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近年来, 具有谷赝自旋自由度的拓扑谷态物理备受关注. 声子晶体中的拓扑谷边界态因其背向散射免疫传输特性, 在高效声波和弹性波波导与传感方面具有重要的应用前景. 本文基于弹性波量子谷霍尔效应类比构建了一种三角晶格谷拓扑声子晶体板, 系统研究了面外偏振弹性波谷边缘态在多层拓扑异质超胞结构中耦合行为, 揭示了有限尺寸的多层异质结构对弹性波耦合谷边缘态的形成机理与调控规律. 进一步通过拓扑传输计算, 揭示了弹性波耦合谷边缘态的多模干涉效应并验证其传输鲁棒性. 最后, 作为一种应用示例, 基于谷边缘态多模干涉效应设计了一种弹性波拓扑波长解复用器. 利用不同耦合频率下边缘态的耦合波长差异, 实现入射弹性波在抗缺陷通道中的定向分离. 本文研究为弹性波拓扑传输调控提供了新范式, 有望推动新型多功能弹性波耦合与传感器件的实用化设计.In recent years, topological valley physics with the degrees of freedom of valley pseudospin has attracted great attention. The topological valley boundary states in phononic crystals have important application prospects in efficient guidance and sensing for acoustic and elastic wave due to their unique transmission characteristics with backscattering immunity. However, the coupling effect of the valley edge states in multi-layer topological heterostructure is still a challenge in the elastic system due to the complicated multi-mode polarization of elastic waves. In this work, a valley topological phononic crystal plate with a multi-layer heterostructure is constructed to explore the multi-mode interference characteristics of the valley edge states based on the analogy of elastic wave quantum valley Hall effect. The coupling behavior of valley edge states for the out-of-plane polarized elastic wave in multi-layer topological heterostructure is systematically studied. By adjusting the layer numbers of the topological heterostructures, the formation mechanism and regulation law of coupled valley edge states for elastic wave in finite size multi-layer heterogeneous structures are revealed. Furthermore, through topological transmission calculations, the multi-mode interference effect of coupled valley edge states for elastic wave is achieved and its transmission robustness is well verified. Finally, as an application example, an elastic topological wavelength demultiplexing device is designed based on the multi-mode interference effect of valley edge state. By utilizing the difference in coupling wavelengths of elastic valley edge states at different coupling frequencies, directional separation of incident elastic waves in defect resistant channels is achieved, which can be used as a prototype model for the novel application of elastic wavelength demultiplex device. This work provides a new paradigm for the manipulation of elastic wave topological transport, which is also expected to promote the practical design of new multifunctional elastic wave coupling and sensing devices.
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Keywords:
- coupled valley edge states /
- elastic wave /
- topological phononic crystals /
- multi-mode interference
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图 1 (a)声子晶体板的整体结构和声子晶体的单胞结构以及各尺寸参数; (b)六边形声子晶体中三角形棱柱体不同旋转角度θ=0°, θ=30°和θ=–30°的能带结构, 不同旋转角度的单胞形状位于每个图的下方, 图(a)中的插图为六边形晶格的布里渊区
Fig. 1. (a) Overall structure of the PC plate and unit cell configuration with dimensional parameters; (b) band structures of hexagonal PC with triangular prisms rotated at different angles θ=0°, θ=30°, and θ=–30°. The unit cell geometries corresponding to each rotation angle are shown below their respective band diagrams. The inset in Figure (b) illustrates the Brillouin zone of the hexagonal lattice.
图 2 (a)由旋转角度θ引起的K点处的拓扑相变, K1和K2能谷频率随散旋转角度θ的变化情况; (b) θ=30°和θ=–30°单胞在K点处第一和第二体能带的能流分布; (c)由A相和B相组成两种不同的超胞结构以及蓝点和红点所对应的位移场图, 其中θ=30°的声子晶体为A相, θ=–30°的声子晶体为B相; (d)两个不同相位声子晶体之间拓扑边缘态的投影色散, 蓝色线表示A-B结构的拓扑边缘态1, 红色线表示B-A界面的拓扑边缘态2, 实线和虚线分别表示从K和K'谷投影的边缘态
Fig. 2. (a) Topological phase transition at K-valley induced by rotation angle θ, showing variations of valley-specific frequencies at K1 and K2 with rotation angle; (b) energy flux distributions of the first and second bulk bands at K-valley for unit cells with θ=30° and θ=–30°; (c) two distinct supercell configurations composed of Phase A and Phase B, with corresponding displacement fields marked by blue and red dots. Here, PC with θ=30° constitute phase A, while those with θ=–30° form phase B; (d) projected band dispersion of topological edge states (TES) between two different topological phases. The blue curve denotes TES1 at the A-B interface, and the red curve represents TES2 at the B-A interface. Solid and dashed lines indicate TES projected from K and K' valleys, respectively.
