  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.
