搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

二维三组元声子晶体中的半狄拉克点及奇异特性

高汉峰 张欣 吴福根 姚源卫

引用本文:
Citation:

二维三组元声子晶体中的半狄拉克点及奇异特性

高汉峰, 张欣, 吴福根, 姚源卫

Semi-Dirac cone and singular features of two-dimensional three-component phononic crystals

Gao Han-Feng, Zhang Xin, Wu Fu-Gen, Yao Yuan-Wei
PDF
导出引用
  • 设计了一种二维三组元声子晶体结构, 利用偶然简并的方法在布里渊区中心实现了半狄拉克点, 探究了随着组元几何参数的改变半狄拉克点的演变过程. 利用有限元方法研究发现在半狄拉克点频率附近沿着X 方向声子晶体表现出与零折射率材料相似的行为, 许多奇异特性如单向透射等均可以观察到. 另外还发现在半狄拉克点频率附近声子晶体是各向异性的, 沿着不同方向声波的传播现象是不同的, 这种特性是狄拉克点及类狄拉克点所不具备的. 这种各向异性的声波传播特性有许多重要的应用, 如单方向完美透射和单方向波前整形等.
    Due to accidental degeneracy, a semi-Dirac point is realized at the center of the Brillouin zone in a two-dimensional phononic crystal (PC) consisting of a square array of core-shell-structure elliptical cylinders in water. In the vicinity of the semi-Dirac point, the dispersion is linear along the X direction, but it is quadratic along the Y direction. The semi-Dirac point is formed by the degeneracy of dipole and quadrupole modes, through accurately adjusting the radius of the cores and shells, the two modes will coincide and the dispersion relation will become linear. It is worth to be emphasised that the frequency of the semi-Dirac point is very low in our designed PC, and this is exactly the special advantage of a three-component system. Since the dispersion relation is different in the vicinity of the semi-Dirac point, some new features may be seen. Firstly, the anisotropic transmission phenomenon is demonstrated. A PC slab is placed in a rectangular waveguide where the sound hard boundary conditions are used on the upper and lower walls; a plane wave impinges on the PC slab along the X direction at the semi-Dirac point frequency, and total transmission can be achieved, so that the sound energy transmissivity is also equal to one. In the meantime, the waves experience no spatial phase changes when they are transmitting through the PC slab; this behavior indicates that the PC can be equivalent to zero index medium along the X direction. However, when the plane wave is incident along the Y direction, the transmitted field is very weak, and the sound energy transmission is nearly zero. Secondly, the properties of the semi-Dirac point can be applied to design acoustic diode. The scatterers of the PC are arranged in triangular prism shapes and placed into a straight waveguide; when the wave is incident along the X direction, it can be transmitted through the PC slab and emerge in the right area, but when the waves is incident from the opposite direction, it will be totally reflected back. Therefore, the semi-Dirac point in PC provides a way to realize the acoustic diode. Finally, the unidirectional wave-front shape effect can also be observed in our considered system. We put a square sample with 16-by-16 coating rods into water medium. When a tightly focused Gaussian beam impinges on the PC sample along the X direction at the semi-Dirac point frequency, the outgoing wave will be modulated to a plan wave. Whereas, when the incident wave along the Y direction, the Gaussian beam will be totally reflected. In conclusion, the singular features of semi-Dirac point in PC will provides an advantageous means to manipulate acoustic waves and exploit new functional materials.
      通信作者: 张欣, xinxintwinkle@163.com
    • 基金项目: 国家自然科学基金(批准号: 11374066, 11374068)和广东省自然科学基金重点项目(批准号: S2012020010885)资助的课题.
      Corresponding author: Zhang Xin, xinxintwinkle@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11374066, 11374068) and the Natural Science Foundation of Guangdong, China (Grant No. S2012020010885).
    [1]

    Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109

    [2]

    Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201

    [3]

    Katsnelson M I 2006 Eur. Phys. J. B 51 157

    [4]

