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

二维近零折射率声学材料的负向Schoch位移

刘向东 吴福根 姚源卫 张欣

引用本文:
Citation:

二维近零折射率声学材料的负向Schoch位移

刘向东, 吴福根, 姚源卫, 张欣

Negative Schoch displacement of two-dimensional acoustic metamaterials with near-zero refractive index

Liu Xiang-Dong, Wu Fu-Gen, Yao Yuan-Wei, Zhang Xin
PDF
HTML
导出引用
  • 对二维声学超材料与常规材料界面处的负向Schoch位移进行了研究. 研究表明, 在界面处增加合适厚度的覆盖层, 当声波在某一频率附近从常规材料向近零折射率材料传播时, 反射声波相对于入射声波会在界面处发生负向Schoch位移, 此时, 超材料的有效体积模量倒数值趋近于零从而使它成为一种折射率近零的声学材料; 同时, 超材料有效阻抗的极大值和反射系数的极大值都在这一特殊频率处且反射系数虚部相位在对应频率处有π rad的相位突变; 研究还发现, 发生负向Schoch位移的频率位于MK方向第一带隙中且靠近上边界的通带频率. 常规材料界面处的Schoch位移通常是正向的且大小可忽略不计的, 本文利用近零折射率声学材料实现了负向的Schoch位移, 为设计出基于界面声波的声学器件提供了一种新的理论参考.
    In this paper, the Schoch displacement at the interface between different two-dimensional triangular phononic crystal metamaterial and natural material is studied by using finite element software. As is well known, the Schoch displacement is highly dependent on the surface wave and leakage wave excited at the interface between different materials. So, the negative Schoch displacement can be more easily obtained by adding a suitable thickness of covering layer at the interface between metamaterial material and natural material. The numerical results show that when the negative Schoch displacement happens, the effective parameters of metamaterials are close to zero. It means that the effective refraction index is near to zero and the reduced frequency of the incident acoustic wave is correlated with the reduced frequency of the band gap. It is also found from the results that the reduced frequency of the incident acoustic wave is located at the edge of the band gap when the negative Schoch displacement occurs. The maximum of the metamaterial effective impedance and the maximum of the reflection coefficient are almost at the same frequency. The phase of the imaginary part of the reflection coefficient has a phase mutation in π rad at the corresponding frequency. The frequency of negative Schoch displacement is located in the first band gap of MK direction and near the upper boundary. The Schoch displacement at the interface between conventional materials is usually positive and negligible in previous reports. In this paper, the negative Schoch displacement is obtained by using the near-zero refraction index metamaterials. This not only enriches the physics contents of Schoch effect but also provides a theoretical reference for designing the acoustic devices based on acoustic wave displacement at the interface.
      通信作者: 吴福根, wufg@gdut.edu.cn ; 姚源卫, yaoyuan100w@gdut.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11374066, 11374068)资助的课题
      Corresponding author: Wu Fu-Gen, wufg@gdut.edu.cn ; Yao Yuan-Wei, yaoyuan100w@gdut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos.11374066, 11374068)
    [1]

    Schoch A 1950 Schallreflexion, Schallbrechung und Schallbeugung (Berlin, Heidelberg: Springer) pp127−234

    [2]

    Schoch A 1952 Acta Acust. United Acust. 2 372Google Scholar

    [3]

    Bertoni H L, Tamir T 1973 Appl. Phys. 2 157Google Scholar

    [4]

    Declercq N F, Degrieck J, Briers R, Leroy O 2003 Appl. Phys. Lett. 82 2533Google Scholar

    [5]

    Declercq N F, Degrieck J, Briers R, Leroy O 2004 J. Appl. Phys. 96 6869Google Scholar

    [6]

    Herbison S W, Declercq N F, Breazeale M A 2009 J. Acoust. Soc. Am. 126 2939Google Scholar

    [7]

    Declercq N F 2014 Ultrasonics 54 609Google Scholar

    [8]

    陈宗旺, 姚源卫, 吴福根, 张欣, 董华锋, 陆水芳, 韩理想 2017 中国科学: 物理学 力学 天文学 47 064301Google Scholar

    Chen Z W, Yao Y W, Wu F G, Zhang X, Dong H F, Lu S F, Han L X 2017 Sci. China-Phys. Mech. Astron. 47 064301Google Scholar

