二维声子晶体带结构的多散射分析及解耦模式

利用多散射方法研究了二维声子晶体中的带结构，通过对柱散射波各阶分波之间的耦合分析，发现在带隙边缘的模式存在与对称性相关的解耦现象. 由此在低阶带隙边缘出现独立的自洽的零阶多散射模式. 通过引入周期结构因子和Mie散射因子，得到表征低阶带隙起始频率的解析公式. 利用该公式，采用图解法，定量地说明了带隙起始频率随周期性和单散射体Mie散射特性变化的规律. 关键词： 声子晶体 多散射     

长波条件下二维声子晶体中的弹性波传播及各向异性

利用多散射方法研究了长波条件下二维声子晶体中弹性波的传播特性.由长波条件下散射体幂散射特性和结构周期特性分析得到了等效波速的解析表达式.通过对幂散射波各阶分波之间由于结构周期特性而产生的耦合作用进行分析,发现幂散射波的正负二阶分量之间的耦合作用具有明显的方向性,长波条件下弹性波的传播特性是否具有各向异性取决于幂散射波的二阶分量在多散射过程中是否有明显的作用.     

Tri-component phononic crystals for underwater anechoic coatings

Localized resonance in phononic crystal, composed of three-dimensional arrays of composite units, has been discovered recently. The composite unit is a high-density sphere coated by soft silicon rubber. In this Letter, the absorptive properties induced by the localized resonance are systemically investigated. The mode conversions during the Mie scattering of a single coated lead sphere in unbounded epoxy are analyzed by referring the elements of the scattering matrix. Then the anechoic properties of a slab containing a plane of such composite scatterers are investigated with the multiple-scattering method by accounting the effects of the multiple scattering and the viscous dissipation. The results show that the longitudinal to transverse mode conversion nearby the locally resonant region is an effective way to enhance the anechoic performance of the finite slab of phononic crystal. Then, the influences of the viscoelasticity of the silicon rubber and the coating thickness on the acoustic properties of the finite slab are investigated for anechoic optimization. Finally, we synthetically consider the destructive scattering in the finite slab of phononic crystal and the backing, and design an anechoic slab composed of bi-layer coated spheres. The results show that the most of the incident energy is absorbed at the desired frequency band.     

基于局域共振单元实现声子晶体低频多通道滤波

从理论上提出一种由局域共振单元组成的声子晶体低频多通道滤波模型.在二维三组元局域共振声子晶体中引入不同填充率的共振单元构成波导结构,通过有限元法计算出其能带结构、透射曲线和透射场图.结果显示:这种设计能够在低频带隙范围内不同填充率散射体的共振频率附近产生新的分立模,且这些分立模能够使相应的声波在声子晶体中沿波导方向传播;这些分立模只与相应的共振单元相关,抗干扰能力强.所得结果为低频多通道滤波器的设计提供了一种新的理论依据.     

平板二维声子晶体声波能带结构研究

利用超元胞法,研究由钢板上生长有限长度的钢柱体形成的散射体嵌入环氧树脂基体中所构成的平板二维声子晶体的声波能带结构,分析散射体的几何参数如柱体的高、半径和板的厚度对声波带隙的影响。研究结果表明:(1)这种新型的声子晶体具有很宽的带隙,且带隙出现在低频范围内;(2)散射体的几何参数对带隙的宽度有很大的影响,它们是控制带隙宽度的主要因素。     

微纳粒子光学散射分析

为实现利用光学方式对微纳尺度粒子性质的研究,探讨了亚微米线及亚微米球对光电磁波的散射效应.微纳米尺度粒子的光学散射,散射粒子尺寸与入射光波长尺寸可满足米氏(Mie)散射条件.利用Matlab数值模拟的方式,将分析结果以模拟图的形式清晰地展现出来.满足尺寸条件的层状粒子以及任意多个散射粒子存在时对电磁波的散射都可采用Mie散射分析方法,并且针对多粒子散射,分析了散射体位于不同位置时对散射造成的影响.通过分析光学散射光场相关的微分散射截面及近场散射电磁场分布,可得出散射光场随散射角度的变化趋势,以及散射光场受各类因素的影响,包括入射光偏振态、散射粒子尺寸、散射粒子结构及粒子构成层数、散射粒子数量等的影响,也包括一些隐含因素对散射光场的影响,如散射粒子与周围介质的相对折射率.本文的科学意义体现在:与入射光波长尺寸可比的亚微米尺度的粒子,可用作传感器,对于其位移的探测可通过光学方式来实现,而由于粒子本身特性对散射光的影响具有一定的参考价值,从而使通过光学方式对机械位移的读出具有更高准确度.研究结果对于光学方式探测亚微米线机械振动具有指导意义.     