    Katsnelson M I, Novoselov K S, Geim A K 2006 Nat. Phys. 2 620

    [5]

    Sepkhanov R A, Bazaliy Y B, Beenakker C W J 2007 Phys. Rev. A 75 063813

    [6]

    Zhang X D, Liu Z Y 2008 Phys. Rev. Lett. 101 264303

    [7]

    Yu S Y, Wang Q, Zheng L Y, He C, Liu X P, Lu M H, Chen Y F 2015 Appl. Phys. Lett. 106 151906

    [8]

    Liu F M, Huang X Q, Chan C T 2012 Appl. Phys. Lett. 100 071911

    [9]

    Liu F M, Lai Y, Huang X Q, Chan C T 2011 Phys. Rev. B 84 224113

    [10]

    Peng P, Mei J, Wu Y 2012 Phys. Rev. B 86 134304

    [11]

    Smith M J A, McPhedran R C Meylan M H 2014 Wave Random Complex 24 35

    [12]

    Mei J, Wu Y, Chan C T, Zhang Z Q 2012 Phys. Rev. B 86 035141

    [13]

    Chen Z G, Ni X, Wu Y, He C, Sun X C, Zheng L Y, Lu M H, Chen Y F 2014 Sci. Rep. 4 4613

    [14]

    Lu J Y, Qiu C Y, Xu S J, Ye Y T, Ke M Z, Liu Z Y 2014 Phys. Rev. B 89 134302

    [15]

    Li Y, Wu Y, Mei J 2014 Appl. Phys. Lett. 105 014107

    [16]

    Torrent D, Snchez-Dehesa J 2012 Phys. Rev. Lett. 108 174301

    [17]

    Wei Q, Cheng Y, Liu X J 2013 Appl. Phys. Lett. 102 174104

    [18]

    Fleury R, Al A 2013 Phys. Rev. Lett. 111 055501

    [19]

    Pardo V, Pickett W E 2009 Phys. Rev. Lett. 102 166803

    [20]

    Banerjee S, Singh R R P, Pardo V, Pickett W E 2009 Phys. Rev. Lett. 103 016402

    [21]

    Huang X Q, Chen Z T 2015 Acta Phys. Sin. 64 184208 (in Chinese) [黄学勤, 陈子亭 2015 物理学报 64 184208]

    [22]

    Wang X, Chen L C, Liu Y H, Shi Y L, Sun Y 2015 Acta Phys. Sin. 64 174206 (in Chinese) [王晓, 陈立潮, 刘艳红, 石云龙, 孙勇 2015 物理学报 64 174206]

    [23]

    Wu Y 2014 Opt. Express 22 1906

    [24]

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

    [25]

    Liu Z Y, Chan C T, Sheng P 2005 Phys. Rev. B 71 014103

    [26]

    Li J, Liu Z Y, Qiu C Y 2006 Phys. Rev. B 73 054302

    [27]

    Li Y, Liang B, Gu Z M, Zou X Y, Cheng J C 2013 Appl. Phys. Lett. 103 053505

    [28]

    Li Y, Mei J 2015 Opt. Express 23 12089

    [29]

    Liang B, Yuan B, Cheng J C 2009 Phys. Rev. Lett. 103 104301

    [30]

    Liang B, Guo X S, Tu J, Zhang D, Cheng J C 2010 Nat. Mater. 10 1038

  • [1]

    Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109

    [2]

    Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201

    [3]

    Katsnelson M I 2006 Eur. Phys. J. B 51 157

    [4]

    Katsnelson M I, Novoselov K S, Geim A K 2006 Nat. Phys. 2 620

    [5]

    Sepkhanov R A, Bazaliy Y B, Beenakker C W J 2007 Phys. Rev. A 75 063813

    [6]

    Zhang X D, Liu Z Y 2008 Phys. Rev. Lett. 101 264303

    [7]

