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 multimode 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 theoretical model has been developed to accommodate phase-space distributions observed experimentally for a practical laser source and launch optics, and for the specific case of fibres having a quadratic index distribution. The model shows that an optimum launch condition exists. For the ideal case of an input beam with elliptical phase space used at the optimum launch condition, the ratio of output/input beam quality is unity. 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. The output-beam quality was measured as a function of launch conditions, including a measurement of the input-beam phase space. The results were in accordance with the theoretical prediction, the optimum launching condition was identified, and an optimum ratio of output/input beam quality of 1.2 was demonstrated.