Modern technology has introduced new photonic metamaterials that can extend optical properties beyond what standard materials can offer. For example a negative index of refraction is now possible which can lead to extraordinary abilities such as invisibility (optical cloaking) of massive objects, etc.
So we once believed that our ability to resolve an image was limited to, for example the diffraction limit derived by Abbe which is a function of the wavelength of the light, and index of refraction of the material.
Given these new metamaterials, do these laws still apply? Can we, again for example, just plug-in the negative index of refraction to Abbe's expression for diffraction limit? If so, how does one interpret a negative diffraction limit?
It also leads me to the question of what does a zero index of refraction mean? What physically amazing things might a zero index entail, and is a zero index of refraction even possible to engineer with metamaterials?