Elastic Waves Scattering without Conversion in Metamaterials with Simultaneous Zero Indices for Longitudinal and Transverse Waves

We theoretically investigate elastic waves propagating in metamaterials with simultaneous zero indices for both the longitudinal and transverse waves. With scattering objects (here cylinders) present in the metamaterial slabs, while the elastic waves can mostly transmit through the metamaterial slabs perfectly, exhibiting the well-known cloaking effect of zero-index metamaterials, they nevertheless become totally blocked at resonances, indicating strong elastic wave scattering by the objects in the cases. However, despite the occurrence of the elastic wave scattering, there is, counterintuitively, no mode conversion between the longitudinal and transverse waves in the process, completely in contrast to that in conventional elastic media. A design of a two-dimensional phononic crystal with these peculiar properties is presented.