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.
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