Controlling sound with acoustic metamaterials

Nature Reviews Materials

Volumn 1, Issue , 2016, Pages

  Cummer, Steven A ^a   Christensen, Johan ^b   Alù, Andrea ^c  

^a Duke University   (United States)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^c The University of Texas at Austin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85019940164     PISSN: None     EISSN: 20588437     Source Type: Journal    
DOI: 10.1038/natrevmats.2016.1     Document Type: Review

References (153)

1. Brillouin, L. Wave Propagation in Periodic Structures (Dover, 1946).
2. Yablonovitch, E. Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58, 2059 (1987).
3. Hussein, M. I., Leamy, M. J. & Ruzzene, M. Dynamics of phononic materials and structures: historical origins, recent progress, and future outlook. App. Mech. Rev. 66, 040802 (2014).
4. Liu, Z. et al. Locally resonant sonic materials. Science 289, 1734-1736 (2000).
5. Zheludev, N. I. & Kivshar, Y. S. From metamaterials to metadevices. Nat. Mater. 11, 917-924 (2012).
6. Christensen, J., Kadic, M., Kraft, O. & Wegener, M. Vibrant times for mechanical metamaterials. MRS Commun. 5, 43-462 (2015).
7. Dolling, G., Enkrich, C., Wegener, M., Soukoulis, C. M. & Linden, S. Simultaneous negative phase index and group velocity of light in a metamaterial. Science 312, 892-894 (2006).
8. Pendry, J. B. & Smith, D. R. The quest for the superlens. Sci. Am. 295, 60-67 (2006).
9. Goffaux, C. et al. Evidence of Fano-like interference phenomena in locally resonant materials. Phys. Rev. Lett. 88, 225502 (2002).
10. Sheng, P., Mei, J., Liu, Z. & Wen, W. Dynamic mass density and acoustic metamaterials. Phys. B 394, 256-261 (2007).
11. Huang, H. H., Sun, C. T. & Huang, G. L. On the negative effective mass density in acoustic metamaterials. Int. J. Eng. Sci. 47, 610-617 (2009).
12. Li, J., Fung, K. H., Liu, Z. Y., Sheng, P. & Chan, C. T. Generalizing the concept of negative medium to acoustic waves. Springer Ser. Mater. Sci. 98, 183-215 (2007).
13. Brunet, T. et al. Soft 3D acoustic metamaterial with negative index. Nat. Mater. 14, 384-388 (2015).
14. Li, J. & Chan, C. T. Double-negative acoustic metamaterial. Phys. Rev. E 70, 055602(R) (2004).
15. Stewart, G. W. Acoustic wave filters. Phys. Rev. 20, 528-551(1922).
16. Fang, N. et al. Ultrasonic metamaterials with negative modulus. Nat. Mater. 5, 452-456 (2006).
17. Lee, S. H., Park, C. M., Seo, Y. M., Wang, Z. G. & Kim, C. K. Acoustic metamaterial with negative modulus. J. Phys. Condens. Matter 21, 175704 (2009).
18. Christensen, J., Martín-Moreno, L. & García-Vidal, F. J. All-angle blockage of sound by an acoustic double-fishnet metamaterial. Appl. Phys. Lett. 97, 134106 (2010).
19. Bell, J. S. et al. Low acoustic transmittance through a holey structure. Phys. Rev. B 85, 214305 (2012).
20. Yang, Z., Mei, J., Yang, M., Chan, N. H. & Sheng, P. Membrane-type acoustic metamaterial with negative dynamic mass. Phys. Rev. Lett. 101, 204301 (2008).
21. Lee, S. H., Park, C. M., Seo, Y. M., Wang, Z. G. & Kim, C. K. Acoustic metamaterial with negative density. Phys. Lett. A 373, 4464-4469 (2009).
22. Liang, Z., Willatzen, M. & Christensen, J. Metadevices for the confinement of sound and broadband double-negativity behavior. Phys. Rev. B 88, 100301(R) (2013).
23. Lee, S. H. et al. Composite acoustic medium with simultaneously negative density and modulus. Phys. Rev. Lett. 104, 054301 (2010).
24. Liang, Z. & Li, J. Extreme acoustic metamaterials by coiling up space. Phys. Rev. Lett. 108, 114301 (2012).
25. Xie, Y., Popa, B.-I., Zigoneanu, L. & Cummer, S. A. Measurement of a broadband negative index with space-coiling acoustic metamaterials. Phys. Rev. Lett. 110, 175501 (2013).
