Graded index media have a spatially varying refractive index. In ray optics, the path of a light ray can easily be calculated as in this example: The ray is launched from the upper left corner towards the center.

The scale on the right shows the local refractive index.

What happens to a realistic ray, a collimated light beam? This website's top/left background picture shows color-coded the H-field of a Gaussian beam being deflected in a graded-index medium. Since this can't be treated analytically (in general), the best approach is to do experiments, which are in progress.

Opt. Commun. 283, 3367 (2010)