The ability to precisely directing and controlling longitudinal (P) and transverse (S) waves in 2D solids along an arbitrary trajectory has attracted significant research interest and is crucial for practical applications such as imaging, cloaking, and wave focusing. Here, we report, design and examine an inhomogeneous lattice-based polar medium for ideal elastic waveguide, whose microstructures are inversely determined by the discrete transformation elasticity (DTE). Microstructures of the suggested medium, which are realized through global linear transformation and local affine transformation, enables arbitrary waveguides to transport elastic waves with minimal energy loss. Numerical simulation is then conducted to demonstrate that the lattice-based polar waveguide can efficiently steer both in-plane P and S wave modes over a broad frequency band. We also leverage the medium for Rayleigh wave control on curved surfaces. The constructed polar surface can break the conventional limit of the Rayleigh wave propagation on both concave and convex surfaces with extreme curvatures. This study is not only a concrete manifestation of the polar material, discrete transform elasticity, and their advantages but also provides a great potential in engineering applications such as signal detection, vibration control, and earthquake protection.

沿着任意轨迹精确引导和控制二维固体中的纵向 (P) 和横向 (S) 波的能力引起了广泛的研究兴趣，并且对于成像、隐身和波聚焦等实际应用至关重要。在这里，我们报告、设计和检查了理想弹性波导的非均匀晶格极性介质，其微观结构由离散变换弹性 (DTE) 反向决定。通过全局线性变换和局部仿射变换实现的建议介质的微观结构使任意波导能够以最小的能量损失传输弹性波。然后进行数值模拟以证明基于晶格的极化波导可以在宽频带上有效地控制面内 P 波和 S 波模式。我们还利用该介质在曲面上进行瑞利波控制。所构造的极面可以打破瑞利波在具有极端曲率的凹凸表面上传播的常规限制。本研究不仅是极性材料、离散变换弹性及其优点的具体体现，而且在信号检测、振动控制、地震防护等工程应用中具有巨大潜力。所构造的极面可以打破瑞利波在具有极端曲率的凹凸表面上传播的常规限制。本研究不仅是极性材料、离散变换弹性及其优点的具体体现，而且在信号检测、振动控制、地震防护等工程应用中具有巨大潜力。所构造的极面可以打破瑞利波在具有极端曲率的凹凸表面上传播的常规限制。该研究不仅是极性材料、离散变换弹性及其优点的具体体现，而且在信号检测、振动控制、地震防护等工程应用中具有巨大潜力。