High-Order Diffractive Elastic-Wave Manipulations Based on Piezoelectric Metasurfaces
Abstract
Elastic metasurfaces offer powerful capabilities for manipulating wave propagation, with applications ranging from vibration attenuation and noise isolation to structural health monitoring. However, the multimodal nature and strong dispersion of elastic-waves impede the realization of stable, broadband control. While piezoelectric materials provide a pathway toward active tunability, the manipulation of higher-order diffracted guided waves remains a significant challenge, restricting practical engineering utility. Here, we propose a tunable piezoelectric elastic metasurface that overcomes these limitations. By adjusting piezoelectric parameters via simple external circuits—without modifying the structural substrate—we demonstrate versatile control over elastic-waves and their higher-order diffraction modes,includingadaptive anomalous refraction,tunable subwavelength focusing,source illusion etc. This approach enables diverse exotic wave phenomena, bridging the gap between theoretical research and the practical application of intelligent wave manipulation.
Keywords
Elastic-waves, high-order diffraction, piezoelectric metasurfaces, phase modulation, asymmetric transmission
References
- [1] Cawley P. Guided waves in long range nondestructive testing and structural health monitoring: Principles, history of applications and prospects. NDT & E International 2024; 142: 103026.
- [2] Ricci F, Monaco E, Boffa N, Maio L, Memmolo. Guided waves for structural health monitoring in composites: A review and implementation strategies. Prog Aeosp Sci 2022; 129: 21.
- https://doi.org/10.1016/j.paerosci.2021.100790
- [3] Hu Y, Li Y, Liu Y, Li B, Christensen J. Giant elastic-wave asymmetry in a linear passive circulator. Nat Commun 2025; 16(1): 10.
- https://doi.org/10.1038/s41467-025-59313-0
- [4] Yang Z, Yi J, Li F, Li Z, Ye L, Li B, et al. Static mechanical cloaking and camouflage from disorder. Nat Commun 2025; 16(1): 12.
- https://doi.org/10.1038/s41467-025-63939-5
- [5] Cao L, Yang Z, Xu Y, Fan S, Zhu Y, Chen Z, et al. Flexural wave absorption by lossy gradient elastic metasurface. J Mech Phys Solids 2020; 143: 23.
- https://doi.org/10.1016/j.jmps.2020.104052
- [6] Wang W, Iglesias J, Jin Y, Djafari-Rouhani B, Khelif A. Experimental realization of a pillared metasurface for flexural wave focusing. APL Mater 2021; 9(5): 7.
- https://doi.org/10.1063/5.0052278
- [7] Jiang Y, Liu Y, Kou M, Li H, Wu X, Zeng X, et al. Multi-parameter independent manipulation for flexural wave by notched metasurface. Int J Mech Sci 2022; 214: 16.
- https://doi.org/10.1016/j.ijmecsci.2021.106928
- [8] Zhang J, Su X, Liu Y, Zhao Y, Jing Y, Hu N. Metasurface constituted by thin composite beams to steer flexural waves in thin plates. Int J Solids Struct 2019; 162: 14-20.
- https://doi.org/10.1016/j.ijsolstr.2018.11.025
- [9] Yuan S, Chen A, Wang Y. Switchable multifunctional fish-bone elastic metasurface for transmitted plate wave modulation. J Sound Vibr 2020; 470: 13.
- https://doi.org/10.1016/j.jsv.2019.115168
- [10] Zhang S, Shu S, Bian X. Tunability for anomalous refraction of flexural wave in a magneto-elastic metasurface by magnetic field and pre-stress. Appl Phys Express 2022; 15(2): 6. https://doi.org/10.35848/1882-0786/ac4925
- [11] Wang Y, Wang Y, Wu B, Chen W, Wang Y. Tunable and Active Phononic Crystals and Metamaterials. Appl Mech Rev 2020; 72(4): 35.
- https://doi.org/10.1115/1.4046222
- [12] Zhang Q, Guo D, Hu G. Tailored Mechanical Metamaterials with Programmable Quasi-Zero-Stiffness Features for Full-Band Vibration Isolation. Advanced Functional Materials 2021; 31(33): 9.
- https://doi.org/10.1002/adfm.202101428
- [13] Casadei F, Ruzzene M, Dozio L, Cunefare K. Broadband vibration control through periodic arrays of resonant shunts: experimental investigation on plates. Smart Mater Struct 2010; 19(1): 13.
- https://doi.org/10.1088/0964-1726/19/1/015002
- [14] Airoldi L, Ruzzene M. Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos. New J Phys 2011; 13: 21.
