Fresnel equations and the refractive index of active media

There exists a class of realizable, active media for which the refractive index cannot be defined as an analytic function in the upper half-plane of complex frequency. The conventional definition of the refractive index based on analyticity is modified such that it is valid for active media in general, and associated Fresnel equations are proved. In certain active media, the presence of a ``backward'' wave, for which both phase velocity and Poynting's vector point towards the excitation source, is demonstrated.