# Negative radiation pressure from negative refractive index?

I see this claim being originally made by Vesselago (the discoverer of the principles of metamaterials) and indeed in contemporary papers. It means that such a metamaterial would be pulled towards its illuminating light source. Why does this not violate conservation of momentum?

In most media, the refractive index is positive, and the Poynting vector $\vec{S}$ and the wave vector $\vec{k}$ point in the same direction. In a medium with a negative refractive index, the Poynting vector points in the opposite direction from the wave vector.
The wave vector of the light is what you control when you set up the light source. If you point the source towards the positive $x$ axis, for example, then $\vec{k} = |\vec{k}|\hat x$. On the other hand, the Poynting vector is what controls the light wave's momentum, and therefore the radiation pressure.