26. Liang, Z. et al. Space-coiling metamaterials with double negativity and conical dispersion. Sci. Rep. 3, 1614 (2013).
27. Christensen, J. & García de Abajo, F. J. Anisotropic metamaterials for full control of acoustic waves. Phys. Rev. Lett. 108, 124301 (2012).
28. García-Chocano, V. M., Christensen, J. & Sánchez-Dehesa, J. Negative refraction and energy funneling by hyperbolic materials: an experimental demonstration in acoustics. Phys. Rev. Lett. 112, 144301 (2014).
29. Graciá-Salgado, R., García-Chocano, V. M., Torrent, D. & Sánchez-Dehesa, J. Negative mass density and ρ-near-zero quasi-two-dimensional metamaterials: design and applications. Phys. Rev. B 88, 224305 (2013).
30. Fleury, R. & Alù, A. Extraordinary sound transmission through density-near-zero ultranarrow channels. Phys. Rev. Lett. 111, 055501 (2013).
31. Leroy, V. et al. Superabsorption of acoustic waves with bubble metascreens. Phys. Rev. B 91, 020301(R) (2015).
32. Pierre, J., Dollet, B. & Leroy, V. Resonant acoustic propagation and negative density in liquid foams. Phys. Rev. Lett. 112, 148307 (2014).
33. Mei, J., Liu, Z., Wen, W. & Sheng, P. Effective dynamic mass density of composites. Phys. Rev. B 76, 134205 (2007).
34. Fokin, V., Ambati, M., Sun, C. & Zhang, X. Method for retrieving effective properties of locally resonant acoustic metamaterials. Phys. Rev. B 76, 144302 (2007).
35. Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966-3969 (2000).
36. Ambati, M., Fang, N., Sun, C. & Zhang, X. Surface resonant states and superlensing in acoustic metamaterials. Phys. Rev. B 75, 195447 (2007).
37. Deng, K. et al. Theoretical study of subwavelength imaging by acoustic metamaterial slabs. J. Appl. Phys. 105, 124909 (2009).
38. Park, C. M. et al. Amplification of acoustic evanescent waves using metamaterial slabs. Phys. Rev. Lett. 107, 194301 (2011).
39. Park, J. J., Park, C. M., Lee, K. J. B. & Lee, S. H. Acoustic superlens using membrane-based metamaterials. Appl. Phys. Lett. 106, 051901 (2015).
40. Kaina, N., Lemoult, F., Fink, M. & Lerosey, G. Negative refractive index and acoustic superlens from multiple scattering in single negative metamaterials. Nature 525, 77-81 (2015).
41. Ao, X. & Chan, C. T. Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials. Phys. Rev. E 77, 025601(R) (2008).
42. Li, J., Fok, L., Yim, X., Bartal, G. & Zhang, X. Experimental demonstration of an acoustic magnifying hyperlens. Nat. Mater. 8, 931-934 (2009).
43. Belov, P. A., Simovski, C. R. & Ikonen, P. Canalization of subwavelength images by electromagnetic crystals. Phys. Rev. B 71, 193105 (2005).
44. Jia, H. et al. Subwavelength imaging by a simple planar acoustic superlens. Appl. Phys. Lett. 97, 173507 (2010).
45. Zhu, J. et al. A holey-structured metamaterial for acoustic deep-subwavelength imaging. Nat. Phys. 7, 52-55 (2011).
46. Cheng, Y. et al. Acoustic subwavelength imaging of subsurface objects with acoustic resonant metalens. Appl. Phys. Lett. 103, 224104 (2013).
47. Zhou, X. & Hu, G. Superlensing effect of an anisotropic metamaterial slab with near-zero dynamic mass. Appl. Phys. Lett. 98, 263510 (2011).
48. Xu, X., Li, P., Zhou, X. & Hu, G. Experimental study on acoustic subwavelength imaging based on zero-mass metamaterials. Eur. Phys. Lett. 109, 28001 (2015).
49. Lerosey, G., de Rosny, J., Tourin, A. & Fink, M. Focusing beyond the diffraction limit with far-field time reversal. Science 315, 1120-1122 (2007).
