Surface resonant states and superlensing in acoustic metamaterials

Ambati, Muralidhar; Fang, Nicholas X.; Sun, Cheng; Zhang, Xiang

doi:10.1103/physrevb.75.195447

Cited by 211 publications

(142 citation statements)

References 31 publications

(30 reference statements)

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“…[3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] In particular, their effective mass density and modulus can be singly or simultaneously negative, 3-13 allowing intriguing phenomena for sound waves such as low-frequency band gaps, 3-10 negative refraction, and superlensing. 1, [12][13][14] Negative effective mass density or modulus can occur at certain frequencies if an appropriate resonance is included into the structures. 3-13 A famous example is the threecomponent phononic crystal with locally resonant structures, 3 which exhibits a negative effective mass density e due to a dipolar resonance.…”

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confidence: 99%

Homogenization of acoustic metamaterials of Helmholtz resonators in fluid

Chan

et al. 2008

Phys. Rev. B

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By using a two-step homogenization approach, we derive analytical formulas of effective mass density e and effective bulk modulus B e for two-and three-dimensional acoustic metamaterials of Helmholtz resonators ͑HRs͒ in fluid. A negative B e is found at certain frequencies due to the monopolar resonance, leading to a low-frequency acoustic band gap. A unified picture is presented for metamaterials of HRs and three-component metamaterials of negative e . Our work supports recent observations in a one-dimensional array of HRs ͓N. Fang et al., Nat. Mater. 5, 452 ͑2006͔͒ and presents important high-dimensional extensions for exploring more fascinating phenomena. DOI: 10.1103/PhysRevB.77.172301 PACS number͑s͒: 42.25.Bs, 41.20.Jb, 46.40.Ϫf, 62.30.ϩd Recently, acoustic and/or elastic metamaterials ͑artificial structured materials 1,2 ͒ have received considerable interest due to their exotic acoustic and/or elastic properties. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] In particular, their effective mass density and modulus can be singly or simultaneously negative, 3-13 allowing intriguing phenomena for sound waves such as low-frequency band gaps, 3-10 negative refraction, and superlensing. 1,[12][13][14] Negative effective mass density or modulus can occur at certain frequencies if an appropriate resonance is included into the structures. 3-13 A famous example is the threecomponent phononic crystal with locally resonant structures, 3 which exhibits a negative effective mass density e due to a dipolar resonance. 4,5 Very recently, a lowfrequency band gap was demonstrated in a one-dimensional ͑1D͒ array of Helmholtz resonators ͑HRs͒. 6 By using further retrieval analysis of wave-scattering coefficients, 7-9 a negative effective bulk modulus B e was confirmed in the 1D metamaterials of HRs. 9 Unlike other designs for negative B e using air bubbles or soft-rubber spheres, 12,13 this metamaterial consists of a rigid body but still possesses a sizable working frequency range. However, high-dimensional metamaterials of HRs, which are essential for more fascinating phenomena, 6,14,15 remain unexplored.In this Brief Report, we study two-dimensional ͑2D͒ and three-dimensional ͑3D͒ acoustic metamaterials consisting of cylindrical and spherical HRs in fluid ͑such as water or air͒, respectively. By using a two-step homogenization approach, we can derive analytical formulas for the e and B e within coherent-potential approximation ͑CPA͒. 18 The accuracy of these formulas is confirmed by accurate retrieval results using multiple-scattering techniques. We show that our metamaterials of HRs can exhibit a negative B e at certain frequencies due to a monopolar resonance. Systematic analyses are done for the frequency range of negative B e and the low-frequency-limit behavior. Based on our derivations, a unified picture is presented for metamaterials of HRs and three-component metamaterials of negative e .Our HRs are cylindrical and/or spherical rigid shells with uniformly distributed slits and/or holes, as shown in Fig. 1...