    Yu S Y, Wang Q, Zheng L Y, He C, Liu X P, Lu M H, Chen Y F 2015 Appl. Phys. Lett. 106 151906

    [8]

    Liu F M, Huang X Q, Chan C T 2012 Appl. Phys. Lett. 100 071911

    [9]

    Liu F M, Lai Y, Huang X Q, Chan C T 2011 Phys. Rev. B 84 224113

    [10]

    Peng P, Mei J, Wu Y 2012 Phys. Rev. B 86 134304

    [11]

    Smith M J A, McPhedran R C Meylan M H 2014 Wave Random Complex 24 35

    [12]

    Mei J, Wu Y, Chan C T, Zhang Z Q 2012 Phys. Rev. B 86 035141

    [13]

    Chen Z G, Ni X, Wu Y, He C, Sun X C, Zheng L Y, Lu M H, Chen Y F 2014 Sci. Rep. 4 4613

    [14]

    Lu J Y, Qiu C Y, Xu S J, Ye Y T, Ke M Z, Liu Z Y 2014 Phys. Rev. B 89 134302

    [15]

    Li Y, Wu Y, Mei J 2014 Appl. Phys. Lett. 105 014107

    [16]

    Torrent D, Snchez-Dehesa J 2012 Phys. Rev. Lett. 108 174301

    [17]

    Wei Q, Cheng Y, Liu X J 2013 Appl. Phys. Lett. 102 174104

    [18]

    Fleury R, Al A 2013 Phys. Rev. Lett. 111 055501

    [19]

    Pardo V, Pickett W E 2009 Phys. Rev. Lett. 102 166803

    [20]

    Banerjee S, Singh R R P, Pardo V, Pickett W E 2009 Phys. Rev. Lett. 103 016402

    [21]

    Huang X Q, Chen Z T 2015 Acta Phys. Sin. 64 184208 (in Chinese) [黄学勤, 陈子亭 2015 物理学报 64 184208]

    [22]

    Wang X, Chen L C, Liu Y H, Shi Y L, Sun Y 2015 Acta Phys. Sin. 64 174206 (in Chinese) [王晓, 陈立潮, 刘艳红, 石云龙, 孙勇 2015 物理学报 64 174206]

    [23]

    Wu Y 2014 Opt. Express 22 1906

    [24]

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

    [25]

    Liu Z Y, Chan C T, Sheng P 2005 Phys. Rev. B 71 014103

    [26]

    Li J, Liu Z Y, Qiu C Y 2006 Phys. Rev. B 73 054302

    [27]

    Li Y, Liang B, Gu Z M, Zou X Y, Cheng J C 2013 Appl. Phys. Lett. 103 053505

    [28]

    Li Y, Mei J 2015 Opt. Express 23 12089

    [29]

    Liang B, Yuan B, Cheng J C 2009 Phys. Rev. Lett. 103 104301

    [30]

