Electromagnetic Wave Propagation in Dispersive Negative Group Velocity Media

We study theoretically the propagation of electromagnetic waves in an infinite, isotropic, and homogenous, medium with both temporal and spatial dispersion included. We derive a partial differential equation connecting temporal and spacial dispersion to achieve negative group velocity. An exact solution of the equation is found and is shown to lead to negative-refraction media even when both E and p are positive. The formal solution suggests the possibility to engineer new artificial materials by carefully manipulating the spatial dispersion profile. We also analyze the power flow and suggests a path beyond the group velocity concept.