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本文以二维固体局域共振声子晶体为例，对次波长区域缺陷态的实现机理及其特点进行了探讨. 众所周知，工作于次波长区域的声子晶体可以用有效媒质理论来描述，其色散关系对其构成单元的排列结构并不敏感，因而使得共振型声子晶体的带结构难以被其构成单元的局域空间无序所打破. 本文发现共振型声子晶体在其带隙附近的色散关系可由共振单元间的长程相互作用来理解. 基于这一理解，对目前文献中提出的两种实现局域态的方法进行了研究，结果表明缺陷态的引入正是通过打破这种长程相互作用来实现的. 另外，在此理解的基础上，通过引入非各向同性缺陷共振单元，实现了纵波与横波导波模式的分离.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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[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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