R-Charged Black Holes and Holographic Optics

We analyze momentum dependent vector modes in the context of gauge theories dual to R-charged black holes in $D=4$, $5$ and $7$. For a variety of examples, the master variables are constructed, for which the linearized equations for the perturbations decouple. These allow for the computation of momentum dependent correlation functions. Away from the hydrodynamic limit, numerical analysis using the decoupled equations of motion is used to obtain the analogues of the Depine-Lakhtakia (DL) index. For specified ranges of frequencies, a negative index of refraction is seen to occur in all cases.