Home Journals Articles Updates About
CN
image
收藏切换
Ultrathin Acoustic Parity-Time Symmetric Metasurface Cloak
收藏切换
PDF
Hao-xiang Li1, María Rosendo-López2, Yi-fan Zhu1, Xu-dong Fan1, Daniel Torrent3, Bin Liang1, Jian-chun Cheng1, Johan Christensen2
Research. Vol 2019 Article ID 8345683
Less
收藏切换
Research. Vol 2019 Article ID 8345683
• Research Article •
Ultrathin Acoustic Parity-Time Symmetric Metasurface Cloak
Full
Hao-xiang Li1, María Rosendo-López2, Yi-fan Zhu1, Xu-dong Fan1, Daniel Torrent3, Bin Liang1, Jian-chun Cheng1, Johan Christensen2
Affiliations
  • 1Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics, Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
  • 2Department of Physics, Universidad Carlos III de Madrid, 28916 Leganés, Madrid, Spain
  • 3GROC, UJI, Institut de Noves Tecnologies de la Imatge (INIT), Universitat Jaume I, 12080 Castellè, Spain
Published: 2019-08-20 doi: 10.34133/2019/8345683
Outline
收藏切换

Invisibility or unhearability cloaks have been made possible by using metamaterials enabling light or sound to flow around obstacle without the trace of reflections or shadows. Metamaterials are known for being flexible building units that can mimic a host of unusual and extreme material responses, which are essential when engineering artificial material properties to realize a coordinate transforming cloak. Bending and stretching the coordinate grid in space require stringent material parameters; therefore, small inaccuracies and inevitable material losses become sources for unwanted scattering that are decremental to the desired effect. These obstacles further limit the possibility of achieving a robust concealment of sizeable objects from either radar or sonar detection. By using an elaborate arrangement of gain and lossy acoustic media respecting parity-time symmetry, we built a one-way unhearability cloak able to hide objects seven times larger than the acoustic wavelength. Generally speaking, our approach has no limits in terms of working frequency, shape, or size, specifically though we demonstrate how, in principle, an object of the size of a human can be hidden from audible sound.

Hao-xiang Li, María Rosendo-López, Yi-fan Zhu, Xu-dong Fan, Daniel Torrent, Bin Liang, Jian-chun Cheng, Johan Christensen. Ultrathin Acoustic Parity-Time Symmetric Metasurface Cloak[J]. Research, 2019 , 2019 (8) : 8345683 - . DOI: 10.34133/2019/8345683
Full Text
Less
1. Introduction
Less
For centuries people have dreamt of an invisibility cloak that can make someone indiscernible for the naked eye when hidden underneath it. An ideal cloak would involve the suppression of back reflected light to render an object camouflaged, but the shadow behind it must also diminish for truly being able to make an object disappear. More than a decade ago an approach was brought forward based on transformation optics permitting the path of light to be bent around objects to be hidden [1–7]. This transformational approach to engineer space has ever since been extended to other areas of wave physics for cloaks of unhearability comprising sound and mechanical vibrations [8–13]. Despite those advances, it remains a fundamental challenge to create an unhearability cloak of ultrathin layer width involving minuscule loss-free materials. Here we propose theoretically and demonstrate experimentally that a parity-time symmetric metasurface incorporating acoustic gain and loss can act as such cloak when insonified from one direction. In contrast to transformation acoustics that implies a coordinate-transformation-based deformation of sound through the accurate distribution of the material properties, our approach to perfectly absorb incoming sound and to reemit it behind the hidden object solely implies the engineering of a complex acoustic metasurface-impedance. The use of parity-time symmetry enables unique cloaking properties useful in the audible range but also applicable to hide submarines from sonar detection.
Non-Hermitian systems that respect parity-time (PT)-symmetry have recently become an active frontier in wave physics due to unprecedented possibilities in guiding both sound and light [14, 15]. Most notably, designing complex eigenstates through appropriate balancing of gain and loss provides an unexpected paradigm for exploring non-Hermitian wave control in flourishing areas such as waveguiding, sensing, communication, and topological insulators [16–24]. In this work we demonstrate that a sizeable acoustically rigid obstacle (7 times larger than the wavelength) appears hidden to sound waves when coated by a PT symmetric metasurface due to the cancellation of reflections and reradiation of the impinging field to the far-side. When adjusting the gain-loss contrast to a point where this scenario is reached, unidirectional invisibility (unhearability) is obtained through a concurrent acoustic stealth and shadow cancellation.
