Light amplification by active metamirrors

We consider a scheme of a thin film deposited on periodically modulated amplifying materials. We demonstrate that the reflection from such a metainterface can undergo amplification due to Fano resonances in the film. The amplification increases when the film waveguiding modes approach the edge of the continuum and degenerate into the leaky surface modes, guided by a thin film. Such modes possess a strong evanescent tail that extends into the active substrate and are therefore amplified. The study is performed by simplified analytical models, as well as by rigorous coupled wave analysis.