    [9]

    Yang Z, Mei J, Yang M, Chan N H, Sheng P 2008 Phys. Rev. Lett. 101 204301Google Scholar

    [10]

    Mei J, Ma G C, Yang M, Yang Z Y, Wen W J, Sheng P 2012 Nat. Commun. 3 756Google Scholar

    [11]

    沈惠杰, 温激鸿, 郁殿龙, 蔡力, 温熙森 2012 物理学报 61 134303Google Scholar

    Shen H J, Wen J H, Yu D L, Cai L, Wen X S 2012 Acta Phys. Sin. 61 134303Google Scholar

    [12]

    陈凡, 郝军, 李红根, 曹庄琪 2011 物理学报 60 074223Google Scholar

    Chen F, Hao J, Li H G, Cao Z Q 2011 Acta Phys. Sin. 60 074223Google Scholar

    [13]

    Xu Y D, Chan C T, Chen H Y 2015 Sci. Rep. 5 8681Google Scholar

    [14]

    陆志仁, 梁斌明, 丁俊伟, 陈家璧, 庄松林 2016 物理学报 65 154208Google Scholar

    Lu Z R, Liang B M, Ding J W, Chen J B, Zhuang S L 2016 Acta Phys. Sin. 65 154208Google Scholar

    [15]

    Fan Y C, Shen N H, Zhang F L, Wei Z Y, Li H Q, Zhao Q, Fu Q H, Zhang P, Koschny T, Soukoulis C M 2016 Adv. Opt. Mater. 4 1824Google Scholar

    [16]

    He J L, Yi J, He S L 2006 Opt. Express 14 3024Google Scholar

    [17]

    Shadrivov I V, Ziolkowski R W, Zharov A A, Kivshar Y S 2005 Opt. Express 13 481Google Scholar

    [18]

    Declercq N F, Lamkanfi E 2008 Appl. Phys. Lett. 93 054103Google Scholar

    [19]

    Lamkanfi E, Declercq N F, Van Paepegem W, Degrieck J 2009 J. Appl. Phys. 105 114902Google Scholar

    [20]

    Mei J, Liu Z Y, Wen W J, Sheng P 2006 Phys. Rev. Lett. 96 024301Google Scholar

    [21]

    Mei J, Liu Z Y, Wen W J, Sheng P 2007 Phys. Rev. B 76 134205

    [22]

    Fokin V, Ambati M, Sun C, Zhang X 2007 Phys. Rev. B 76 144302

    [23]

    Zhao D, Zhong D, Hu Y H, Ke S L, Liu W W 2019 Opt. Quantum Electron. 51 113Google Scholar

    [24]

    Huang X Q, Lai Y, Hang Z H, Zheng H H, Chan C. T. 2011 Nat. Mater. 10 582Google Scholar

    [25]

    Wan Y H, Zheng Z, Kong W J, Zhao X, Liu Y, Bian Y S, Liu J S 2012 Opt. Expres 20 8998Google Scholar

    [26]

    Enoch S, Tayeb G, Maystre D 1999 Opt. Commun. 161 171Google Scholar

    [27]

    Zhang J L, Jiang H T, Enoch S, Tayeb G, Gralak B, Lequime M 2008 Appl. Phys. Lett. 92 053104Google Scholar

    [28]

    Felbacq D, Smaali R 2004 Phys. Rev. Lett. 92 193902Google Scholar

    [29]

    Felbacq D, Moreau A, Smaali R 2003 Opt. Lett. 28 1633Google Scholar

    [30]

    Hou Z L, Fu X J, Liu Y Y 2004 Phys. Rev. B 70 014304Google Scholar

    [31]

    Tamir T, Bertoni H L 1971 J. Opt. Soc. Am. 61 1397Google Scholar

    [32]

    Berman P R 2002 Phys. Rev. E 66 067603Google Scholar

  • 图 1  (a) 模型结构, 从上到下分别为水银、水层和声学超材料; (b) 超材料的单个晶胞, 其中圆柱散射体为橡胶, 基体为水

    Fig. 1.  (a) Model structure, which consists of mercury, water layer and acoustic metamaterial from top to bottom; (b) single crystal cell of metamaterial, where the cylindrical scatterer is rubber and the matrix is water.

