On the generalized Snell’s law for the design of elastic metasurface

Various metasurfaces have been designed based on the generalized Snell’s law (GSL), but their performances are undermined by extra propagating waves that do not follow the GSL, especially when the phase gradient is large [1]. Although a modified version of GSL has been proposed for acoustic metasurfaces to describe the extra waves [2], the underlying mechanism of extra wave generation remains unclear. For elastic metasurfaces, such extra waves also exist as shown in Figure 1, indicating that the GSL might be invalid under some circumstances. In light of this, a systematic numerical study on the GSL for elastic waves is performed. It is found that mismatched impedance, material discontinuity, and phase discontinuity are the sources of the extra waves. The generation mechanisms of the extra waves from these sources are identified and theoretically justified. Based on these results, a guideline on metasurface design for improved performance is devised.