Characteristic analysis of laser diode to multimode fiber coupling using a plano-convex GRIN lens

A ray model for a laser diode to analyze a multimode fiber coupling system is extended by taking the directivity into account. The validity is examined from the point of view of a far-field pattern. It is shown that the maximum coupling efficiency obtained at the best position of the fiber is strongly affected by the directivity, while the best position of the fiber existing between the paraxial image point and the best focus is almost independent of the directivity. The result of an extensive tolerance analysis of the longitudinal and lateral shifts of laser diode and optical fiber and of the curvature, the error in lens length, and the fourth-order index coefficient of the GRIN-rod lens is also shown as a contour map of coupling efficiency.