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Homogenization of acoustic metamaterials of Helmholtz resonators in fluid

Chan

et al. 2008

Phys. Rev. B

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“…We note that the density can be isotropic if the thickness of the CMM is chosen to be the same as the aberrating layer. In this case, however, the refractive index is −1, and the k vector along the interface goes to infinity [22]. In other words, such a CMM will be very unit-cellsize sensitive and can be difficult to demonstrate.…”

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Anisotropic Complementary Acoustic Metamaterial for Canceling out Aberrating Layers

et al. 2014

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In this paper, we investigate a type of anisotropic, acoustic complementary metamaterial (CMM) and its application in restoring acoustic fields distorted by aberrating layers. The proposed quasi two-dimensional (2D), nonresonant CMM consists of unit cells formed by membranes and side branches with open ends. Simultaneously, anisotropic and negative density is achieved by assigning membranes facing each direction (x and y directions) different thicknesses, while the compressibility is tuned by the side branches. Numerical examples demonstrate that the CMM, when placed adjacent to a strongly aberrating layer, could acoustically cancel out that aberrating layer. This leads to dramatically reduced acoustic field distortion and enhanced sound transmission, therefore virtually removing the layer in a noninvasive manner. In the example where a focused beam is studied, using the CMM, the acoustic intensity at the focus is increased from 28% to 88% of the intensity in the control case (in the absence of the aberrating layer and the CMM). The proposed acoustic CMM has a wide realm of potential applications, such as cloaking, all-angle antireflection layers, ultrasound imaging, detection, and treatment through aberrating layers. In many medical ultrasound or nondestructive evaluation (NDE) applications, ultrasound needs to be transmitted through an aberrating layer [1][2][3][4][5][6][7], where either the transmission is desired to be maximized or the reflection needs to be minimized. One of the most representative examples is transcranial ultrasound beam focusing, which could find usage in both brain imaging and treatment [6,7]. However, transcranial beam focusing is extremely challenging because of the presence of the skull. A common approach to achieve transcranial beam focusing is based on the timereversal or phase-conjugate technique and ultrasound phased arrays [8,9]. Although the focal position can be corrected, one significant shortcoming of this strategy is that it does not compensate for the large acoustic energy loss due to the impedance mismatch between the skull and the background medium (water). Recent development of acoustic metamaterials [10][11][12] could open up the possibility for noninvasive ultrasound transmission through aberrating layers. For example, an acoustic metamaterial could be used to cancel out or cloak the aberrating layer, allowing the acoustic wave to pass through the layer without energy loss (Fig. 1). Conventional cloaking strategies [11,13,14], however, compress the space and hide the object inside an enclosure in which there is no interaction with the outside world; therefore, it is not suited to the problem of interest in this study. Lai et al. demonstrated that cloaking or illusion based on electromagnetic wave (EM) complementary metamaterials (CMM) [15] can open up a virtual hole in a wall without distortion [16,17]. In addition, this type of approach does not require the cloaked object to be inside an enclosure or cloaking shell, and it is valid in free space [18]. Because of the s...

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“…An interesting feature of such systems is the possibility of the localization of mechanical energy on low dimensional structures. [8][9][10][11] . Typically, when such modes exist in well ordered systems, they are confined to regions near defects in crystals or at surfaces 12,13 .…”

Section: Introductionmentioning

confidence: 99%

Sparse phonon modes of a limit-periodic structure

Marcoux

Socolar

2016

Phys. Rev. B

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Limit-periodic structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. We study a ball and spring model with a limit-periodic pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to limit-periodic systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the limit-periodic structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.

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Surface resonant states and superlensing in acoustic metamaterials

Cited by 211 publications

References 31 publications

Homogenization of acoustic metamaterials of Helmholtz resonators in fluid

Homogenization of acoustic metamaterials of Helmholtz resonators in fluid

Anisotropic Complementary Acoustic Metamaterial for Canceling out Aberrating Layers

Sparse phonon modes of a limit-periodic structure

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