Optimum beam launching conditions for graded index optical fibres: theory and practice

A theoretical model is presented, describing the relationship between the quality of a laser beam at the input and output of a multi-mode graded-index optical-fibre beam delivery system, as a function of the beam launching conditions. The launching conditions are described in terms of the diameter and numerical aperture of the laser beam at the input to the fibre, relative to the core diameter and acceptance angle of the fibre. The beam quality transfer function is shown to depend on the position-dependent divergence of the input beam, which is described in terms of its phase space. The model has been tested experimentally, using a high average power Nd:YAG laser of a type commonly used for material processing operations and a graded-index fibre of core diameter 600 μm