Abstract

A ray-tracing procedure has been developed for general gradient refraction index (GRIN) media where the distribution and the media surface position are given as discrete point sets of arbitrary distributions. Ray trajectories in the GRIN media are calculated from the numerical solution of the ray equation with automatic step size monitoring. The moving least squares method is employed for local reconstructions of refraction index fields. The developed ray-tracing procedure is applied to simulation of the Luneburg lens. The spot radius of the Luneburg lens is less than 10 nanometers for 1 millimeter radius of the lens, and hence the ratio of the error to the problem dimension is less than 10⁻⁵.

© 2010 Optical Society of America