On the generalized Snell's law for the design of elastic metasurfaces

Abstract

As the most popular mechanism, the generalized Snell's law has been applied extensively to design metasurfaces for wave manipulation. By modulating phase profile using metasurfaces, various novel wave transformations have been demonstrated. However, it has been found that the performance of these metasurfaces cannot be fully determined by the generalized Snell's law and in some cases, the wave fields appear to be contradictory to what predicted by the generalized Snell's law. In this work, a systematic numerical study is conducted to investigate the generalized Snell's law for elastic waves. The inherent assumptions of the generalized Snell's law are examined first followed by the study of the effects of various implementation issues on the performance of the metasurfaces. In particular, the fundamental mechanism for producing wave components that do not obey the generalized Snell's lay is identified and theoretically justified. Design guidelines for metasurfaces for improved performance are provided.