Extreme transmission of elastic metasurface for deep subwavelength focusing
doi: 10.1007/s10409-021-09073-z
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摘要: 本文提出了由之字形单元组成的弹性波超构表面来实现对弯曲波的深亚波长尺度操控. 通过遗传算法对单元进行参数优化, 可以找到具有全透射率和全相位控制的单元, 而其宽度仅为波长的1/5. 结合传输模态和Kirchhoff薄板理论, 发展了理论模型并解释了这些单元产生优越性能的原因. 接着, 设计了直线型和曲线型超构表面实现不同位置的弯曲波聚焦, 其仿真结果都显示出了优异的性能. 进一步加工制作直线型超构表面并进行实验测试, 实验结果与仿真结果非常吻合, 结果同时表明入射波能量在焦点处提高了6倍以上. 本工作提出的超构表面可用于设计紧凑高效的弹性波器件.Abstract: In this paper, elastic metasurfaces composed of zigzag units are proposed to manipulate flexural waves at a deep subwavelength scale. Through the parameter optimization of the genetic algorithm, units with full transmission and full phase control can be found, while the width is only one-fifth of the wavelength. The outstanding capability of the units is explained by analyzing their wave fields. The flat and the curved metasurfaces for focusing are designed and simulated, showing excellent performance. Experimental results of the flat metasurface show that the incident wave energy at the focal point is enhanced over 6 times, verifying the simulation results. The proposed metasurfaces could be useful in the design of compact and efficient elastic devices.
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Key words:
- Extreme transmission /
- Flexural waves /
- Elastic metasurface /
- Deep subwavelength focusing
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1. The elastic metasurface for focusing: a schematic diagram of the elastic metasurface, and b the cross-section of the functional unit, where the unit size (H and l) and the 13 adjustable geometric parameters are shown.
2. The schematic diagram of the strip with a unit for numerical and analytical calculations. x1−x3 mark out the coordinates of the three evaluation points. The red arrows represent the direction of the incident and transmitted waves, and the blue arrow for the reflected waves.
3. a Out-of-plane displacement distributions normalized by A0 for the ten specific units obtained by numerical simulation. b Normalized phase shift ∆φ (red curve and scattered squares) and transmission η (blue curve and scattered circles) for the ten units. The numerical and analytical results are marked with scattered symbols and curves, respectively.
4. Schematic diagram of Fermat’s principle in two-dimension. Point P is the wave source and point Q is the targeted focal point after the wave passes through the metasurface.
5. a Out-of-plane displacement field distribution and b its normalized form for wave focusing by a flat metasurface. c and d show the normalized intensity fields at the focal point along the x- and y- directions from the simulation (blue curves) and the experiment (red dashed curves).
6. a Out-of-plane displacement field distribution and b its normalized form for the oblique focusing by a flat metasurface. The direction of the new coordinate system x′-y′ is defined by the focusing position. c and d show the normalized intensity fields at the focal point along the focusing direction (x′) and its vertical direction (y′) from the simulation.
7. The schematic of a the units’ arrangement and b the phase profile of the curved metasurface for focusing. The blue lines indicate the theoretical phase, and the red dots indicate the phase of the adopted units.
8. a Out-of-plane displacement field distribution and b its normalized form for the wave focusing by a curved metasurface. c and d show the normalized intensity fields at the focal point along the x- and y-directions from the simulation.
9. a The model diagram of the test piece at different scales. Eleven piezoelectric patches (PZT-5,
20 mm × 20 mm × 0.5 mm) are glued to the upper surface of the plate (Grade 304,700 mm × 750 mm × 2 mm) with separation of20 mm. The plate is engraved with a metasurface(475.9 mm × 11.2 mm) and the machining accuracy is0.05 mm. b Experimental distributions of out-of-plane displacement measured at6 kHz. The intersection of the longitudinal and transverse dashed lines marks the theoretical focal point. MAX is 64.46 nm.Table 1. Geometric parameters of the basic unit (unit: mm)
l H hi (i = 1-3) bi (i = 1-3) ri (i = 1-3) ti (i = 1-4) λ/5 λ/4 [bi, H−0.2] [0.5, 2.2] [0.2, 5.8] [0.5, H−0.2] 
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