise so as to effect a cut at the portion in dependence upon the impingement. No translation of the laser beam across the fibre or waveguide is effected during cutting. The proposed cutting action bears definite advantages over conventional cutting techniques and finds utility for many optical fibre or waveguide applications. For example, the proposed cutting action can produce a substantially flat optical fibre or waveguide surface or a lens of enhanced quality at the end of the fibre or waveguide portion.