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Taking the flexural wave propagating in elastic thin plate as an example, we investigate the mechanism for gap opening in the resonator-based acoustic metamaterials. Results show that the band gap in such a kind of structure depends not only on the abrupt phase change of the wave when it is scattered by the resonators, but also on the retarded phase of wave when it is propagating in host. This means that the dispersion of wave in the structure can be adjusted either by the scattering or by the propagating phase. Based on this understanding, we show that the defect state at subwavelength scale (obtained either by changing locally the resonating property of the resonator or by changing locally the distance between the resonators) can be understood simply by the band gap condition. We show further in this paper that, because the dispersion of the metamaterial can be adjusted by the propagating phase, the structures with negative band at a subwavelength scale can also be achieved by arranging the resonators into a compound lattice.
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Keywords:
- acoustic metamaterials /
- negative refraction /
- defect state
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[27] Oudich M, Assouar M B, Hou Z L 2010 Appl. Phys. Lett. 97 193503
[28] Torrent D, Mayou D, Sanchez-Dehesa J 2013 Phys. Rev. B 87 115143
[29] Xiao Y, Wen J H, Wen X S 2012 J. Phys. D. Appl. Phys. 45 195401
[30] Colombi A, Roux P, Rupin M 2014 J. Acoust. Soc. Am. 136 EL192
[31] Hou L N, Hou Z L, Fu X J 2014 Acta Phys. Sin. 63 034305 (in Chinese) [侯丽娜, 侯志林, 傅秀军 2014 63 034305]
[32] Yang M, Ma G C, Yang Z Y, and Sheng P 2013 Phys. Rev. Letts. 110 134301
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[1] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[2] Schurig D, Mock J J, Justice B J, Cummer S A, Pendry J B, Starr A F, Smith D R 2006 Science 314 977
[3] Smith D R, Padilla W J, Vier D C, Nemat-Nasser S C, Schultz S 2000 Phys. Rev. Lett. 84 4184
[4] Fang N, Xi D J, Xu J Y, Ambati M, Srituravanich W, Sun C, Zhang X 2006 Nature Materials. 5 452
[5] Sheng P, Mei J, Liu Z Y, Wen W J 2007 Phys. B 394 256
[6] Li J S, Chan C T 2004 Phys. Rev. E 70 055602
[7] Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K 2010 Phys. Rev. Lett. 104 054301
[8] Yang Z, Mei J, Yang M, Chan N H, Sheng P 2008 Phys. Rev. Lett. 101 204301
[9] Torrent D, Sanchez-Dehesa J 2007 New. J. Phys. 9 323
[10] Deng K, Ding Y Q, He Z J, Zhao H P, Shi J, Liu Z Y 2009 J. Appl. Phys. 105 124909
[11] Ambati M, Fang N, Sun C, Zhang X 2007 Phys. Rev. B 75 195447
[12] Farhat M, Enoch S, Guenneau S, Movchan A B 2008 Phys. Rev. Lett. 101 134501
[13] Kushwaha M S, Halevi P, Dobrzynski L, Djafari-Rouhani B 1993 Phys. Rev. Lett. 71 2022
[14] Liu Z Y, Zhang X X, Mao Y W, Zhu Y Y, Yang Z Y, Chan C T, Sheng P 2000 Science 289 1734
[15] Wu F G, Liu Z Y, Liu Y Y 2004 Phys. Rev. E 69 066609
[16] Wu F G, Hou Z L, Liu Z Y, Liu Y Y 2001 Phys. Lett. A 292 198
[17] Vasseur J O, Hladky-Hennion A C, Djafari-Rouhani B, Duval F, Dubus B, Pennec Y, Deymier P A 2007 J. Appl. Phys. 101 114904
[18] Vasseur J O, Deymier P A, Djafari-Rouhani B, Pennec Y, Hladky-Hennion A C 2008 Phys. Rev. B 77 085415
[19] Khelif A, Choujaa A, Benchabane S, Djafari-Rouhani B, Laude V 2004 Appl. Phys. Lett. 84 4400
[20] Achaoui Y, Laude V, Benchabane S, Khelif A 2013 J. Appl. Phys. 114 104503
[21] Rupin M, Lemoult F, Lerosey G, Roux P 2014 Phys. Rev. Lett. 112 234301
[22] Pourabolghasem R, Khelif A, Mohammadi S, Eftekhar A A, Adibi A 2014 J. Appl. Phys. 116 013514
[23] Lemoult F, Kaina N, Fink M, Lerosey G 2013 Nature Phys. 9 55
[24] Liu M, Hou Z L, Fu X J 2012 Acta Phys. Sin. 61 104302 (in Chinese) [刘敏, 侯志林, 傅秀军 2012 61 104302]
[25] Larabi H, Pennec Y, Djafari-Rouhani B, Vasseur J O 2007 Phys. Rev. E 75 066601
[26] Sainidou R, Stefanou N 2006 Phys. Rev. B 73 184301
[27] Oudich M, Assouar M B, Hou Z L 2010 Appl. Phys. Lett. 97 193503
[28] Torrent D, Mayou D, Sanchez-Dehesa J 2013 Phys. Rev. B 87 115143
[29] Xiao Y, Wen J H, Wen X S 2012 J. Phys. D. Appl. Phys. 45 195401
[30] Colombi A, Roux P, Rupin M 2014 J. Acoust. Soc. Am. 136 EL192
[31] Hou L N, Hou Z L, Fu X J 2014 Acta Phys. Sin. 63 034305 (in Chinese) [侯丽娜, 侯志林, 傅秀军 2014 63 034305]
[32] Yang M, Ma G C, Yang Z Y, and Sheng P 2013 Phys. Rev. Letts. 110 134301
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