Coherent effects in a thin film of metamaterial

The refraction is theoretically considered of ultimately short pulses at interface of two dielectrics that contains a thin film of nonlinear metamaterial. For the model of metamaterial composed of nanoparticles and magnetic nanocircuits (split-ring resonators) the equations are obtained suitable for describing the coherent responses of such film. The numerical simulation demonstrates the emergence of oscillatory echo in inhomogeneous system of meta-atoms. It is supposed that the reported methods are applicable for investigation of thin metamaterial films.