    图 2  (a) 具有明显负向Schoch位移的声压场图($R = $$ 0.224 a$, F = fa/c0 = 0.456 = FS, a = 1 m), 其中纵轴和横轴分别表示本文结构的高度y和宽度x, 右侧的颜色条对应的物理量为总声压场强Pt; (b) 在FS = 0.456附近, 负向Schoch位移随约化频率F的变化

    Fig. 2.  (a) Acoustic pressure field with significant negative Schoch displacement ($R = 0.224 a$, F = fa/c0 = 0.456 = FS, a = 1 m); (b) relation of Schoch displacement to reduced frequency F near FS = 0.456.

    图 3  (a) $F = 0.456$, 水层和超材料界面附近出现大量后向漏波; (b)$F = 0.{{503}}$, 水层和超材料界面附近完全没有漏波

    Fig. 3.  (a) $F = 0.456$, there are a large number of backward leaky Rayleigh waves appear near the interface between the water layer and the metamaterial; (b)$F = $$ 0.{{503}}$, there is no leaky Rayleigh wave near the water layer and the metamaterial interface.

    图 4  声学超材料不同的物理参数特性 ($R = 0.224 a$, FS = 0.456) (a) 相对阻抗(Zeff)和反射系数(reff)随F的变化; (b) 有效折射率(neff)、有效质量密度(ρeff)、有效体积模量的倒数(1/κeff)随F的变化, 图像右下角内嵌图形为B点附近的放大

    Fig. 4.  Different physical parameters of acoustic metamaterials ($R = 0.224 a$, FS = 0.456): (a) Relationship between relative impedance (Zeff) and reflection coefficient(reff) with F; (b) relationship of effective refractive index (neff)、effective mass density (ρeff) and inverse of effective volume modulus (1/κeff) to F, the embedded figure in the lower right corner of the image is an enlargement near point B.

    图 5  (a) 反射系数虚部相位在$F = 0.456$处发生突变($R = $$ 0.224 a$, FS = 0.456); (b) 晶格的本征模声压场图

    Fig. 5.  (a) Phase of the imaginary part of the reflection coefficient mutates at $F = 0.456$ ($R = 0.224 a$, FS = 0.456); (b) eigen mode acoustic pressure field diagram of the lattice.

    图 6  (a) 发生Schoch位移时FSR的变化; (b) 负向Schoch位移随覆盖层厚度${h_0}$的变化($R = 0.224 a$, FS = 0.456); (c) 负向Schoch位移随入射声波半腰宽wi的变化; (d) 反射声波半腰宽wr随覆盖层厚度的变化

    Fig. 6.  (a) Relationship of FS to R when the Schoch displacement happens; (b) relationship between negative Schoch displacement and overburden thickness ${h_0}$; (c) relationship between negative Schoch displacement and the half-waist width of the incident acoustic wave; (d) relationship between the half-width of the reflected acoustic wave and the thickness of the covering layer.

    图 7  (a) 超材料的带结构($R = 0.2{{24}}a$); (b) neff, ρeff, 1/κeffF的变化; (c) 声波以带隙下边界频率($F{{ = 0}}{{.309}}$)入射时超材料的声压场图

    Fig. 7.  (a) Band structures of metamaterial ($R = 0.2{{24}}a$); (b) relationship of neff, ρeff and 1/κeff to F; (c) acoustic pressure field diagram of metamaterial when acoustic waves incident at the lower band-gap boundary frequency.

  • [1]

    Schoch A 1950 Schallreflexion, Schallbrechung und Schallbeugung (Berlin, Heidelberg: Springer) pp127−234

    [2]

    Schoch A 1952 Acta Acust. United Acust. 2 372Google Scholar

    [3]

    Bertoni H L, Tamir T 1973 Appl. Phys. 2 157Google Scholar

    [4]

    Declercq N F, Degrieck J, Briers R, Leroy O 2003 Appl. Phys. Lett. 82 2533Google Scholar

    [5]

    Declercq N F, Degrieck J, Briers R, Leroy O 2004 J. Appl. Phys. 96 6869Google Scholar

    [6]

    Herbison S W, Declercq N F, Breazeale M A 2009 J. Acoust. Soc. Am. 126 2939Google Scholar

    [7]

    Declercq N F 2014 Ultrasonics 54 609Google Scholar

    [8]