    Liang B, Guo X S, Tu J, Zhang D, Cheng J C 2010 Nat. Mater. 10 1038

  • [1] 顾梓恒, 臧强, 郑改革. 外尔半金属调制的范德瓦耳斯声子极化激元色散性质. 物理学报, 2023, 72(19): 197102. doi: 10.7498/aps.72.20230167
    [2] 钱黎明, 孙梦然, 郑改革. α相三氧化钼中各向异性双曲声子极化激元的耦合性质. 物理学报, 2023, 72(7): 077101. doi: 10.7498/aps.72.20222144
    [3] 周晓霞, 陈英, 蔡力. 基于零折射率介质的超窄带光学滤波器. 物理学报, 2023, 72(17): 174205. doi: 10.7498/aps.72.20230394
    [4] 丁燕, 钟粤华, 郭俊青, 卢毅, 罗昊宇, 沈云, 邓晓华. 黑磷各向异性拉曼光谱表征及电学特性. 物理学报, 2021, 70(3): 037801. doi: 10.7498/aps.70.20201271
    [5] 张高见, 王逸璞. 腔光子-自旋波量子耦合系统中各向异性奇异点的实验研究. 物理学报, 2020, 69(4): 047103. doi: 10.7498/aps.69.20191632
    [6] 陆志仁, 梁斌明, 丁俊伟, 陈家璧, 庄松林. 近零折射率材料的古斯汉欣位移的特性研究. 物理学报, 2016, 65(15): 154208. doi: 10.7498/aps.65.154208
    [7] 耿滔, 吴娜, 董祥美, 高秀敏. 基于磁流体光子晶体的可调谐近似零折射率研究. 物理学报, 2016, 65(1): 014213. doi: 10.7498/aps.65.014213
    [8] 卢敏, 黄惠莲, 余冬海, 刘维清, 魏望和. 不同晶面银纳米晶高温熔化的各向异性. 物理学报, 2015, 64(10): 106101. doi: 10.7498/aps.64.106101
    [9] 黄学勤, 陈子亭. k=0处的类狄拉克锥. 物理学报, 2015, 64(18): 184208. doi: 10.7498/aps.64.184208
    [10] 曹惠娴, 梅军. 声子晶体中的半狄拉克点研究. 物理学报, 2015, 64(19): 194301. doi: 10.7498/aps.64.194301
    [11] 张永伟, 殷春浩, 赵强, 李富强, 朱姗姗, 刘海顺. TiO2电子结构与其双折射性、各向异性关联的理论研究. 物理学报, 2012, 61(2): 027801. doi: 10.7498/aps.61.027801
    [12] 凌瑞良, 冯进, 冯金福. 三维各向异性耦合谐振子体系的量子化能谱与精确波函数. 物理学报, 2010, 59(12): 8348-8358. doi: 10.7498/aps.59.8348
    [13] 李晓春, 高俊丽, 刘绍娥, 周科朝, 黄伯云. 无序对二维声子晶体平板负折射成像的影响. 物理学报, 2010, 59(1): 376-380. doi: 10.7498/aps.59.376
    [14] 万勇, 韩文娟, 刘均海, 夏临华, Xavier Mateos, Valentin Petrov, 张怀金, 王继扬. 单斜结构的Yb:KLu(WO4)2晶体光谱和激光性质的各向异性. 物理学报, 2009, 58(1): 278-284. doi: 10.7498/aps.58.278.1
    [15] 周建华, 刘虹遥, 罗海陆, 文双春. 各向异性超常材料中倒退波的传播研究. 物理学报, 2008, 57(12): 7729-7736. doi: 10.7498/aps.57.7729
    [16] 蔡 力, 韩小云, 温熙森. 长波条件下二维声子晶体中的弹性波传播及各向异性. 物理学报, 2008, 57(3): 1746-1752. doi: 10.7498/aps.57.1746
    [17] 穆全全, 刘永军, 胡立发, 李大禹, 曹召良, 宣 丽. 光谱型椭偏仪对各向异性液晶层的测量. 物理学报, 2006, 55(3): 1055-1060. doi: 10.7498/aps.55.1055
    [18] 庄 飞, 沈建其. 双轴各向异性负折射率材料光纤中光子波函数几何相位研究. 物理学报, 2005, 54(2): 955-960. doi: 10.7498/aps.54.955
    [19] 庄飞, 肖三水, 何江平, 何赛灵. 二维正方各向异性碲圆柱光子晶体完全禁带中缺陷模的FDTD计算分析和设计. 物理学报, 2002, 51(9): 2167-2172. doi: 10.7498/aps.51.2167
    [20] 庄飞, 何赛灵, 何江平, 冯尚申. 大带隙的二维各向异性椭圆介质柱光子晶体. 物理学报, 2002, 51(2): 355-361. doi: 10.7498/aps.51.355
计量
  • 文章访问数:  6028
  • PDF下载量:  237
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-08-30
  • 修回日期:  2015-10-23
  • 刊出日期:  2016-02-05

/

返回文章
返回