All known natural materials have epsilon and mu > 0. However, there is an intense effort to manufacture so-called metamaterials, where both of these are <0. In such a case, given n = sqrt[epsilon x mu], one would take the negative root and n is still a real number, but n <0 why do we take the negative?

What is so interesting about this?

What does this say about the propagation of v=c/n, does this mean light is going backwards?