图 3 三层异质结构的超胞结构, 能带投影和位移场分布 (a)超胞结构示意图; (b), (d)和(f)分别为AB1A, AB2A和AB3A超胞异质结构以及第一和第二边缘态对应的位移场分布; (c), (e)和(g)为中间耦合区域不同单胞个数超胞的投影能带图, 灰点表示体态, 红蓝拼接线表示耦合后的边缘态; (h)带隙宽度随耦合区域单胞层数变化情况, 蓝色点线表示第0边缘态的最大值, 红色点线表示第1边缘态的最小值
Fig. 3. Sandwich-type supercell configurations, projected band structures, and displacement field distributions: (a) Supercell architecture; (b), (d), and (f) AB1A, AB2A, and AB3A supercell configurations with displacement fields corresponding to first and second edge states, respectively; (c), (e), and (g) the projected band structures of supercells with varying numbers of unit cells in the intermediate coupling region, gray dots denote bulk states, while red-blue hybrid curves represent coupled edge states; (h) the variation of bandgap width with the number of single cells in the coupling region, where the blue dotted line represents the maximum value of the 0 th edge state, and the red dotted line represents the minimum value of the 1st edge state.
图 4 不同排列组合的多层异质夹层结构超胞能带图和位移场分布 (a), (c), (e)分别表示AB3A3B, AB3A3B3A和AB3A3B3A3B夹层结构的超胞能带和边缘态对应的位移场分布; (b), (d), (f)分别为BA3B3A, BA3B3A3 B和BA3B3A3B3A结构排列的超胞能带和边缘态对应的位移场分布图. 灰点表示体态, 红蓝拼接线表示耦合后的边缘态, 其中绿色线表示未发生耦合的边缘态
Fig. 4. Band structures and displacement field distributions of sandwich supercells with different structural arrangements: (a), (c), (e) Band diagrams and displacement fields of edge states for AB3A3B, AB3A3B3A, and AB3A3B3A3B configurations, respectively; (b), (d), (f) corresponding diagrams for BA3B3A, BA3B3A3B, and BA3B3A3B3A arrangements. Gray dots denote bulk states, red-blue hybrid curves represent coupled edge states, and green curves indicate uncoupled edge states.
图 5 (a) AB3A3B夹层异质结构传输示意图; (b), (c) AB3A3B夹层异质结构中多模干涉效应和其他频率段位移场分布图; (d)AB3A3B3A3B夹层异质结构传输示意图; (e), (f) AB3A3B3A3B夹层异质结构中多模干涉效应和其他频率段位移场分布图
Fig. 5. (a) Wave propagation schematic in the AB3A3B sandwich heterostructure; (b), (c) the displacement field distribution maps of the multimode interference effect and other frequency ranges in the AB3A3B intercalated heterostructure; (d) wave propagation schematic in the AB3A3B3A3B sandwich heterostructure; (e), (f) the displacement field distribution maps of the multimode interference effect and other frequency ranges in the AB3A3B3A3B intercalated heterostructure.
图 6 采用两种不同缺陷类型验证夹层异质结构的传输鲁棒性 (a)具有空腔缺陷和无序扰动的AB3A3B夹层异质结构的位移分布图; (b)具有空腔缺陷和无序扰动的AB3A3BA3B夹层异质结构的位移分布图, 缺陷位置采用黄色虚线标出; (c)存在缺陷和正常AB3A3B夹层异质结构从P0口到P1和P3口传输效率曲线对比图; (d)存在缺陷和正常AB3A3BA3B夹层异质结构从P0口到P1、P3和P5口传输效率曲线对比图, 不同颜色表示不同的输出端口, 黄色区域表示边缘态范围
Fig. 6. Robustness verification of sandwich heterostructures against two defect types: (a) Displacement field distribution in AB3A3B heterostructure with cavity defects and disordered perturbations; (b) displacement field distribution in AB3A3BA3B heterostructure with cavity defects and disordered perturbations. Defect locations are marked by yellow dashed lines; (c) a comparison of the transmission efficiency from port P0 to ports P1 and P3 between defective and pristine AB3A3B heterostructures; (d) the corresponding comparison from P0 to ports P1, P3, and P5 for the AB3A3BA3B heterostructure. In both plots, the curves are color-coded by their output ports, and the edge state frequency range is highlighted in yellow.
图 7 (a)波长解复用器的结构模型; (b)—(e)为f=29850, 34450, 35500和35800 Hz不同频率下弹性波从不同端口输出的位移场分布图
Fig. 7. (a) Structural model of the wavelength demultiplexer; (b)—(e) displacement field distributions showing elastic wave output through different ports at excitation frequencies f=29850, 34450, 35500 and 35800 Hz, respectively.
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