Electromagnetic Wave Propagation in Non- Local Media — Negative Group Velocity and Beyond

We study theoretically the propagation of electromagnetic waves in an infinite and homogenous medium with both temporal and spatial dispersion included. We derive a partial differential equation connecting temporal and spatial dispersion to achieve negative group velocity. Exact solutions of the equation are found and shown to lead to the possibility of exciting constant negative group velocity waves. We then investigate the effect of spatial dispersion on the power flow and derive the first-, second-, and third-order corrections of power flow due to the nonlocality in the medium. This derivation suggests a path beyond the group velocity concept.