The inverse method based on the numerical solution of Laplace's equation is introduced for the design of acoustic metamaterial devices. An arbitrary shaped acoustic concentrator and an external cloak are designed numerically and validated by full wave simulation. Besides, an acoustic reciprocal cloak and a field rotator are proposed. Compared with the analytical method, the inverse method is much more universal, and arbitrary shaped acoustic metamaterial devices can be flexibly designed without any knowledge of the transformation equations.
Issue Section:
Research Papers
References
1.
Shelby
, R. A.
, Smith
, D. R.
, and Schultz
, S., 2001
, “Experimental Verification of a Negative Index of Refraction
,” Science
, 292
, pp. 77
–79
.10.1126/science.10588472.
Pendry
, J. B.
, 2000
, “Negative Refraction Makes a Perfect Lens
,” Phys. Rev. Lett.
, 85
, pp. 3966
–3969
.10.1103/PhysRevLett.85.39663.
Al-Naib
, A. I.
, Jansen
, C.
, and Koch
, M.
, 2008
, “Thin-Film Sensing With Planar Asymmetric Metamaterial Resonators
,” Appl. Phys. Lett.
, 93
, p. 083507
.10.1063/1.29766364.
Yang
, J. J.
, Huang
, M.
, Yu
, J.
, and Lan
, Y. Z.
, 2011
, “Surface Whispering-Gallery Mode
,” Europhys. Lett.
, 96
, p. 57003
.10.1209/0295-5075/96/570035.
Huang
, M.
, and Yang
, J. J.
, 2011
, “Microwave Sensor Using Metamaterials
,” Wave Propagation
, A.
Petrin
(ed.), InTech Inc. Press
, Austria
, pp. 13
–36
.6.
Chen
, P. Y.
, and Alù
, A.
, 2010
, “Sub-Wavelength Elliptical Patch Antenna Loaded With μ-Negative Metamaterials
,” IEEE Trans. Antenna. Propag.
, 58
, pp. 2909
–2919
.10.1109/TAP.2010.20525787.
Zheludev
, N. I.
, 2010
, “The Road Ahead for Metamaterials
,” Science
, 328
, pp. 582
–853
.10.1126/science.11867568.
Zhu
, R.
, Huang
, G. L.
, and Hu
, G. K.
, 2012
, “Effective Dynamic Properties and Multi-Resonant Design of Acoustic Metamaterials
,” ASME J. Vib. Acoust.
, 134
, p. 031006
.10.1115/1.40058259.
Huang
, G. L.
, and Sun
, C. T.
, 2010
, “Band Gaps in a Multiresonator Acoustic Metamaterial
,” ASME J. Vib. Acoust.
, 132
, p. 031003
.10.1115/1.400078410.
Pendry
, J. B.
, Schurig
, D.
, and Smith
, D. R.
, 2006
, “Controlling Electromagnetic Fields
,” Science
, 312
, pp. 1780
–1782
.10.1126/science.112590711.
Leonhardt
, U.
, 2006
, “Optical Conformal Mapping
,” Science
, 312
, pp. 1777
–1780
.10.1126/science.112649312.
Schurig
, D.
, Mock
, J. J.
, Justice
, B. J.
, Cummer
, S. A.
, Pendry
, J. B.
, Starr
, A. F.
, and Smith
, D. R.
, 2006
, “Metamaterial Electromagnetic Cloak at Microwave Frequencies
,” Science
, 314
, pp. 977
–979
.10.1126/science.113362813.
Liu
, R.
, Ji
, C.
, Mock
, J. J.
, Chin
, J. Y.
, Cui
, T. J.
, Smith
, D. R.
, 2009
, “Broadband Ground-Plane Cloak
,” Science
, 323
, pp. 366
–369
.10.1126/science.116694914.
Liu
, X.
, Li
, C.
, Yao
, K.
, Meng
, X.
, Feng
, W.
, Wu
, B.
, and Li
, F.
, 2009
, “Experimental Verification of Broadband Invisibility Using a Cloak Based on Inductor-Capacitor Networks
,” Appl. Phys. Lett.
, 95
, p. 191107
.10.1063/1.326314915.
Yang
, J. J.
, Huang
, M.
, Yang
, C. F.
, and Yu
, J.
, 2011
, “Reciprocal Invisibility Cloak Based on Complementary Media
,” Eur. Phys. J. D.
, 61
, pp. 731
–736
.10.1140/epjd/e2010-10507-216.
Yang
, J. J.
, Huang
, M.
, Yang
, C. F.
, Xiao
, Z.
, and Peng
, J. H.
, 2009
, “Metamaterial Electromagnetic Concentrators With Arbitrary Geometries
,” Opt. Express
, 17
, pp. 19656
–19661
.10.1364/OE.17.01965617.
Yang
, C. F.
, Yang
, J. J.
, Huang
, M.
, Xiao
, Z.
, and Peng
, J. H.
, 2011
, “An External Cloak With Arbitrary Cross Section Based on Complementary Medium and Coordinate Transformation
,” Opt. Express
, 19
, pp. 1147
–1156
.10.1364/OE.19.00114718.
Jiang
, W. X.
, Cui
, T. J.
, Yang
, X. M.
, Ma
, H. F.
, and Cheng
, Q.
, 2011
, “Shrinking an Arbitrary Object as One Desires Using Metamaterials
,” Appl. Phys. Lett.
, 98
, p. 204101
.10.1063/1.359020319.
Rahm
, M.
, Cummer
, S. A.
, Schurig
, D.
, Pendry
, J. B.
, and Smith
, D. R.
, 2008
, “Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations
,” Phys. Rev. Lett.
