Uniform refraction in negative refractive index materials.

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, in both the near- and far-field cases. In the near-field problem, unlike the case when both materials have positive refractive indices, we show that the resulting surfaces can be neither convex nor concave.