50. Lemoult, F., Lerosey, G., de Rosny, J. & Fink, M. Resonant metalens for breaking the diffraction barrier. Phys. Rev. Lett. 104, 203901 (2010).
51. Lemoult, F., Fink, M. & Lerosey, G. Acoustic resonators for far-field control of sound on a subwavelength scale. Phys. Rev. Lett. 107, 064301 (2011).
52. Lanoy, M. et al. Subwavelength focusing in bubbly media using broadband time reversal. Phys. Rev. B 91, 224202 (2015).
53. Christensen, J. & García de Abajo, F. J. Acoustic field enhancement and subwavelength imaging by coupling to slab waveguide modes. Appl. Phys. Lett. 97, 164103 (2010).
54. Molerón, M. & Daraio, C. Acoustic metamaterial for subwavelength edge detection. Nat. Commun. 6, 8037 (2015).
55. Morse, P. M. & Ingard, K. Theoretical Acoustics (McGraw-Hill, 1968).
56. Arenas, J. P. & Crocker, M. J. Recent trends in porous sound-absorbing materials. J. Sound Vibr. 44, 12-18 (2010).
57. Cai, X., Guo, Q., Hu, G. & Yang, J. Ultrathin low-frequency sound absorbing panels based on coplanar spiral tubes or coplanar Helmholtz resonators. Appl. Phys. Lett. 105, 121901 (2014).
58. Yang, Z., Dai, H., Chan, N., Ma, G. & Sheng, P. Acoustic metamaterial panels for sound attenuation in the 50-1000 Hz regime. Appl. Phys. Lett. 96, 041906 (2010).
59. Mei, J. et al. Dark acoustic metamaterials as superabsorbers for low-frequency sound. Nat. Commun. 3, 756 (2012).
60. Li, Y. et al. Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces. Sci. Rep. 3, 2546 (2013).
61. Tang, K. et al. Anomalous refraction of airborne sound through ultrathin metasurfaces. Sci. Rep. 4, 6517 (2014).
62. Ma, G., Min, Y., Xiao, S., Yang, Z. & Sheng, P. Acoustic metasurface with hybrid resonances. Nat. Mater. 13, 873-878 (2014).
63. Xie, Y. et al. Wavefront modulation and subwavelength diffractive acoustics with an acoustic metasurface. Nat. Commun. 5, 5553 (2014).
64. Ding, C., Zhao, X., Chen, H., Zhai, S. & Shen, F. Reflected wavefronts modulation with acoustic metasurface based on double-split hollow sphere. Appl. Phys. A 120, 487-493 (2015).
65. Li, Y. et al. Experimental realization of full control of reflected waves with subwavelength acoustic metasurfaces. Phys. Rev. Appl. 2, 064002 (2014).
66. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780-1782 (2006).
67. Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977-980 (2006).
68. Liu, R. et al. Broadband ground-plane cloak. Science 323, 366-369 (2009).
69. Valentine, J., Li, J., Zentgraf, T., Bartal, G. & Zhang, X. An optical cloak made of dielectrics. Nat. Mater. 8, 568-571 (2009).
70. Milton, G. W., Briane, M. & Willis, J. R. On cloaking for elasticity and physical equations with a transformation invariant form. New J. Phys. 8, 248 (2006).
71. Cummer, S. A. & Schurig, D. One path to acoustic cloaking. New J. Phys. 9, 45 (2007).
72. Chen, H. & Chan, C. T. Acoustic cloaking in three dimensions using acoustic metamaterials. Appl. Phys. Lett. 91, 183518 (2007).
73. Greenleaf, A., Lassas, M. & Uhlmann, G. Anisotropic conductivities that cannot be detected by EIT. Physiol. Meas. 24, 413-419 (2003).
74. Huang, X., Zhong, S. & Stalnov, O. Analysis of scattering from an acoustic cloak in a moving fluid. J. Acoust. Soc. Am. 135, 2571-2580 (2014).
75. Norris, A. N. Acoustic cloaking theory. Proc. R. Soc. A 464, 2411-2434 (2008).
76. Norris, A. N. Acoustic metafluids. J. Acoust. Soc. Am. 125, 839-849 (2009).
77. Milton, G. W & Cherkaev, A. V. Which elasticity tensors are realizable? J. Eng. Mater. Technol. 117, 483-493 (1995).
78. Popa, B.-I. & Cummer, S. A. Design and characterization of broadband acoustic composite metamaterials. Phys. Rev. B 80, 174303 (2009).