, 100
, p. 063903
.10.1103/PhysRevLett.100.06390320.
Chen
, H.
, Chan
, C. T.
, and Sheng
, P.
, 2010
, “Transformation Optics and Metamaterials
,” Nature Mater.
, 9
, pp. 387
–396
.10.1038/nmat274321.
Chen
, H. Y.
, and Chan
, C. T.
, 2007
, “Acoustic Cloaking in Three Dimensions Using Acoustic Metamaterials
,” Appl. Phys. Lett.
, 91
, p. 183518
.10.1063/1.280331522.
Cummer
, S. A.
, Popa
, B.
, Schurig
, D.
, Smith
, D. R.
, Pendry
, J.
, Rahm
, M.
, and Starr
, A.
, 2008
, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell
,” Phys. Rev. Lett.
, 100
, p. 024301
.10.1103/PhysRevLett.100.02430123.
Chen
, H. Y.
, and Chan
, C. T.
, 2010
, “Acoustic Cloaking and Transformation Acoustics
,” J. Phys. D: Appl. Phys.
, 43
, p. 113001
.10.1088/0022-3727/43/11/11300124.
25.
Popa
, B. I.
, Zigoneanu
, L.
, and Cummer
, S. A.
, 2011
, “Experimental Acoustic Ground Cloak in Air
,” Phys. Rev. Lett.
, 106
, p. 253901
.10.1103/PhysRevLett.106.25390126.
Zhou
, X.
, and Hu
, G.
, 2006
, “Design for Electromagnetic Wave Transparency With Metamaterials
,” Phys. Rev. E
, 74
, p. 026607
.10.1103/PhysRevE.74.02660727.
Liu
, B.
, and Huang
, J. P.
, 2009
, “Acoustically Conceal an Object With Hearing
,” Eur. Phys. J. Appl. Phys.
, 48
, p. 20501
.10.1051/epjap/200912728.
Zhu
, X.
, Liang
, B.
, Kan
, W.
, Zou
, X.
, and Cheng
, J.
, 2011
, “Acoustic Cloaking by a Superlens With Single-Negative Materials
,” Phys. Rev. Lett.
, 106
, p. 014301
.10.1103/PhysRevLett.106.01430129.
Yang
, J. J.
, Huang
, M.
, Yang
, C.
, Peng
, J. H.
, and Jun
, C.
, 2010
, “An External Acoustic Cloak With N-Sided Regular Polygonal Cross Section Based on Complementary Medium
,” Comp. Mater. Sci.
, 49
, pp. 9
–14
.10.1016/j.commatsci.2010.03.05030.
Yang
, J. J.
, Huang
, M.
, Yang
, C. F.
, and Cai
, G. H.
, 2011
, “A Metamaterial Acoustic Concentrator With Regular Polygonal Cross Section
,” ASME J. Vib. Acoust.
, 133
, p. 061016
.10.1115/1.400467831.
Yang
, T.
, Cao
, R. F.
, Luo
, X. D.
, and Ma
, H. R.
, 2010
, “Acoustic Superscatterer and Its Multilayer Realization
,” Appl. Phys. A
, 99
, pp. 843
–847
.10.1007/s00339-010-5609-032.
Ma
, H.
, Qu
, S.
, Xu
, Z.
, and Wang
, J.
, 2008
, “Numerical Method for Designing Approximate Cloaks With Arbitrary Shapes
,” Phys. Rev. E
, 78
, p. 036608
.10.1103/PhysRevE.78.03660833.
Chen
, X.
, Fu
, Y.
, and Yuan
, N.
, 2009
, “Invisible Cloak Design With Controlled Constitutive Parameters and Arbitrary Shaped Boundaries Through Helmholtz's Equation
,” Opt. Express
, 17
, pp. 3581
–3586
.10.1364/OE.17.00358134.
Hu
, J.
, Zhou
, X.
, and Hu
, G.
, 2009
, “Design Method for Electromagnetic Cloak With Arbitrary Shapes Based on Laplace’s Equation
,” Opt. Express
, 17
, pp. 1308
–1320
.10.1364/OE.17.00130835.
Hu
, J.
, Zhou
, X.
, and Hu
, G.
, 2009
, “A Numerical Method for Designing Acoustic Cloak With Arbitrary Shapes
,” Comput. Mater. Sci.
, 46
, pp. 708
–712
.10.1016/j.commatsci.2009.02.00636.
Qiu
, C. W.
, Novitsky
, A.
, and Gao
, L.
, 2010
, “Inverse Design Mechanism of Cylindrical Cloaks Without Knowledge of the Required Coordinate Transformation
,” J. Opt. Soc. Am. A
, 27
, pp. 1079
–1082
.10.1364/JOSAA.27.00107937.
Ding
, Y
, Liu
, Z.
, Qiu
, C.
, and Shi
, J.
, 2007
, “Metamaterial With Simultaneously Negative Bulk Modulus and Mass Density
,” Phys. Rev. Lett.
, 99
, p. 093904
.10.1103/PhysRevLett.99.09390438.
Christensen
, J.
, and García de Abajo
, F. J.
, 2012
, “Negative Refraction and Backward Waves in Layered Acoustic Metamaterials
,” Phys. Rev. B
, 86
, p. 024301
.10.1103/PhysRevB.86.02430139.
Lai
, Y.
, Chen
, H.
, Zhang
, Z. Q.
, and, Chan
, C. T.
, 2009
, “Complementary Media Invisibility Cloak That Cloaks Objects at a Distance Outside the Cloaking Shell
,” Phys. Rev. Lett.
, 102
, p. 093901
.10.1103/PhysRevLett.102.093901Copyright © 2013 by ASME
You do not currently have access to this content.