Designing PT symmetry is based on manipulating absorption using judicious structures with gain regions and vice versa. The Hamiltonian commutes with the combined PT operator when loss and gain are equally balanced giving rise to entirely real eigenmode frequencies representing the unbroken or exact phase. When the loss and gain contrast exceeds a certain threshold to reach the broken phase, one of the complex eigenmodes exhibits exponential growth while the other one decays exponentially. The transition between these two phases is the non-Hermitian singularity, also known as an exceptional point (EP) where the modes coalesce.
One-way invisibility has been explored already in the context of layered non-Hermitian one-dimensional systems whose physics is well explained by the PT-symmetry breaking transitions of the scattering matrix. The anisotropic transmission resonance (ATR) is associated with the flux-conservation process leading to full transparency, i.e., unity transmittance T=1, but one-sided reflectionless wave propagation. A special case of the ATR is the unidirectional invisibility phenomenon that not only fulfills the condition of full transmission and vanishing of the reflection from either left RL or right RR incidence, but also implies a zero transmission phase signifying the apparent absence of an obstacle to be heard or seen [25, 26]. Several studies, in the fields of both optics and acoustics, have already investigated unidirectional invisibility in one-dimensional PT symmetric structures enabling shadow-free acoustic sensors and Bragg-scattering suppression in photonic lattices [27, 28]. Here we demonstrate the ability to acoustically cloak a rigid obstacle by covering it by an ultrathin PT metasurface as has been previously simulated for microwave radiation [29]. The approach consists in camouflaging the portion of the insonified metasurface through absorption and providing the time-reversed image, i.e., acoustic gain, to the shadow region behind the rigid obstacle (Figure 1). Through PT symmetric field properties associated with sound impinging at and emanating from the metasurface cloak, we provide a theoretical insight into the complex two-dimensional scattering problem.
2. Complete Absorption of Sound
Less
We begin the study by designing the insonified portion of the cloak, whereas the gain portion will be treated afterwards. Hence, in order to engineer complete scattering cancellation to an incoming plane wave we cover the rigid cylinder of radius a by a lossy metasurface as shown in Figure 1. The aim is to impedance match the metasurface to the surrounding air to totally absorb the incident wave without reflection. Under the assumption that the air gap separating the ultrathin cloak from the rigid cylinder is substantially smaller than the wavelength of the sound wave, i.e., k(b-a)≪1, we can write down the necessary complex surface impedance to fulfill camouflaging of the obstacle (see supplementary information (available here) for derivations):
(1)ReZs≈Z0ba1cos⁡θImZs≈Z0bakb-a,
where θ is the angular position in polar coordinates and k=2π/λ where λ is the wavelength. Equation (1) states that an impedance match of the metasurface to its surrounding with respect the geometrical parameters a and b is essential in order to achieve complete acoustic energy absorption. In (1), the free space impedance Z0=ρ0c0 where ρ0 and c0 are the mass density and speed of sound in air, respectively. Interestingly, if one would attempt to engineer scattering cancellation of a sound soft cylinder, e.g., an air cylinder submerged in water, then one would end up with exactly the same surface impedance as found for an equivalent microwave problem [29] (see supplementary material for the derivation). There is a plethora of passive and active metamaterials solutions available capable of completing sound absorption [13]. For the realization of a one-sided compact and lightweight unhearability cloak we use Helmholtz resonators that can be fabricated to absorb sound at broad spectral windows. In the present case, we focus on the audible range and therefore begin the design by engineering sound absorption at a frequency of f = 3 KHz although the approach could be readily realized at other desired frequencies. Strong air oscillations in the neck of these resonators in the presence of viscous losses are responsible for efficient energy dissipation. Conclusively, most absorbed acoustic energy is localized at the neck region; therefore, in order to fully camouflage an object, we pattern the rigid obstacle of radius a= 40 cm by Helmholtz resonators (Figure 2(a)) and adjust the individual neck parameters w and t accordingly (see supplementary information for their values) to account for the angular variation. By computing the averaged acoustic pressure 〈p〉 and velocity normal to the resonator surface 〈v⊥〉 through full-wave simulations in Comsol, we are able to determine the impedance of the metasurface Zs=〈p〉/〈v⊥〉. The aforementioned viscothermal losses are introduced in the neck region through the dynamic viscosity μ=1.802·10-5kg/ms, the heat capacity cP=1007J/kgK, and the thermal conductivity k=0.02476W/mK. In the absence of acoustic backscattering, we predict total absorption of a plane wave at each individual Helmholtz resonator as displayed in Figure 2(b) via their specific angular position. Correspondingly, we are able to explain full acoustic absorption via surface impedance matching as predicted in (1) where the real part of the relative metasurface impedance scales according to 1/cos⁡(θ) and its imaginary counterpart approaches zero for a vanishing gap separation a≈b.
