Geometric Optics Analysis of Multi-Step Index Optical Fibers

The double aim of the present article is to give a brief description of our research group's main results achieved in recent years and to provide a comprehensive analysis of light propagation properties in multi-step index (MSI) fibers based on the geometric optics method. Therefore, in the initial part we present our research team and its main lines of research on plastic optical fibers (POF). Afterward, the discussion focuses on a new theory we have developed for the propagation in MSI fibers. First of all, we derive the ray invariants ~β and ~l, which allow us to instantly determine the direction of the ray at any position along its trajectory, and we discuss the characteristics of the ray path, setting the classification of rays into bound, refracting and tunneling categories. Then, we calculate the ray-path parameters, namely the path length Lp, the ray half period zp and the ray transit time t. Furthermore, we analyze the ray temporal dispersion. Specifically, we take a practical case in which the width of each layer is maintained constant, allowing, in contrast, for the respective refractive indices to take any value, and we derive closed expressions for the ray dispersion. Finally, we investigate the light power acceptance properties of an MSI fiber, calculating the effectiveness of both diffuse and collimated light sources in launching bound rays and the coupling losses with lateral and longitudinal misalignments.