Fresnel equations and the refractive index of active media

A class of realizable active media exists 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.