    陈宗旺, 姚源卫, 吴福根, 张欣, 董华锋, 陆水芳, 韩理想 2017 中国科学: 物理学 力学 天文学 47 064301Google Scholar

    Chen Z W, Yao Y W, Wu F G, Zhang X, Dong H F, Lu S F, Han L X 2017 Sci. China-Phys. Mech. Astron. 47 064301Google Scholar

    [9]

    Yang Z, Mei J, Yang M, Chan N H, Sheng P 2008 Phys. Rev. Lett. 101 204301Google Scholar

    [10]

    Mei J, Ma G C, Yang M, Yang Z Y, Wen W J, Sheng P 2012 Nat. Commun. 3 756Google Scholar

    [11]

    沈惠杰, 温激鸿, 郁殿龙, 蔡力, 温熙森 2012 物理学报 61 134303Google Scholar

    Shen H J, Wen J H, Yu D L, Cai L, Wen X S 2012 Acta Phys. Sin. 61 134303Google Scholar

    [12]

    陈凡, 郝军, 李红根, 曹庄琪 2011 物理学报 60 074223Google Scholar

    Chen F, Hao J, Li H G, Cao Z Q 2011 Acta Phys. Sin. 60 074223Google Scholar

    [13]

    Xu Y D, Chan C T, Chen H Y 2015 Sci. Rep. 5 8681Google Scholar

    [14]

    陆志仁, 梁斌明, 丁俊伟, 陈家璧, 庄松林 2016 物理学报 65 154208Google Scholar

    Lu Z R, Liang B M, Ding J W, Chen J B, Zhuang S L 2016 Acta Phys. Sin. 65 154208Google Scholar

    [15]

    Fan Y C, Shen N H, Zhang F L, Wei Z Y, Li H Q, Zhao Q, Fu Q H, Zhang P, Koschny T, Soukoulis C M 2016 Adv. Opt. Mater. 4 1824Google Scholar

    [16]

    He J L, Yi J, He S L 2006 Opt. Express 14 3024Google Scholar

    [17]

    Shadrivov I V, Ziolkowski R W, Zharov A A, Kivshar Y S 2005 Opt. Express 13 481Google Scholar

    [18]

    Declercq N F, Lamkanfi E 2008 Appl. Phys. Lett. 93 054103Google Scholar

    [19]

    Lamkanfi E, Declercq N F, Van Paepegem W, Degrieck J 2009 J. Appl. Phys. 105 114902Google Scholar

    [20]

    Mei J, Liu Z Y, Wen W J, Sheng P 2006 Phys. Rev. Lett. 96 024301Google Scholar

    [21]

    Mei J, Liu Z Y, Wen W J, Sheng P 2007 Phys. Rev. B 76 134205

    [22]

    Fokin V, Ambati M, Sun C, Zhang X 2007 Phys. Rev. B 76 144302

    [23]

    Zhao D, Zhong D, Hu Y H, Ke S L, Liu W W 2019 Opt. Quantum Electron. 51 113Google Scholar

    [24]

    Huang X Q, Lai Y, Hang Z H, Zheng H H, Chan C. T. 2011 Nat. Mater. 10 582Google Scholar

    [25]

    Wan Y H, Zheng Z, Kong W J, Zhao X, Liu Y, Bian Y S, Liu J S 2012 Opt. Expres 20 8998Google Scholar

    [26]

    Enoch S, Tayeb G, Maystre D 1999 Opt. Commun. 161 171Google Scholar

    [27]

    Zhang J L, Jiang H T, Enoch S, Tayeb G, Gralak B, Lequime M 2008 Appl. Phys. Lett. 92 053104Google Scholar

    [28]

    Felbacq D, Smaali R 2004 Phys. Rev. Lett. 92 193902Google Scholar

    [29]

    Felbacq D, Moreau A, Smaali R 2003 Opt. Lett. 28 1633Google Scholar

    [30]

    Hou Z L, Fu X J, Liu Y Y 2004 Phys. Rev. B 70 014304Google Scholar

    [31]

    Tamir T, Bertoni H L 1971 J. Opt. Soc. Am. 61 1397Google Scholar

    [32]

