Aberration-limited coupling efficiency from a plano-convex lens into an optical fiber.

Ray-tracing calculations of the coupling efficiency from a plano-convex lens of relatively low f/number ( approximately 2.35) into highly multimode step-index optical fibers have been performed for both orientations of the lens. The results of the calculations yield surprising discontinuities and asymmetries in the slope of the coupling efficiency versus longitudinal displacement. These features are explained in terms of the multiplicity of roots in the mapping of incident-ray heights onto the fiber core radius. In addition, it is found that the paraxial coupling efficiency result is in marked qualitative and quantitative disagreement with exact theoretical results, except at coupling efficiencies of less than a few percent. The relationship of these features to longitudinal spherical aberration, paraxial coupling, and the ray caustic is discussed.