3. Acoustic Gain Adjustment
Less
Perfect absorption removes acoustic backscattering and is the first ingredient of a PT symmetric system. The time-reversed image of this response constitutes acoustic amplification that we implement with an active electric circuit to control a semicircular array of loudspeakers (Figure 3(a)) [21, 28]. In order to implement sound amplification of equal but opposite strength to the absorbing counterpart, we begin by doing so mathematically. Operating parity P inversion and time reversal T on the loss portion of the cloak relates its impedance to the one at the gain portion Zs(θ)=-Zs∗(π+θ) with respect to Figure 3(a). Further, we are able to employ those two operations to the pressure field P(π+θ) at the lossy metasurface, to relate it to its gain counterpart:
(2)PPπ+θ,t=Pθ,t,TPπ+θ,t=P∗π+θ,-t.
These two actions result in P(θ)=PT[P(π+θ)] from which one analytically is able to determine the acoustic intensities residing at either side of the non-Hermitian metasurface cloak (see supplementary information for details)
(3)Iθ=Iπ+θ.
Equation (3) signifies that when the PT symmetric metasurface cloak is irradiated at the loss portion, the acoustic intensity in the nearest vicinity of an individual Helmholtz resonator (located at (π+θ)) equals the intensity at the exact opposite active loudspeaker (located at θ). Incidentally, whenever an object appears undetectable to sound or microwaves, the wave intensity is constant in space and equal to the incident wave power flux. This property is extremely useful when adjusting the individual loudspeakers to realize a one-way unhearability cloak. First, as detailed in the supplementary information, we placed the two jointed semishells surrounding the rigid obstacle inside an acoustic waveguide whose rigid walls are covered by absorbing cotton. The acoustic source is formed by an array of loudspeakers that generate plane waves with frequency f = 3 KHz. In order to emit signals from the gain semishell perfectly synchronized with the impinging signal, a microphone measures the incoming sound field in front of the Helmholtz resonators whose phase and amplitude is processed through a phase shifting and amplifier circuit. The adjustment is performed in relation to the discrete and opposite locations of the Helmholtz resonator and loudspeaker couples whose intensity relation is shown in Figure 3(b). Due to size limitations of the source and the geometrical restrictions of the waveguide, our detection range exhibits a unitary intensity relation up to ±48∘ beyond which deviations start to grow. In other words, the subsequent cloaking experiment will be conclusively limited to this range.
4. PT Symmetry Cloak
Less
Figure 4(a) displays the metasurface cloak in its entirety comprising the jointed non-Hermitian semishells. The obstacle to be cloaked was realized via a cylindrical acrylic shell with an outer diameter of 80 cm. The Helmholtz resonators responsible for the loss components and the active loudspeakers providing acoustic gain were mounted onto the shell. The individual Helmholtz resonators were 3D printed with thermoplastics whose geometrical parameters are tabulated in the supplementary information. At an operation frequency of 3 KHz corresponding to an acoustic wavelength of 11 cm, simulations and experimental measurements display how the pressure waves impinging the undecorated acrylic obstacle back-scatter at the side of irradiation but leave and almost soundless shadow at the obstacle’s far-side (Figure 4(b)). Contrary to this, when sound irradiates the non-Hermitian semishells that have been tuned to fulfill PT symmetry adhering to the aforementioned constant intensity setting, the acrylic obstacle, whose diameter is about 7 times larger than the acoustic wavelength, is acoustically camouflaged to match its surrounding via complete absorption, but, more importantly, the acoustic shadow gets eliminated through reconstruction of the impinging wave (Figure 4(c)). The experimental measurements show that, within the test areas, both in front of and behind the obstacle, almost perfect plane waves have been sustained rendering the object to be hidden perfectly unhearable and concealed. Additional simulations confirm that the present design is a stringent one-way implementation for sound at normal incidence (see supplementary information).
