Gradient-index optics

Summary

Gradient-index optics studies media whose refractive index varies continuously from point to point. In such a medium light rays bend gradually instead of only at surfaces, following the curves of stationary optical length given by Fermat's principle. Mathematically the rays are the geodesics of the metric $n^2 \abs{dx}^2$, so gradient-index optics is a meeting point of optics and Riemannian geometry. Classical examples are Maxwell's fish-eye lens and the Luneburg lens, and practical uses include rod lenses and graded-index optical fibres.