79. Pendry, J. B. & Li, J. An acoustic metafluid: realizing a broadband acoustic cloak. New J. Phys. 10, 115032 (2008).
80. Torrent, D. & Sánchez-Dehesa, J. Anisotropic mass density by two-dimensional acoustic metamaterials. New J. Phys. 10, 023004 (2008).
81. Schoenberg, M. & Sen, P. N. Properties of a periodically stratified acoustic half-space and its relation to a Biot fluid. J. Acoust. Soc. Am. 73, 61-67 (1983).
82. Torrent, D. & Sánchez-Dehesa, J. Acoustic cloaking in two dimensions: a feasible approach. New J. Phys. 10, 063015 (2008).
83. Cheng, Y., Yang, F., Xu, J. Y. & Liu, X. J. A multilayer structured acoustic cloak with homogeneous isotropic materials. Appl. Phys. Lett. 92, 151913 (2008).
84. Zigoneanu, L., Popa, B.-I., Starr, A. & Cummer, S. A. Design and measurements of a broadband two-dimensional acoustic metamaterial with anisotropic effective mass density. J. Appl. Phys. 109, 054906 (2011).
85. Zhang, S., Xia, C. & Fang, N. Broadband acoustic cloak for ultrasound waves. Phys. Rev. Lett. 106, 024301 (2011).
86. Li, J. & Pendry, J. B. Hiding under the carpet: a new strategy for cloaking. Phys. Rev. Lett. 101, 203901 (2008).
87. Popa, B.-I., Zigoneanu, L. & Cummer, S. A. Experimental acoustic ground cloak in air. Phys. Rev. Lett. 106, 253901 (2011).
88. Zigoneanu, L., Popa, B.-I. & Cummer, S. A. Three-dimensional broadband omnidirectional acoustic ground cloak. Nat. Mater. 13, 352-355 (2014).
89. Kan, W. et al. Acoustic illusion near boundaries of arbitrary curved geometry. Sci. Rep. 3, 1427 (2013).
90. Scandrett, C. L., Boisvert, J. E. & Howarth, T. R. Acoustic cloaking using layered pentamode materials. J. Acoust. Soc. Am. 127, 2856-2864 (2010).
91. Kadic, M., Bückmann, T., Stenger, N., Thiel, M. & Wegener, M. On the practicability of pentamode mechanical metamaterials. Appl. Phys. Lett. 100, 191901 (2012).
92. Schittny, R., Bückmann, T., Kadic, M. & Wegener, M. Elastic measurements on macroscopic three-dimensional pentamode metamaterials. Appl. Phys. Lett. 103, 231905 (2013).
93. Kadic, M., Bückmann, T., Schittny, R., Gumbsch, P. & Wegener, M. Pentamode metamaterials with independently tailored bulk modulus and mass density. Phys. Rev. Appl. 2, 054007 (2014).
94. Popa, B.-I. & Cummer, S. A. Homogeneous and compact acoustic ground cloaks. Phys. Rev. B 83, 224304 (2011).
95. Martin, T. P., Layman, C. N., Moore, K. M. & Orris, G. J. Elastic shells with high-contrast material properties as acoustic metamaterial components. Phys. Rev. B 85, 161103 (2012).
96. Farhat, M., Enoch, S., Guenneau, S. & Movchan, A. B. Broadband cylindrical acoustic cloak for linear surface waves in a fluid. Phys. Rev. Lett. 101, 134501 (2008).
97. Stenger, N., Wilhelm, M. & Wegener, M. Experiments on elastic cloaking in thin plates. Phys. Rev. Lett. 108, 014301 (2012).
98. Farhat, M. Guenneau, S. & Enoch, S. Ultrabroadband elastic cloaking in thin plates. Phys. Rev. Lett. 103, 024301 (2009).
99. Bückmann, T., Thiel, M., Kadic, M., Schittny, R. & Wegener, M. An elasto-mechanical unfeelability cloak made of pentamode metamaterials. Nat. Commun. 5, 4130 (2014).
100. Brûlé, S., Javelaud, E. H., Enoch, S. & Guenneau, S. Experiments on seismic metamaterials: molding surface waves. Phys. Rev. Lett. 112, 133901 (2014).
