Refractors in anisotropic media associated with norms

TL;DR

This paper establishes the existence of specific interfaces between anisotropic materials that direct light refraction to match a prescribed energy pattern, using a vector Snell law based on convex norms.

Contribution

It introduces a vector Snell law for anisotropic media with convex norm wave fronts, enabling control over light refraction patterns.

Findings

Existence of interfaces matching prescribed refraction patterns

Formulation of a vector Snell law for anisotropic media

Application to media with convex norm wave fronts

Abstract

We show existence of interfaces between two anisotropic materials so that light is refracted in accordance with a given pattern of energy. To do this we formulate a vector Snell law for anisotropic media when the wave fronts are given by norms for which the corresponding unit spheres are strictly convex.