Uniform Refraction in Negative Refractive Index Materials

TL;DR

This paper investigates the design of optical surfaces that separate media with negative refractive index, developing a vector Snell's law and analyzing the geometric properties of such surfaces in different field scenarios.

Contribution

It introduces a vector form of Snell's law for negative refractive index materials and studies the geometric nature of the resulting refracting surfaces.

Findings

Surfaces with negative refractive index can be neither convex nor concave in the near field.

Develops a new mathematical framework for refraction in negative index media.

Analyzes near and far field cases of uniform refraction surfaces.

Abstract

We study the problem of constructing an optical surface separating two homogeneous, isotropic media, one of which has a negative refractive index. In doing so, we develop a vector form of Snell's law, which is used to study surfaces possessing a certain uniform refraction property, both in the near and far field cases. In the near field problem, unlike the case when both materials have positive refractive index, we show that the resulting surfaces can be neither convex nor concave.