Effects of matrices on Mie scattering in the mid-infrared region

Various Mie scattering systems, each having a transparent matrix, are studied in the mid-infrared region. Our three theoretical scattering systems correspond to a lossless scatterer, an anomalous dispersive dielectric scatterer and a metal scatterer, each in a non-air usual matrix. The refractive-index effects of the matrix on scattering and extinction efficiencies in the mid-infrared region are found to be quite different in different cases. Although the non-air usual matrix reduces scattering and extinction efficiencies in the first kind of system, it may or may not help scatter and extinguish the mid-infrared radiation in the second, and it has little effect on them in the third.     

Correlation between single-cylinder properties and bandgap formation in photonic structures

The origin of frequency gaps in the dispersion relation of periodic, quasi-periodic, and random photonic structures consisting of different arrangements of dielectric cylinders has been investigated. For TM polarization it was found that the formation and properties of gaps are strongly affected by Mie resonances of a single cylinder. Both the spectral position and size depend on the properties of this single scatterer. In contrast, for TE polarization no correlation between the scattering properties and bandgap formation was found, as Mie resonances are spectrally not well separated. For the inverted structure consisting of air cylinders in a dielectric material, the frequency gaps depend on the spatial arrangement of the cylinders because no pronounced Mie resonances exist in this case.     

Determinant of Wave Operator as a Measure for Resonance and Bound States in One-Dimensional Potential Scattering System

The determinant of the wave operator or its transposed operator (source operator) works as a measure for resonance and bound states in one-dimensional potential scattering system. This fact is based on an identity proved here: the determinant of the wave or source operator equals to the transmission coefficient, which represents the field amplitude in the forward side of the scatterer. Utilizing this measure, resonance and bound states in one-dimensional system are properly assigned without solving wave equation. In future, local enhancement of optical near-field in three-dimensional system, i.e., local plasmon resonance will be treated, generalizing the present method.     

Scattering of antiplane shear waves by layered circular elastic cylinder

An exact analytical solution for the scattering of antiplane elastic waves by a layered elastic circular cylinder is obtained. The solution and its degenerate cases are compared with other simpler models of circular cylindrical scatterers. The effects of the geometrical and physical properties of the interphase are studied. Numerical results confirm the existence of a resonance mode in which the scatterer's core undergoes a rigid-body motion when the outer layer of the scatterer is very compliant. This resonance mode has been attributed [Liu et al., Science 289, 1734 (2000)] to a new mechanism for the band gap formed in the extremely low frequency range for phononic crystals made of layered spherical scatterers. Numerical results also show the existence of a similar resonance mode when the outer layer of the scatterer has very high mass density.     

二维空心散射体声子晶体板的低频带隙特性及其形成机理

利用有限元方法,对设计的涂有硅橡胶包裹层的空心铅柱体嵌入到4个环氧树脂短连接板中构成的声子晶体板的低频带隙特性进行了研究,分析了其能带结构、传输损失及位移场。与正方连接板粘连结构、嵌入结构和细连接短板粘连结构这3种传统声子晶体板的带隙特性作对比,说明具有包裹层、短连接板结构的声子晶体板更容易产生低频宽带;观察位移矢量场的振动模态,并结合弹簧质量模型,解释了带隙形成的机理;通过讨论连接板的宽度、散射体的内外半径及高度对第一完全带隙的影响,说明连接板宽度越窄,厚度越小,散射体内半径越小,外半径越大,高度越高,越有利于带隙的扩展。     

Effect of interface/surface stress on the elastic wave band structure of two-dimensional phononic crystals

In the present Letter, the multiple scattering theory (MST) for calculating the elastic wave band structure of two-dimensional phononic crystals (PCs) is extended to include the interface/surface stress effect at the nanoscale. The interface/surface elasticity theory is employed to describe the nonclassical boundary conditions at the interface/surface and the elastic Mie scattering matrix embodying the interface/surface stress effect is derived. Using this extended MST, the authors investigate the interface/surface stress effect on the elastic wave band structure of two-dimensional PCs, which is demonstrated to be significant when the characteristic size reduces to nanometers.     

