Resolving the wave vector and the refractive index from the coefficient of reflectance

We resolve the existing controversy concerning the selection of the sign of the normal-to-the-interface component of the wave vector k_z of an electromagnetic wave in an active (gain) medium. Our method exploits the fact that no ambiguity exists in the case of a film of the active medium, since its coefficient of reflectance is invariant under the inversion of the sign of k_z. Then we show that the limit of the infinite film thickness determines a unique and physically consistent choice of the wave vector and the refractive index. Important practical implications of the theory are identified and discussed.