Beam profile approach to lens design for fiber optics

The common approach to designing multimode fiber coupling lenses is based on fiber end-face imaging. A model, proposed here, deals with beam profiles. Paraxial ray tracing shows that the output of a graded-index multimode fiber has a hyperbolic profile, similar to a singlemode beam. Focusing this beam by a lens is similar to a Gaussian beam focusing. Light focused from a step-index multimode fiber has two waists. Matching their size and NA to fiber parameters is not enough for good coupling: the beam profile should in fact be corrected. The propagation properties of graded-index multimode fiber beams are similar to singlemode beams and differ from step-index multimode fiber beams. The beam profile approach defines these properties, while the imaging approach often fails. A ray model, describing the beam profile, is convenient in computer simulation of lens systems for fiber optics. It visualizes beams in ray-tracing codes such as ZEMAX and allows aberration optimization regarding minimal beam distortion. Gaussian beam diffraction is not an issue, if there is no beam clipping - the ray model is consistent with the traditional wave model. These results are important for correct design of fiber coupling lenses.