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利用局部相位补偿调制的方式设计了一种超薄的弧形声学超表面地毯隐身斗篷. 该斗篷由52个亥姆霍兹空腔共振结构单元组成, 且结构单元厚度小于波长的0.2倍. 数值模拟结果显示: 文中所设计的隐身斗篷在深亚波长范围内隐身效果良好, 其工作频宽为5850—7550 Hz. 进一步探究声波斜入射时地毯斗篷的工作效果, 发现在30°的入射角范围内都具有良好的隐身效果. 此外, 利用余弦相似度(cosine similarity, CSI)函数精确量化分析了该隐身斗篷的工作性能, 计算结果展示, 在斗篷工作的带宽范围内, 覆盖斗篷后的CSI值趋近于无斗篷覆盖地面的CSI值, 展示了其在的良好隐身性. 本文所设计的斗篷均以超薄的亥姆霍兹共振结构为组成单元, 结构简单, 易于实现, 有利于未来的实际应用.
With the development of metamaterials, the acoustic cloaking has attracted extensive attention due to its novel physics and potential applications. In recent years, based on the phase compensation modulation from Generalized Snell’s law and coordinate transformation, the acoustic cloakings in underwater and air have been widely and deeply studied. However, there is still an urgent need to design acoustic cloaks that are thinner and less affected by the incident angle of acoustic waves. Further, the designed cloaks should have a wider operating band and be more suitable for irregular objects. In this paper, an ultrathin curved acoustic metasurface carpet cloaking is studied by using of phase compensation modulation. The phase modulation is based on Helmholtz resonance (HR). The metasurface carpet is immersed in air, since the vibration mode of acoustic wave in the air is relatively single, thus the physical essence can be elucidated more clearly. The carpet cloak is composed of 52 Helmholtz resonant units, and the size of resonant unit is less than 0.2 of working wavelength. The phase change of HR unit is solved analytically by using the Generalized Snell’s law, and confirmed by the Multiphysics COMSOL software. The parameter effects of HR unit on the phase change are studied, demonstrating that the phase change of HR unit is sensitive to the change of height and radius of HR unit, while the change of width of HR cavity neck can make the phase of HR unit change smoothly. Therefore, when building 52 HR units, the width of the HR cavity neck is designed, and the height and radius of HR unit stay fixed. The simulating results demonstrate that the designed cloak works well in a frequency range from 5850 Hz to 7550 Hz. Also, we study the cloaking effect for oblique incidence, and the results show that the carpet cloak works well for incident angle less than 30°. To quantitatively analyze the bandwidth of the cloaking, we calculate the cosine similarity value. It elucidates that the value of the cloak is very close to that of the flat ground in a corresponding working frequency range. The cloak designed in this work is made of ultrathin Helmholtz Resonant structures. This cloak is simple and easy to realize and conducive to potential applications. -
Keywords:
- acousitc metasurface /
- generalized Snell’s law /
- ultra-thin structure /
- carpet cloak
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图 1 利用反射波波前操纵的二维声学超表面地毯隐身示意图 (a)平坦地面; (b) 任意弯曲表面
Fig. 1. Illustration of a 2D acoustic carpet cloaking metasurface for reflected wavefront manipulation: (a) Flat surface; (b) arbitrary curved surface.
图 2 (a)地毯隐身超表面示意图, 弧形隐身斗篷及斗篷单个共振单元结构(红色框插图), 入射波从–z方向入射; (b), (c) 共振腔中r取不同值时单个共振单元反射相位随w的变化, 其中(b)入射波频率为3430 Hz, (c)入射波频率为6860 Hz; (d)共振腔中w取不同值时单个共振单元反射相位随h的变化; (e)共振腔中w取不同值时单个共振单元反射相位随r的变化; (f) 入射波频率为6860 Hz时, 弧形隐身斗篷中每个共振单元的反射相位(红色曲线)和由(5)式理论计算的相位(黑色曲线)
Fig. 2. (a) Schematic sketch of the metasurface for carpet cloaking, the illustration of arc-shaped carpet cloak, inset showing the schematic diagram of the unit-cell for the carpet. The acoustic waves are incident from –z direction. The reflection phase of single HR unit varing with w for acoustic waves normal incidence with different frequency: (b) 3430 Hz; (c) 6860 Hz. For different w, the reflection phase of single HR unit varing with h (d) and varing with r (e) for acoustic waves normal incidence with frequence 6860 Hz. (f) The reflection phase of each HR unit in the designed AMCC (red curve) and that of theoretical calculation from Eq. (5) (black curve) for acoustic waves normal incidence with frequence 6860 Hz.
图 3 (a)平面波分别垂直入射至平坦地面、弧形障碍物及覆盖于弧形障碍物上的斗篷时的反射声压场分布; (b) 5850, 7550 Hz频率下Z = 800 mm时归一化反射振幅; (c) 5850, 7550 Hz频率下Z = 800 mm时反射波阵面相位
Fig. 3. (a) Reflected pressure field distributions for a plane wave impinging on the flat ground, the arc-shaped object and the arc-shaped cloak; the normalized reflection amplitudes (b) and reflected wavefront phases (c) which located at Z = 800 mm for the incident frequency 5850 Hz and 7550 Hz.
图 4 平面波分别以10°和30°入射角斜入射至平坦地面、弧形障碍物及覆盖于弧形障碍物上的斗篷时的反射声压场分布
Fig. 4. When the incident angles are 10° and 30°, the reflected pressure field distributions for a plane wave impinging on the flat ground, the arc-shaped object and the arc-shaped cloak.
图 5 反射声波通过平坦地面、隐身斗篷和障碍物的CSI值
Fig. 5. The CSI of reflected acoustic waves for flat ground, carpet cloak, and arc-shaped object.
