Analytical study of the numerical aperture of cone-shaped optical fibers: A tool for tailored designs

In this work, a set of analytical expressions to tailor the numerical aperture of cone-shaped step optical fibers is proposed. The expressions are derived from the geometrical study of light-ray tracing at the cone-shaped tip of a regular step-index optical fiber. Analysis of the different physical phenomena that can take place at the tip of the fiber led to numerical apertures ranging from 0 to 1.5 which can be achieved via a variety of cone angles, providing great versatility in the design of light sources or light collecting devices based on step-index optical fibers.