- https://doi.org/10.1088/1367-2630/13/11/113010
- [15] Fu Y, Shen C, Cao Y, Gao L, Chen H, Chan C, et al. Reversal of transmission and reflection based on acoustic metagratings with integer parity design. Nat Commun 2019; 10: 8.
- https://doi.org/10.1038/s41467-019-10377-9
- [16] Bing L, Huiyu X, Lingjuan H, Tianbao Y, Wenxing L, Tongbiao W, et al. Wide-angle asymmetric sound wave transmission in the single-layer metasurface. Technical Acoustics 2019; 38(3): 253-7.
- [17] Li B, Hu Y, Chen J, Su G, Liu Y, Zhao M, et al. Efficient Asymmetric Transmission of Elastic Waves in Thin Plates with Lossless Metasurfaces. Phys Rev Appl 2020; 14(5): 8.
- https://doi.org/10.1103/PhysRevApplied.14.054029
- [18] Yu N, Genevet P, Kats M, Aieta F, Tetienne J, Capasso F, et al. Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction. Science 2011; 334(6054): 333-7.
- https://doi.org/10.1126/science.1210713
- [19] Shao S, Xia R, Li Z. Tunable piezoelectric metasurface for manipulating multi-mode guided waves in plate. Eng Struct 2022; 270: 12.
- https://doi.org/10.1016/j.engstruct.2022.114917
- [20] Wang W, Xu W, Yang Z, Yu X, Cheng S. Switchable bidirectional asymmetric transmission structure based on knob-controlled metasurfaces. Phys Lett A 2023; 490: 6.
- https://doi.org/10.1016/j.physleta.2023.129189
- [21] Zheng M, Park C, Liu X, Zhu R, Hu G, Kim Y. Non-resonant metasurface for broadband elastic wave mode splitting. Appl Phys Lett 2020; 116(17): 5.
- https://doi.org/10.1063/5.0005408
- [22] Zhang H, Chen Y, Liu X, Hu G. An asymmetric elastic metamaterial model for elastic wave cloaking. J Mech Phys Solids 2020; 135: 12.
- https://doi.org/10.1016/j.jmps.2019.103796
- [23] Pan R, Liu Z, Zhu W, Du S, Gu C, Li J. 3D Bended Metasurfaces: Asymmetrical Chirality in 3D Bended Metasurface (Adv. Funct. Mater. 31/2021). Advanced Functional Materials 2021; 31(31).
- [24] Fan H, Luo J. Research progress of non-Hermitian electromagnetic metasurfaces. Acta Phys Sin 2022; 71(24): 16.
- https://doi.org/10.7498/aps.71.20221706
- [25] Chung C, Lai F, Huang S, Chen Y. Anisotropic Metasurface With Asymmetric Propagation of Electromagnetic Waves and Enhancements of Antenna Gain. IEEE Access 2021; 9: 90295-305.
- https://doi.org/10.1109/access.2021.3091464
- [26] Wang X, Fang X, Mao D, Jing Y, Li Y. Extremely Asymmetrical Acoustic Metasurface Mirror at the Exceptional Point. Phys Rev Lett 2019; 123(21): 6.
- https://doi.org/10.1103/PhysRevLett.123.214302
- [27] Zhang X, Li L, Li K, Liu T, Zhang J, Hu N. Flexural wave splitting via elastic metagratings based on high-order diffraction theory. Appl Acoust 2023; 202: 11.
- https://doi.org/10.1016/j.apacoust.2022.109170
- [28] Li H, Hu Y, Huang H, Chen J, Zhao M, Li B. Broadband low-frequency vibration attenuation in 3D printed composite meta-lattice sandwich structures. Compos Pt B-Eng 2021; 215: 15.
- https://doi.org/10.1016/j.compositesb.2021.108772
- [29] Li C, Song Z. Tailoring terahertz wavefront with state switching in VO2 Pancharatnam-Berry metasurfaces. Opt Laser Technol 2023; 157: 9.
- https://doi.org/10.1016/j.optlastec.2022.108764
- [30] Fan Y, Wang J, Fu X, Li Y, Pang Y, Zheng L, et al. Recent developments of metamaterials/metasurfaces for RCS reduction. EPJ Applied Metamaterials 2019; 6: 15.
- [31] Shen Y, Xu Y, Liu F, Yang Z. Metasurface-guided flexural waves and their manipulations. Int J Mech Sci 2023; 257: 15.
- https://doi.org/10.1016/j.ijmecsci.2023.108538