表 1 隐身斗篷每个共振单元颈宽w和半径r参数表
Table 1. Parameter list of neck width w and radii r of resonant unit in the cloak.
序号 w/mm r/mm 序号 w/mm r/mm 1 2.920 1.5 14 0.380 2.4 2 4.455 2.4 15 0.426 2.4 3 4.457 2.4 16 0.472 2.4 4 4.458 2.4 17 0.520 2.4 5 4.459 2.4 18 0.531 2.4 6 4.461 2.4 19 0.621 2.4 7 4.462 2.4 20 0.685 2.4 8 0.060 2.4 21 0.755 2.4 9 0.119 2.4 22 0.852 2.4 10 0.177 2.4 23 0.980 2.4 11 0.233 2.4 24 1.234 2.4 12 0.286 2.4 25 1.574 2.4 13 0.377 2.4 26 3.749 2.4 
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[1] Cummer S A, Christensen J, Alù A 2016 Nat. Rev. Mater. 1 16001
Google Scholar
[2] Lu M H, Feng L, Chen Y F 2009 Mater. Today 12 34
Google Scholar
[3] Liao G X, Luan C C, Wang Z W, Liu J P, Yao X H, Fu J Z 2021 Adv. Mater. Technol. 6 2000787
Google Scholar
[4] Zigoneanu L, Popa B I, Cummer S A 2014 Nat. Mater. 13 352
Google Scholar
[5] Bi Y, Jia H, Sun Z, Yang Y, Zhao H, Yang J 2018 Appl. Phys. Lett. 112 223502
Google Scholar
[6] Chen H, Chan C T 2007 Appl. Phys. Lett. 91 183518
Google Scholar
[7] Guild M D, Haberman M R, Alù A 2012 Phys. Rev. B 86 104302
Google Scholar
[8] Wei Q, Cheng Y, Liu X J 2012 Phys. Rev. B 86 024303
Google Scholar
[9] Zhou Z, Huang S, Li D, Zhu J, Li Y 2022 Natl. Sci. Rev. 9 nwab171
Google Scholar
[10] Zhang Y, Tong Y 2021 Opt. Commun. 483 126590
Google Scholar
[11] Bi Y, Jia H, Lu W, Ji P, Yang J 2017 Sci. Rep. 7 1
Google Scholar
[12] Chen Y, Zheng M, Liu X, Bi Y, Sun Z, Xiang P, Yang J, Hu G 2017 Phys. Rev. B 95 180104
Google Scholar
[13] Sun Z, Sun X, Jia H, Bi Y, Yang J 2019 Appl. Phys. Lett. 114 094101
Google Scholar
[14] Hu W, Fan Y, Ji P, Yang J 2013 J. Appl. Phys. 113 024911
Google Scholar
[15] Zhang S, Xia C, Fang N 2011 Phys. Rev. Lett. 106 024301
Google Scholar
[16] Chen Y, Liu X, Hu G 2015 Sci. Rep. 5 15745
Google Scholar
[17] Guo J, Fang Y, Qu R, Zhang X 2023 Mater. Today 66 321
Google Scholar
[18] Ji W Q, Wei Q, Zhu X F, Wu D J 2019 J. Phys. D: Appl. Phys. 52 325302
Google Scholar
[19] Jiang Z, Liang Q, Li Z, Chen T, Li D, Hao Y 2020 Adv. Opt. Mater. 8 2000827
Google Scholar
[20] Díaz-Rubio A, Tretyakov S A 2017 Phys. Rev. B 96 125409
Google Scholar
[21] Li X S, Wang Y F, Chen A L, Wang Y S 2020 J. Phys. D: Appl. Phys. 53 195301
Google Scholar
[22] Zhang H, He J, Liu C, Ma F 2023 Appl. Acoust. 213 109639
Google Scholar
[23] Tian Y, Wei Q, Cheng Y, Xu Z, Liu X 2015 Appl. Phys. Lett. 107 221906
Google Scholar
[24] Tang K, Qiu C, Ke M, Lu J, Ye Y, Liu Z 2015 Sci. Rep. 4 6517
Google Scholar
[25] Faure C, Richoux O, Félix S, Pagneux V 2016 Appl. Phys. Lett. 108 064103
Google Scholar
[26] Zhu Y, Assouar B 2019 Phys. Rev. B 99 174109
Google Scholar
[27] Zhou H T, Fan S W, Li X S, Fu W X, Wang Y F, Wang Y S 2020 Smart Mater. Struct. 29 065016
Google Scholar
[28] He J, Liang Q, Lv P, Wu Y, Chen T 2022 Appl. Acoust. 197 108957
Google Scholar
[29] Zhou H T, Fu W X, Wang Y F, Wang Y S, Laude V, Zhang C 2021 Mater. Des. 199 109414
Google Scholar
[30] Wang Y, Cheng Y, Liu X 2019 Sci. Rep. 9 1
Google Scholar
[31] Zhu Y, Fan X, Liang B, Cheng J, Jing Y 2017 Phys. Rev. X 7 021034
Google Scholar
[32] Yu G, Qiu Y, Li Y, Wang X, Wang N 2021 Phys. Rev. Appl. 15 064064
Google Scholar
[33] Guo J, Zhou J 2020 J. Phys. D: Appl. Phys. 53 505501
Google Scholar
[34] Ji G, Huber J 2022 Appl. Mater. Today 26 101260
Google Scholar
[35] Zhu Y, Hu J, Fan X, Yang J, Liang B, Zhu X, Cheng J 2018 Nat. Commun. 9 1632
Google Scholar
[36] Zhou P, Jia H, Bi Y, Liao B, Yang Y, Yan K, Zhang J, Yang J 2022 Phys. Rev. Appl. 18 014050
Google Scholar
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