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.