    Berman P R 2002 Phys. Rev. E 66 067603Google Scholar

  • [1] 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
    [2] 徐小虎, 陈永强, 郭志伟, 孙勇, 苗向阳. 等效零折射率材料微腔中均匀化腔场作用下的简正模劈裂现象. 物理学报, 2018, 67(2): 024210. doi: 10.7498/aps.67.20171880
    [3] 孙宏祥, 方欣, 葛勇, 任旭东, 袁寿其. 基于蜷曲空间结构的近零折射率声聚焦透镜. 物理学报, 2017, 66(24): 244301. doi: 10.7498/aps.66.244301
    [4] 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
    [5] 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
    [6] 余田, 张国华, 孙其诚, 赵雪丹, 马文波. 垂直振动激励下颗粒材料有效质量和耗散功率的研究. 物理学报, 2015, 64(4): 044501. doi: 10.7498/aps.64.044501
    [7] 宋永佳, 胡恒山. 含定向非均匀体固体材料的横观各向同性有效弹性模量. 物理学报, 2014, 63(1): 016202. doi: 10.7498/aps.63.016202
    [8] 赵浩, 沈义峰, 张中杰. 光子晶体中基于有效折射率接近零的光束准直出射. 物理学报, 2014, 63(17): 174204. doi: 10.7498/aps.63.174204
    [9] 李丽君, 来永政, 曹茂永, 刘超, 袁雪梅, 张旭, 管金鹏, 史静, 李晶. 光纤纤芯及包层模有效折射率计算及仿真. 物理学报, 2013, 62(14): 140201. doi: 10.7498/aps.62.140201
    [10] 钟时, 杨修群, 郭维栋. 局地零平面位移对非均匀地表有效空气动力学参数的影响. 物理学报, 2013, 62(14): 144212. doi: 10.7498/aps.62.144212
    [11] 魏来明, 周远明, 俞国林, 高矿红, 刘新智, 林铁, 郭少令, 戴宁, 褚君浩, Austing David Guy. 高迁移率InGaAs/InP量子阱中的有效g因子. 物理学报, 2012, 61(12): 127102. doi: 10.7498/aps.61.127102
    [12] 周文飞, 叶小玲, 徐波, 张世著, 王占国. 有效折射率微扰法研究单缺陷光子晶体平板微腔的性质. 物理学报, 2012, 61(5): 054202. doi: 10.7498/aps.61.054202
    [13] 苏妍妍, 龚伯仪, 赵晓鹏. 基于双负介质结构单元的零折射率超材料. 物理学报, 2012, 61(8): 084102. doi: 10.7498/aps.61.084102
    [14] 袁都奇. 原子激射器的空间有效增益范围. 物理学报, 2010, 59(8): 5271-5275. doi: 10.7498/aps.59.5271
    [15] 赵兴涛, 侯蓝田, 刘兆伦, 王 伟, 魏红彦, 马景瑞. 改进的全矢量有效折射率方法分析光子晶体光纤的色散特性. 物理学报, 2007, 56(4): 2275-2280. doi: 10.7498/aps.56.2275
    [16] 赵天恩, 伍瑞新, 杨 帆, 陈 平. 周期性层状铁氧体-电介质复合材料中导模模式的有效负折射率. 物理学报, 2006, 55(1): 179-183. doi: 10.7498/aps.55.179
    [17] 张德生, 董孝义, 张伟刚, 王 志. 用阶跃有效折射率模型研究光子晶体光纤色散特性. 物理学报, 2005, 54(3): 1235-1240. doi: 10.7498/aps.54.1235
    [18] 高汝伟, 冯维存, 王 标, 陈 伟, 韩广兵, 张 鹏, 刘汉强, 李 卫, 郭永权, 李岫梅. 纳米复合永磁材料的有效各向异性与矫顽力. 物理学报, 2003, 52(3): 703-707. doi: 10.7498/aps.52.703
    [19] 包科达. 含椭球包体多相复合介质电导率的有效介质理论. 物理学报, 1992, 41(5): 833-840. doi: 10.7498/aps.41.833
    [20] 廖绍彬, 尹光俊, 刘进, 周丽年. 一种测量微波张量磁化率和有效线宽的方法. 物理学报, 1980, 29(5): 644-650. doi: 10.7498/aps.29.644
计量
  • 文章访问数:  2993
  • PDF下载量:  91
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-12-11
  • 修回日期:  2021-01-14
  • 上网日期:  2021-06-08
  • 刊出日期:  2021-06-20

/

返回文章
返回