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By taking a two-dimensional solid local resonant phononic crystal as an example, we investigated the mechanism of the defect state on a subwavelength scale. It is well known that, when the working wavelength is much greater than the distance between resonators, the dispersion of the phononic crystal is insensitive to the lattice structure, and the whole structure can be described in terms of the effective medium theory. As a result, it is hard to introduce a defect state in the system by a local real-space disorder. It is shown in this paper that the dispersion of the local resonant phononic crystal can be understood from the long-range feature of the interaction between resonators, so the creation of a defect state in the system is in fact to break such a long-range interaction. Based on this understanding, the mechanisms of the recently reported methods, that are used to create defect states, are discussed. In addition, a waveguide structure that can guide the longitude or transverse waves separately is realized by introducing an anisotropic defect resonator.
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Keywords:
- phononic crystal /
- local resonance /
- subwavelength defect state
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[9] Wen X S, Wen J H, Yu D L, Wang G, Liu Y Z, Han X Y 2006 Phononic Crystal (Beijing: National Defence Industry Press) p139 (in Chinese) [温熙森, 温激鸿, 郁殿龙, 王刚, 刘耀宗, 韩小云 2006 声子晶体 (北京: 国防工业出版社)]
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[12] Hsu F C, Hsu J C, Huang T C, Wang C H, Chang P 2011 Appl. Phys. Lett. 98 143505
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[14] Mei J, Ma G C, Yang M, Yang Z Y, Wen W J, Sheng P 2012 Nature Communications. 3 756
[15] Lai Y, Wu Y, Sheng P, Zhang Z Q 2011 Nature Materials. 10 620
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[17] Psarobas I, Stefanou N, Modinos A 2000 Phys. Rev. B 62 5536
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[19] Liu Z Y, Chan C T, Sheng P 2002 Phys. Rev. B 65 165116
[20] Wu Y, Lai Y, Zhang Z Q 2011 Phys. Rev. Lett. 107 105506
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[23] Oudich M, Assouar M B, Hou Z L 2010 Appl. Phys. Lett. 97 193503
[24] Hung H H, Sun C T, 2009 New. J. Phys. 11 013003
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[26] Liu H, Liu Y M, Li T, Wang S M, Zhu S N, Zhang X 2009 Phys. Status Solidi B 246 1397
[27] Li T, Wang S M, Liu H, Li J Q, Wang F M, Zhu S N, Zhang X 2008 J. Appl. Phys. 103 023104
[28] Huang K 1988 Solid State Physics (Beijing: Higher Education Press) (in Chinese) [黄昆 1988 固体物理学 (北京: 高等教育出版社)]
[29] Du G H, Zhu Z M, Gong X F 2001 Fundamentals of Acoustics (2st) (Nanjing: Nanjing University Press) p210 (in Chinese) [杜功焕, 朱哲民, 龚秀芬 2001 声学基础 第二版 (南京: 南京大学出版社)]
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[1] Kushwaha M S, Halevi P, Dobrzynski L, Djafari-Rouhani B 1993 Phys. Rev. Lett. 71 2022
[2] Sánchez-Pérez J, Caballero D, Mártinez-Sala R, Rubio C, Sánchez-Dehesa J, Meseguer F, Llinares J, Gálvez F 1998 Phys. Rev. Lett. 80 5325
[3] Larabi H, Pennec Y, Djafari-Rouhani B, Vasseur J O 2007 Phys. Rev. E 75 066601
[4] Wang G, Liu Y Z, Wen J H, Yu D L 2006 Chin. Phys. 15 407
[5] Gao X W, Chen S B, Chen J B, Zheng Q H, Yang H 2012 Chin. Phys. B 21 064301
[6] Zhao H G, Wen J H, Liu Y Z, Yu D L, Wang G, Wen X S 2008 Chin. Phys. B 17 1305
[7] 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 物理学报 61 104302]
[8] Li X C, Yi X Y, Xiao Q W, Liang H Y 2006 Acta Phys. Sin. 55 2300 (in Chinese) [李晓春, 易秀英, 肖清武, 梁宏宇 2006 物理学报 55 2300]
[9] Wen X S, Wen J H, Yu D L, Wang G, Liu Y Z, Han X Y 2006 Phononic Crystal (Beijing: National Defence Industry Press) p139 (in Chinese) [温熙森, 温激鸿, 郁殿龙, 王刚, 刘耀宗, 韩小云 2006 声子晶体 (北京: 国防工业出版社)]
[10] Li Y, Hou Z L, Fu X J, Badreddine M A 2010 Chin. Phys. Lett. 27 074303
[11] Kafesaki M, Sigalas M M, García N 2000 Phys. Rev. Lett. 85 4044
[12] Hsu F C, Hsu J C, Huang T C, Wang C H, Chang P 2011 Appl. Phys. Lett. 98 143505
[13] Mohammadi S, Eftekhar A A, Hunt W D, Adibi A 2009 Appl. Phys. Lett. 94 051906
[14] Mei J, Ma G C, Yang M, Yang Z Y, Wen W J, Sheng P 2012 Nature Communications. 3 756
[15] Lai Y, Wu Y, Sheng P, Zhang Z Q 2011 Nature Materials. 10 620
[16] Khelif A, Choujaa A, Benchabane S, Djafari-Rouhani B, Laude V 2004 Appl. Phys. Lett. 84 4400
[17] Psarobas I, Stefanou N, Modinos A 2000 Phys. Rev. B 62 5536
[18] Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, Sheng P 2000 Science 289 1734
[19] Liu Z Y, Chan C T, Sheng P 2002 Phys. Rev. B 65 165116
[20] Wu Y, Lai Y, Zhang Z Q 2011 Phys. Rev. Lett. 107 105506
[21] Fok L, Zhang X 2011 Phys. Rev. B 83 214304
[22] Oudich M, Li Y, Assouar B M, Hou Z L 2010 New J. Phys. 12 083049
[23] Oudich M, Assouar M B, Hou Z L 2010 Appl. Phys. Lett. 97 193503
[24] Hung H H, Sun C T, 2009 New. J. Phys. 11 013003
[25] Lemoult F, Kaina N, Fink M, Lerosey G 2012 Nature Phys. 9 55
[26] Liu H, Liu Y M, Li T, Wang S M, Zhu S N, Zhang X 2009 Phys. Status Solidi B 246 1397
[27] Li T, Wang S M, Liu H, Li J Q, Wang F M, Zhu S N, Zhang X 2008 J. Appl. Phys. 103 023104
[28] Huang K 1988 Solid State Physics (Beijing: Higher Education Press) (in Chinese) [黄昆 1988 固体物理学 (北京: 高等教育出版社)]
[29] Du G H, Zhu Z M, Gong X F 2001 Fundamentals of Acoustics (2st) (Nanjing: Nanjing University Press) p210 (in Chinese) [杜功焕, 朱哲民, 龚秀芬 2001 声学基础 第二版 (南京: 南京大学出版社)]
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