The achievement of high-quality wave manipulation and energy concentration has always been considered as state-of-the-art technologies, especially for integrated photonics, acoustics, and mechanics. The exploration of the topological phase of matter provides abundant design tools for robust waveguiding that is immune to backscattering at small defects and sharp bends. Recent research has extended the elastic wave manipulation from 2D edge waveguiding to 3D planar waveguiding. However, most of them are limited to single-mode and single-frequency wave propagation along the designed plane. This paper introduces a novel 3D topological metamaterial structure whose geometrical parameters are specifically configured to obtain dual-mode topological states at distinct frequencies. Parametric studies are presented to demonstrate the controllability of bandgaps and to provide a design principle for preventing the effects of unwanted modes. Topological interface modes with either high group velocity or near-zero group velocity along the direction are found. Full-scale finite element simulations are presented to uncover the elastic wave propagation behavior. The interesting layer-locked and layer-unlocked waveguiding based on excitation polarization and frequency for both straight path and zig-zag path are demonstrated. The outcomes of this work suggest abundant potential applications related to elastic wave control such as wave filters, energy harvesters, mechanical computers, and the like. This work may also help inspire future research on more complex and sophisticated multi-mode waveguiding in 3D spaces.

中文翻译：

---

一种新型 3D 拓扑超材料，用于偏振相关多层弹性波的可控性

高质量波操纵和能量集中的实现一直被认为是最先进的技术，特别是在集成光子学、声学和力学方面。对物质拓扑相的探索为鲁棒波导提供了丰富的设计工具，该波导不受小缺陷和急弯处的反向散射影响。最近的研究将弹性波操纵从 2D 边缘波导扩展到 3D 平面波导。然而，它们大多数仅限于沿设计平面的单模和单频波传播。本文介绍了一种新颖的 3D 拓扑超材料结构，其几何参数经过专门配置，以获得不同频率下的双模拓扑状态。参数研究旨在证明带隙的可控性，并提供防止不需要模式影响的设计原则。发现了沿方向具有高群速度或接近零群速度的拓扑界面模式。提出了全尺寸有限元模拟来揭示弹性波传播行为。演示了基于激励偏振和频率的直线路径和锯齿形路径的有趣的层锁定和层解锁波导。这项工作的结果表明与弹性波控制相关的丰富的潜在应用，例如滤波器、能量采集器、机械计算机等。这项工作还可能有助于激发未来对 3D 空间中更复杂和精密的多模波导的研究。