Wave amplification in double negative elastic metamaterials

For two homogeneous and isotropic media, the angles of the transmitted and reected waves follow the Snell's law, which relate them to the angle of incidence and material properties of each medium. When the angle of incidence is larger than the critical angle (the angle of incidence that makes the transmission angle equals π=2), the transmitted wave will decay exponentially in the direction away from the interface. However, we found that by changing one medium into a double negative metamaterial, the transmitted wave will grow exponentially instead. This research can be used for amplifying evanescent transmitted waves by putting thin metamaterial layer between bilayer elastic media.