Generalized laws of refraction that can lead to wave-optically forbidden light-ray fields

The recent demonstration of a metamaterial phase hologram so thin that it can be classified as an interface in the effective-medium approximation [Science334, 333 (2011)10.1126/science.1210713SCIEAS0036-8075] has dramatically increased interest in generalized laws of refraction. Based on the fact that scalar wave optics allows only certain light-ray fields, we divide generalized laws of refraction into two categories. When applied to a planar cross section through any allowed light-ray field, the laws in the first category always result in a cross section through an allowed light-ray field again, whereas the laws in the second category can result in a cross section through a forbidden light-ray field.