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.

中文翻译：

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弹性双折射超材料和四分之一波片


极值超材料的弹性矩阵具有一个或多个零特征值，允许无能量变形模式。这些弹性超材料可以通过制造的微观结构很好地近似。它们可以表现出前所未有的操纵体波和表面波的能力，而传统固体由于容易变形模式而无法实现这种能力，正如五模材料（PM）所证明的那样。在本文中，我们基于精心设计的四模材料（QM），从理论上研究了双折射超材料和四分之一波片在光波和弹性波之间的直接一一对应关系。这种 QM 超材料仅允许两种横波模式，消除了由于纵模的存在而导致的模式转换。弹性双折射超材料和弹性四分之一波片的特性通过均质化模型和相应的离散模型得到了证明。还提出了一种类似于电子器件中的二极管的自由空间弹性波隔离器，它可以有效地保护上游源或系统免受背反射噪声或干扰。离散模型的另一个好处还在于其通过变形可调节工作频率。这项工作首次对弹性双折射超材料和可调谐弹性四分之一波片进行了研究，可能会刺激极值弹性超材料在控制弹性波偏振方面的应用。