Elastic birefringent metamaterials and quarter-wave plate

The elastic matrices of extremal metamaterials have one or more zero eigenvalues, allowing energy-free deformation modes. These elastic metamaterials can be well approximated by manufactured microstructures. They can exhibit an unprecedented capacity to manipulate bulk and surface waves, which are unavailable with conventional solids due to the easy deformation modes, as already exemplified by pentamode materials (PMs). In this paper, we theoretically investigate a direct one-to-one correspondence of birefringent metamaterial and quarter-wave plate between optical and elastic waves based on a carefully designed quadramode material (QM). This QM metamaterial allows only two transverse wave modes, eliminating mode conversion due to the presence of the longitudinal mode. The characteristics of the elastic birefringent metamaterial and elastic quarter-wave plate are demonstrated by both homogenized and corresponding discrete models. A free space elastic wave isolator, analogous to a diode in electronics, is also proposed, which can effectively protect upstream sources or systems from back-reflected noise or interference. An additional benefit of the discrete model is also revealed for its working frequency tunability through deformation. This work provides the first study on elastic birefringent metamaterials and tunable elastic quarter-wave plate, which may stimulate applications of extremal elastic metamaterials for controlling elastic wave polarization.