5. Discussion
Less
Further improvement can be achieved by enlarging the loudspeaker array to launch a near-ideal plane wave. Also, decorating an object of arbitrary shape with gain and loss units in response to a point source or more complicated wave shapes greatly broadens the usage of PT symmetry based acoustic cloaks. We implemented the proof of concept by means of Helmholtz resonators to suppress back reflected sound via resonant absorption. In analogy to the implemented active gain component, active loss control would enrich the possibility of eliminating backscattering and providing an acoustic camouflage dynamically at a wider spectral range. Yet, increasing the bandwidth of a passive metasurface could be made possible by combining various resonating unit cells [13]. Extension toward an acoustical concealment of three-dimensional bodies by ultrathin non-Hermitian shells is another avenue worth pursuing.
In conclusion, we have derived a theoretical recipe to realize an acoustic unhearability cloak via PT symmetry. By combining loss and gain structures, we showed that reflected sound is eliminated from an insonified body to be concealed and how it is reconstructed at the rear side of it. Full-wave simulations and measurement data support the theoretical predictions in creating a cloak based on a single but non-Hermitian shell structure.
Funding
Less
  • National Key R&D Program of China(2017YFA0303700)
  • National Natural Science Foundation of China(11634006)
  • Innovation Special Zone of National Defense Science and Technology
  • Ministerio de Economía y Competitividad(RYC-2016-21188)
  • H2020 European Research Council(714577)
  • Ministerio de Economía y Competitividad(RYC-2015-17156)
References
Less
1
Pendry J. B., Schurig D., and Smith D. R., “Controlling electromagnetic fields,” Science, vol. 312, no. 5781, pp. 1780–1782, 2006
2
Schurig D., Mock J. J., Justice B. J., Cummer S. A., Pendry J. B., Starr A. F., and Smith D. R., “Metamaterial electromagnetic cloak at microwave frequencies,” Science, vol. 314, no. 5801, pp. 977–980, 2006
3
Li J., and Pendry J. B., “Hiding under the carpet: A new strategy for cloaking,” Physical Review Letters, vol. 101, 2008
4
Valentine J., Li J., Zentgraf T., Bartal G., and Zhang X., “An optical cloak mode of dielectrics,” Nature Materials, vol. 8, p. 568, 2009
5
Ergin T., Stenger N., Brenner P., Pendry J. B., and Wegener M., “Three-dimensional invisibility cloak at optical wavelengths,” Science, vol. 328, no. 5976, pp. 337–339, 2010
6
Ni X., Wong Z. J., Mrejen M., Wang Y., and Zhang X., “An ultrathin invisibility skin cloak for visible light,” Science, vol. 349, no. 6254, pp. 1310–1314, 2015
7
Alù A., “Mantle cloak: invisibility induced by a surface,” Physical Review B: Condensed Matter and Materials Physics, vol. 80, 2009
8
Cummer S. A., and Schurig D., “One path to acoustic cloaking,” New Journal of Physics , vol. 9, article 45, 2007
9
Torrent D., and Sánchez-Dehesa J., “Acoustic cloaking in two dimensions: a feasible approach,” New Journal of Physics , vol. 10, no. 6, 2008
10
Sanchis L. et al., , “Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere,” Physical Review Letters, vol. 110, no. 14, 2013
11
Zigoneanu L., Popa B.-I., and Cummer S. A., “Three-dimensional broadband omnidirectional acoustic ground cloak,” Nature Materials, vol. 13, no. 4, pp. 352–355, 2014
12
Stenger N., Wilhelm M., and Wegener M., “Experiments on elastic cloaking in thin plates,” Physical Review Letters, vol. 108, 2012
13
Cummer S. A., Christensen J., and Alu A., “Controlling sound with acoustic metamaterials,” Nature Materials, vol. 1, 2016
14
Bender C. M., and Boettcher S., “Real spectra in non-hermitian hamiltonians having pt symmetry,” Physical Review Letters, vol. 80, no. 24, pp. 5243–5246, 1998
15
Bender C. M., Brody D. C., and Jones H. F., “Complex extension of quantum mechanics,” Physical Review Letters, vol. 89, 2002
16
Makris K. G., El-Ganainy R., Christodoulides D. N., and Musslimani Z. H., “Beam dynamics in pt symmetric optical lattices,” Physical Review Letters, vol. 100, 2008
17
