Journal of the Optical Society of America A
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.
Cristian E. Gutiérrez and Eric Stachura, "Uniform refraction in negative refractive index materials," J. Opt. Soc. Am. A 32, 2110-2122 (2015)