声子晶体结构在功率超声换能器中的应用

该文提出了一种二维声子晶体结构模型,并将该模型应用于横向尺寸较大的功率超声换能器的前盖板中,避免了形成耦合振动对换能器的影响,从而优化了该类换能器的工作性能.首先设计了一种具有近周期性结构的圆柱形孔的前盖板,然后研究了声子晶体结构前盖板散射体的半径大小和高度对换能器共振频率以及前盖板带隙的影响.结果表明,随着散射体半径...     

一维准周期结构声子晶体透射性质的研究

提出了一维准周期结构的声子晶体模型.对弹性波通过该一维准周期结构声子晶体的透射系数进行了数值计算，并与周期结构的透射系数进行了比较.计算结果表明，弹性波通过一维准周期结构声子晶体时，同样会有带隙的出现，且带隙所在频率范围与周期结构的情形完全一样，不同的是在准周期结构声子晶体中，带隙内有很强的局域共振模.对此局域模性质的研究有助于声波或弹性波滤波器的制作. 关键词： 准周期结构 声子晶体 局域化     

基于Mie散射理论对砷化镓光子晶体安德森定域化研究

基于Mie散射理论和低浓度近似,对砷化镓作为散射体光子晶体中的安德森定域化参量进行了理论计算,并分析了影响定域化现象的各种因素。结果表明:在散射体体积分数为10%,相对折射率大于3.8时,远红外区50~65 μm范围内出现严格的定域化现象;随着散射体半径的增大,定域化区向长波方向移动,且定域化参量先增大后减小。     

局域共振的光子、声子功能材料

介绍一种利用局域共振的原理制造人工光、声子结构材料的方法，此种方法不同于通常建立在布拉格散射基础上的光、声子晶体能带材料，但又表现出与之相同的物理特征，局域共振光、声子模型的优点是样品制作相对简单；不依赖于结构的周期性；可制备出亚波长的能隙结构，为微波及长波声波能带结构的制造提供了一种十分简便而有效的方法。     

Growth of ultrasmall nanoparticles based on thermodynamic size focusing

A physical mechanism of phononic band gap and resonant nanoacoustic scattering in an aggregate of two elastic nanospheres is presented in this paper. By considering the Van der Waals (VdW) force between two nanospheres illuminated by nanoacoustic wave, phononic band gap and frequency shift at the lower frequency side, and largely enhanced nanoacoustic scattering at the other frequency range have been found through calculating the form function of the acoustic scattering from the nanosystem. This VdW-force-induced band gap is different from the known mechanisms of Bragg scattering and local resonances for periodic media. It is shown that when the separation distance between two nanospheres is decreasing from 20 to 1?nm, due to the increasing VdW force, the nanoacoustic scattering is much heightened by two order of magnitude, and meanwhile the frequency shift and phononic band gap at the low frequencies are both widened. These results could provide potential applications of nanoacoustic devices.     

内插扩张室声子晶体管路带隙特性研究

声子晶体管路的带隙特性,可以实现管路系统在特定频率下的噪声控制.利用二维模态匹配法推导出单个内插扩张室元胞的传递矩阵,结合Bloch定理,得到声子晶体管路的能带结构计算方法;验证了二维方法在计算能带结构时的准确性.研究发现,内插扩张室声子晶体管路存在布拉格带隙和局域共振带隙.进一步研究了晶格常数以及内插管长度对能带结构的影响,结果表明,晶格常数主要控制布拉格带隙,而内插管长度对局域共振带隙有较大的影响,并研究了两种参数变化下的带隙耦合.研究结果可以为管路降噪设计提供新的思路.     

Lamb wave band gaps in locally resonant phononic crystal strip waveguides

Using finite element method, we have made a theoretically study of the band structure of Lamb wave in a locally resonant phononic crystal strip waveguide with periodic soft rubber attached on the two sides of epoxy main plate. The numerical results show that the Lamb wave band gap based on local resonant mechanism can be opened up in the stub strip waveguides, and the width of the local resonant band gap is narrower than that based on the Bragg scattering mechanism. The results also show that the stub shape and width have influence on the frequency and width of the Lamb wave band gap.     

Electric field tunable photonic Hall effect with liquid crystals

The Mie theory for electromagnetic scattering is extended to the case of coated metal sphere with liquid crystals. A new set of vector basis functions for the electric displacement vector inside the liquid crystal layer has been constructed. The expansion coefficients of transmitted and scattered fields are obtained analytically by applying the continuous boundary conditions. The dependence of the scattering property on the geometrical parameters has been investigated in detail. The appearance of photonic Hall effect for such a Mie scatterer is confirmed. It is interesting that such a photonic Hall effect not only depends on the ratio of the inner to outer radius of coated sphere, it is also tunable by the application of an external voltage.