101. Alù, A. & Engheta, N. Achieving transparency with plasmonic and metamaterial coatings. Phys. Rev. E 72, 016623 (2005).
102. Zheng, L.-Y. et al. Acoustic cloaking by a near-zero-index phononic crystal. Appl. Phys. Lett. 104, 161904 (2014).
103. Zhou, X., Hu, G. & Lu, T. Elastic wave transparency of a solid sphere coated with metamaterials. Phys. Rev. B 77, 024101 (2008).
104. Guild, M. D., Alù, A. & Haberman, M. R. Cancellation of acoustic scattering from an elastic sphere. J. Acoust. Soc. Am. 129, 1355-1365 (2011).
105. Li, P., Chen, X., Zhou, X., Hu, G. & Xiang, P. Acoustic cloak constructed with thin-plate metamaterials. Int. J. Smart Nano Mater. 6, 73-83 (2015).
106. Guild, M. D., Haberman, M. R. & Alù, A. Plasmonic-type acoustic cloak made of a bilaminate shell. Phys. Rev. B 86, 104302 (2012).
107. Xu, T. et al. Scattering reduction for an acoustic sensor using a multilayered shell comprising a pair of homogeneous isotropic single-negative media. Appl. Phys. Lett. 101, 033509 (2012).
108. Guild, M. D., Alù, A. & Haberman, M. R. Cloaking of an acoustic sensor using scattering cancellation. Appl. Phys. Lett. 105, 023510 (2014).
109. Chen, Y., Liu, H., Reilly, M., Bae, H. & Yu, M. Enhanced acoustic sensing through wave compression and pressure amplification in anisotropic metamaterials. Nat. Commun. 5, 5247 (2014).
110. Sanchis, L. et al. Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere. Phys. Rev. Lett. 110, 124301 (2013).
111. Zhu, X., Ramezani, H., Shi, C., Zhu, J. & Zhang, X. PT symmetric acoustics. Phys. Rev. X 4, 031042 (2014).
112. Fleury, R., Sounas, D. L. & Alù, A. An invisible acoustic sensor based on parity-time symmetry. Nat. Commun. 6, 5905 (2015).
113. Mangulis, V. Kramers-Kronig or dispersion relations in acoustics. J. Acoust. Soc. Am. 36, 211-212 (1964).
114. Kadic, M., Bückmann, T., Schittny, R. & Wegener, M. Metamaterials beyond electromagnetism. Rep. Prog. Phys. 76, 126501 (2013).
115. Akl, W. & Baz, A. Analysis and experimental demonstration of an active acoustic metamaterial cell. J. Appl. Phys. 111, 044505 (2012).
116. Baz, A. Active acoustic metamaterials. J. Acoust. Soc. Am. 128, 2428 (2010).
117. Akl, W. & Baz, A. Experimental characterization of active acoustic metamaterial cell with controllable dynamic density. J. Appl. Phys. 112, 084912 (2012).
118. Popa, B.-I., Zigoneanu, L. & Cummer, S. A. Tunable active acoustic metamaterials. Phys. Rev. B 88, 024303 (2013).
119. Popa, B.-I., Shinde, D., Konneker, A. & Cummer, S. A. Active acoustic metamaterials reconfigurable in real-time. Phys. Rev. B 91, 220303(R) (2015).
120. Chen, X., Xu, X., Ai, S., Chen, H., Pei, Y. & Zhou, X. Active acoustic metamaterials with tunable effective mass density by gradient magnetic fields. Appl. Phys. Lett. 105, 071913 (2014).
121. Liang, Z., Willatzen, M., Li, J. & Christensen, J. Tunable acoustic double negativity metamaterial. Sci. Rep. 2, 859 (2012).
122. Airoldi, L. & Ruzzene, M. Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos. New J. Phys. 13, 113010 (2011).
123. Hutson, A. R., McFee, J. H. & White, D. L. Ultrasonic amplification in CdS. Phys. Rev. Lett. 7, 237-239 (1961).
124. Willatzen, M. & Christensen, J. Acoustic gain in piezoelectric semiconductors at ∈-near-zero response. Phys. Rev. B 89, 041201(R) (2014).
125. Baz, A. M. An active acoustic metamaterial with tunable effective density. J. Vib. Acoust. 132, 041011 (2010).
126. Ruzzene, M. & Baz, A. Active control of wave propagation in periodic fluid-loaded shells. Smart Mater. Struct. 10, 893 (2001).
