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晶格中心插入体的对称性及取向对二维声子晶体带隙的影响

胡家光 徐文 肖宜明 张丫丫

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晶格中心插入体的对称性及取向对二维声子晶体带隙的影响

胡家光, 徐文, 肖宜明, 张丫丫

The two-dimensional phononic crystal band gaps tuned by the symmetry and orientation of the additional rods in the center of unit cell

Hu Jia-Guang, Xu Wen, Xiao Yi-Ming, Zhang Ya-Ya
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  • 以二维钢/气体系声子晶体为模型,采用平面波法研究了圆柱正方及六角晶格中心添加插入体的对称性及取向与带隙的关系,给出了四方、六方、八方及圆柱插入体结构的带隙分布图及带隙随柱体取向的变化关系图.发现在低填充率条件下,插入体的截面形状与晶格类型相同时最有利于能带简并态的分离而获得带隙,但填充率较高时,采用高对称性的插入体可以获得最宽的带隙. 正方晶格中心插入体取向对带隙的影响要比在六角晶格中更为显著.对四方柱正方晶格声子晶体的研究表明, 仅旋转原柱体要比在其中心插入柱体后旋转更容易获得低频宽带隙, 单独运用添加柱体或旋转非圆柱体来降低晶格对称性以获取低频带隙的方法要比同时使用两种方法效果更好.此外,从机理上对计算结果进行了解释.
    The effects of symmetry and orientation of the additional steel rods on the band gaps of two-dimensional phononic crystals with steel-air system are numerically investigated by using the plane wave expansion method. The original steel rods of the phononic crystals are of columns in square and hexagonal lattices, and the additional steel rods are of regular square, hexagon, octagon prisms and columns, which are placed, respectively, in the center of each unit cell of the two kinds of lattices. The gap maps are introduced to illustrate the influences of the filling fraction and orientation of the additional rods on band gaps. It is found that in the case of the additional rods with low filling fraction, the band gaps can be obtained most easily because the degeneracy of bands is lifted when the cross section of additional rod has the same shape as that of lattice, but the widest band gaps appear under the condition of the additional rods with highest symmetry and largest filling fraction. The influence of orientation on band gap in square lattice is more obvious than that in hexagonal lattice. If the column lattice points are changed by square prisms in simple square lattice, the lower and wider band gaps can be produced by rotating the square prisms, which is contrary to the scenario that emerges in square lattice with additional rods at the center of unit cell. Using one of the methods of adding additional rods or rotating the original prisms is more beneficial to the generation of band gaps than combining effect of these two means in simple lattices. Furthermore, the mechanisms of above results are analyzed.
    • 基金项目: 国家自然科学基金(批准号: 10974206)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10974206).
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  • [1]

    Sigalas M M, Economou E N 1992 J. Sound Vib. 158 377

    [2]

    Kushwaha M S, Halevi P, Dobrzynski L, Djafari-Rouhani B 1993 Phys. Rev. Lett. 71 2022

    [3]

    Martinez-Sala R, Sancho J, Sanchez J V, Gomez V, Llinares J, Meseguer F 1995 Nature 378 241

    [4]

    Zhang R Y, Jiang G S, Wang Z Q, Lü Y D 2006 Technical Acoustics 25 35 (in Chinese) [张荣英, 姜根山, 王璋奇, 吕亚东 2006 声学技术 25 35]

    [5]

    Liu Z Y, Zhang X X, Mao Y W, Zhu Y Y, Yang Z Y, Chan C T, Sheng P 2000 Science 289 1734

    [6]

    Yilmaz C, Hulbert G M, Kikuchi N 2007 Phys. Rev. B 76 054309

    [7]

    Sievenpiper D, Zhang L J, Broas R F J, Alexópolous N G, Yablonovitch E 1999 IEEE Trans. on Microwave Theory and Tech. 47 2059

    [8]

    Li X L, Wu F G, Hu H F, Zhong S, Liu Y Y 2003 J. Phys. D: Appl. Phys. 36 L15

    [9]

    Wu F G, Liu Z Y, Liu Y Y 2002 Phys. Rev. E 66 046628

    [10]

    Caballero D, Sánchez-Dehesa J, Rubio C, Mártinez-Sala R, Sánchez-Pérez J V, Meseguer F, Llinares J 1999 Phys. Rev. E 60 R6316

    [11]

    Zhao F, Yuan L B 2005 Acta Phys. Sin. 54 4511 (in Chinese) [赵芳, 苑立波 2005 物理学报 54 4511]

    [12]

    Yao Y W, Hou Z L, Liu Y Y 2007 Phys. Lett. A 362 494

    [13]

    Xu Z L, Wu F G, Mu Z F, Zhang X, Yao Y W 2007 J. Phys. D: Appl. Phys. 40 5584

    [14]

    Dong H F, Wu F G, Mu Z F, Zhong H L 2010 Acta Phys. Sin. 59 754 (in Chinese) [董华锋, 吴福根, 牟中飞, 钟会林 2010 物理学报 59 754]

计量
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  • PDF下载量:  620
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-05-17
  • 修回日期:  2012-06-20
  • 刊出日期:  2012-12-05

晶格中心插入体的对称性及取向对二维声子晶体带隙的影响

  • 1. 云南大学物理科学技术学院, 昆明 650091;
  • 2. 文山学院数理系, 文山 663000
    基金项目: 国家自然科学基金(批准号: 10974206)资助的课题.

摘要: 以二维钢/气体系声子晶体为模型,采用平面波法研究了圆柱正方及六角晶格中心添加插入体的对称性及取向与带隙的关系,给出了四方、六方、八方及圆柱插入体结构的带隙分布图及带隙随柱体取向的变化关系图.发现在低填充率条件下,插入体的截面形状与晶格类型相同时最有利于能带简并态的分离而获得带隙,但填充率较高时,采用高对称性的插入体可以获得最宽的带隙. 正方晶格中心插入体取向对带隙的影响要比在六角晶格中更为显著.对四方柱正方晶格声子晶体的研究表明, 仅旋转原柱体要比在其中心插入柱体后旋转更容易获得低频宽带隙, 单独运用添加柱体或旋转非圆柱体来降低晶格对称性以获取低频带隙的方法要比同时使用两种方法效果更好.此外,从机理上对计算结果进行了解释.

English Abstract

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