Ray Tracing Gradient Index Lenses

Abstract

The trajectories of light rays are studied in media in which the refractive index varies with position. These are known as gradient index media, and the equation of motion of light rays through such media can be written in the same form as Newton's law of motion for a particle moving in a conservative force field. We present ray traced images of two families of gradient index lenses: Luneberg Lenses and gradient index rod lenses. The equation of motion of light rays through the lenses are either solved exactly, or solved accurately by numerical means. Ray tracing is an important tool for visualizing the optical properties of such lenses and other gradient index media.