127. Casadei, F., Delpero, T., Bergamini, A., Ermanni, P. & Ruzzene, M. Piezoelectric resonator arrays for tunable acoustic waveguides and metamaterials. J. App. Phys. 112, 064902 (2012).
128. Bergamini, A. et al. Phononic crystal with adaptive connectivity. Adv. Mater. 26, 1343-1347 (2014).
129. Xiao, S., Ma, G., Li, Y., Yang, Z. & Sheng, P. Active control of membrane-type acoustic metamaterial by electric field. Appl. Phys. Lett. 106, 091904 (2015).
130. Bender, C. M. Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70, 947 (2007).
131. Bender, C. M. & Boettcher, S. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243-5246 (1998).
132. Makris, K. G., El-Ganainy, R., Christodoulides, D. N. & Musslimani, Z. H. Beam dynamics in PT symmetric optical lattices. Phys. Rev. Lett. 100, 103904 (2008).
133. Rüter, C. E. et al. Observation of parity-time symmetry in optics. Nat. Phys. 6, 192-195 (2010).
134. Sounas, D. L., Fleury, R. & Alù, A. Unidirectional cloaking based on metasurfaces with balanced gain and loss. Phys. Rev. Appl. 4, 014005 (2015).
135. Godin, O. A. Reciprocity and energy theorems for waves in a compressible inhomogeneous moving fluid. Wave Motion 25, 143-167 (1997).
136. Fleury, R., Sounas, D. L., Sieck, C. F., Haberman, M. R. & Alù, A. Sound isolation and giant linear non-reciprocity in a compact acoustic circulator. Science 343, 516-519 (2014).
137. Fleury, R., Sounas, D. L. & Alù, A. A subwavelength ultrasonic circulator based on spatiotemporal modulation. Phys. Rev. B 91, 174306 (2015).
138. Boechler, N., Theocharis, G. & Daraio, C. Bifurcation-based acoustic switching and rectification. Nat. Mater. 10, 665-668 (2011).
139. Liang, B., Yuan, B. & Cheng, J. C. Acoustic diode: rectification of acoustic energy flux in one-dimensional systems. Phys. Rev. Lett. 103, 104301 (2009).
140. Liang, B., Guo, X. S., Tu, J. & Zhang, D. An acoustic rectifier. Nat. Mater. 9, 989-992 (2010).
141. Estep, N., Sounas, D., Soric, J. & Alù, A. Magnetic-free non-reciprocity based on parametrically modulated coupled-resonator loops. Nat. Phys. 10, 923-927 (2014).
142. Lin, Q. & Fan, S. Light guiding by effective gauge field for photons. Phys. Rev. X 4, 031031 (2014).
143. Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photonics 8, 821-829 (2014).
144. Popa, B.-I. & Cummer, S. A. Non-reciprocal and highly nonlinear active acoustic metamaterials. Nat. Commun. 5, 3398 (2014).
145. Liu, C., Du, Z., Sun, Z., Gao, H. & Guo, X. Frequency-preserved acoustic diode model with high forward-power-transmission rate. Phys. Rev. Appl. 3, 064014 (2015).
146. Yang, Z. et al. Topological acoustics. Phys. Rev. Lett. 114, 114301 (2015).
147. Khanikaev, A., Fleury, R., Mousavi, H. & Alů, A. Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice. Nat. Commun. 6, 8260 (2015).
148. Ni, X. et al. Topologically protected one-way edge mode in networks of acoustic resonators with circulating air flow. New J. Phys. 17, 053016 (2015).
149. Wang, Z. et al. Harmonic image reconstruction assisted by a nonlinear metamaterial surface. Phys. Rev. Lett. 106, 047402 (2011).
150. Fleury, R. & Alů, A. Metamaterial buffer for broadband non-resonant impedance matching of obliquely incident acoustic waves. J. Acoust. Soc. Am. 136, 2935-2940 (2014).
151. Urzhumov, Y., Ghezzo, F., Hunt, J. & Smith, D. R. Acoustic cloaking transformations from attainable material properties. New J. Phys. 12, 073014 (2010).
152. Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative index of refraction. Science 292, 77-79 (2001).
153. Zheludev, N. I. Obtaining optical properties on demand. Science 348, 973-974 (2015).