Neural network gradient-index mapping

Abstract

A universal method to design gradient-index (GRIN) optical elements is proposed here for a given desired light ray bundle. Fermat’s principle can be transformed into a spatial parametric ray equation where a spatial Cartesian coordinate is used as a parameter of the equation. The ray equation can thus be written in a time-independent form, which ensures that a refractive index distribution is in principle obtainable from a spatial light ray distribution. Based on the ray equation, an iterative GRIN mapping method using the neural network (NN) is then constructed to map a refractive index distribution that enables light rays to trace corresponding desired paths. Maxwell’s fisheye lens is used to demonstrate how well the GRIN mapping method works. The refractive index distribution is shown to be well reconstructed from only knowledge of the light ray paths.