Guo A., Salamo G. J., Duchesne D., Morandotti R., Volatier-Ravat M., Aimez V., Siviloglou G. A., and Christodoulides D. N., “Observation of pt-symmetry breaking in complex optical potentials,” Physical Review Letters, vol. 103, 2009
18
Ruter C. E., Makris K. G., El-Ganainy R., Christodoulides D. N., Segev M., and Kip D., “Observation of parity-time symmetry in optics,” Physical Review Letters, vol. 6, article no 192, 2010
19
Peng B., Özdemir Ş. K., Lei F., Monifi F., Gianfreda M., Long G. L., Fan S., Nori F., Bender C. M., and Yang L., “Parity–time-symmetric whispering-gallery microcavities,” Nature Physics, vol. 10, no. 5, pp. 394–398, 2014
20
Christensen J., Willatzen M., Velasco V. R., and Lu M.-H., “Parity-time synthetic phononic media,” Physical Review Letters, vol. 116, 2016
21
Shi C., Dubois M., Chen Y., Cheng L., Ramezani H., Wang Y., and Zhang X., “Accessing the exceptional points of parity-time symmetric acoustics,” Nature Communications, vol. 7, 2016
22
Wang M., Ye L., Christensen J., and Liu Z., “Valley physics in non-hermitian artificial acoustic boron nitride,” Physical Review Letters, vol. 120, 2018
23
Zhang Z., Rosendo Lopez M., Cheng Y., Liu X., and Christensen J., “Non-hermitian sonic second-order topological insulator,” Non-Hermitian Sonic Second-Order Topological Insulator, vol. 122, 1955
24
Gong Z., Ashida Y., Kawabata K., Takasan K., Higashikawa S., and Ueda M., “Topological phases of non-hermitian systems,” Physical Review X, vol. 8, 2018
25
Lin Z., Ramezani H., Eichelkraut T., Kottos T., Cao H., and Christodoulides D. N., “Unidirectional invisibility induced by PT-symmetric periodic structures,” Physical Review Letters, vol. 106, 2011
26
Ge L., Chong Y. D., and Stone A. D., “Conservation relations and anisotropic transmission resonances in one-dimensional pt-symmetric photonic heterostructures,” Physical Review A, vol. 85, 2012
27
Regensburger A., Bersch C., Miri M.-A., Onishchukov G., Christodoulides D. N., and Peschel U., “Parity-time synthetic photonic lattices,” Nature, vol. 488, no. 7410, pp. 167–171, 2012
28
Fleury R., Sounas D., and Alu A., “An invisible acoustic sensor based on parity-time symmetry,” Nature Communications, vol. 6, 2015
29
Sounas D. L., Fleury R., and Alu A., “Unidirectional cloaking based on metasurfaces with balanced loss and gain,” Physical Review Applied, vol. 4, 2015
Appendix
Less
Year 2019 volume 2019 Issue 8
PDF
75
41
Cite this Article
BibTeX
Article Info
doi: 10.34133/2019/8345683
  • Receive Date：2019-06-11
  • Online Date：2026-10-27
  • Published：2019-08-20
Article Data
Affiliations
History
  • Received：2019-06-11
  • Accepted：2019-07-14
Funding
National Key R&D Program of China(2017YFA0303700)
National Natural Science Foundation of China(11634006)
Innovation Special Zone of National Defense Science and Technology
Ministerio de Economía y Competitividad(RYC-2016-21188)
H2020 European Research Council(714577)
Ministerio de Economía y Competitividad(RYC-2015-17156)
Affiliations
    1Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics, Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
    2Department of Physics, Universidad Carlos III de Madrid, 28916 Leganés, Madrid, Spain
    3GROC, UJI, Institut de Noves Tecnologies de la Imatge (INIT), Universitat Jaume I, 12080 Castellè, Spain
References
Share
https://castjournals.cast.org.cn/joweb/research/EN/10.34133/2019/8345683
Share to
QR

Scan QR to access full text

Cite this article
BibTeX
Citations
表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
关闭全屏
  • BibTeX
  • EndNote
  • RefWorks
  • TxT
Links
Articles
Latest Articles
Most Read
Collections
Updates
Events
News
Multimedia
About
About Us
Contact
No. 86 Xueyuan South Road, Haidian District, Beijing
100081
010-62662699(Operation and Technical Support)
qkjq@cast.org.cn

Copyright © 2025 China Association for Science and Technology. All rights reserved. For all open access content, the relevant licensing terms apply.
Sponsored by the Office of the Leading Group for Cybersecurity and Informatization of CAST, and supported by Science and Technology Review Publishing House