各向异性声子晶体能带结构的计算

边界元法被用于计算各向异性二维声子晶体的能带结构,该体系由各向异性或各向同性夹杂嵌入各向同性或各向异性基体中而形成.在一个单胞内分别对基体和散射体建立边界积分方程,在基体边界上施加Bloch条件,然后代入界面条件得到一个线性的特征值方程.通过对不同体系声子晶体能带结构的计算,并和其它方法的计算结果进行比较,说明边界元法可以有效准确地计算各向异性声子晶体的能带结构;而且,与各向同性体系相比,正交材料旋转角的变化对面外模态的能带结构有一定影响.     

基于边界元法的非完好界面三角晶格声子晶体带隙计算

采用边界元法研究了具有非完好界面条件的二维三角晶格声子晶体的带隙特性.结合Bloch周期原理,针对二组元三角晶格固-固体系声子晶体推导了含非完好界面条件的边界元特征值方程.基于该方程,计算了含有不同截面散射体(圆形截面、椭圆截面、正方截面)的能带结构,讨论了晶格对称性对能带结构的影响;并且分析了圆形截面散射体填充比的变化对带隙位置及宽度的影响.通过与其它计算方法的结果比较,说明边界元法可以有效准确地计算具有不同界面条件和不同散射体形状的声子晶体的能带结构.而且,非完好界面条件的声子晶体可以在低频打开完全带隙,尤其圆形截面最为明显.     

一种计算层状声子晶体弹性波带结构的无网格弱形式RBF方法

本文提出了一种基于紧致径向基函数(RBF)的无网格局部弱形式方法来计算层状声子晶体的能带结构.位移函数由一组径向基函数表示,利用变分原理,考虑周期边界条件,导出了单位单元RBF方法的一般形式.通过求解矩阵特征值问题可以得到能带结构.用有限元法对新的弱形式RBF方法进行了验证.对于不同的声阻抗比和长度比,通过数值算例进行讨论,显示所提出的弱形式RBF方法与有限元和强格式RBF方法相比计算层状声子晶体的能带结构的效率.     

布拉格型声子晶体弦的横向振动带隙研究

从弦的波动方程出发,采用传递矩阵法,分析了无限周期的布拉格型声子晶体弦的横向振动能带结构.研究表明布拉格型声子晶体弦具有横向振动带隙,弦内拉力对带隙特性有显著影响,可以方便地用于带隙调节.利用有限元软件和Matlab软件对有限周期的布拉格型声子晶体弦的横向振动传输特性分别进行了仿真和数值计算,结果表明带隙范围内表现出明显的振动衰减,不同拉力条件下的带隙变化也很好地验证了理论分析结果.     

二维声子晶体线缺陷聚声效应研究

基于数值方法研究了含线缺陷的二维声子晶体的聚声效应.利用结合超元胞技术的平面波展开法及有限元方法,分别对线缺陷二维声子晶体的能带结构及其内部声场分布规律进行了计算分析;以线缺陷轴线上声压梯度放大倍数表征聚声效果,分析了声子晶体结构参数对该放大倍数的影响规律.结果表明,填充率大、结构规模适当的二维线缺陷声子晶体具有更好的聚声效果;线缺陷的理想位置应在声子晶体的几何轴线上.此结果可为高效声能量回收器件的设计提供理论支持.     

基于有限元法与超胞法的结构声表面波缺陷态分析

简要介绍了有限元法与超胞法相结合计算结构声表面波缺陷能带结构的方法,理论上分析了缺陷型表面声子晶体的声限制和声波导.表面声子晶体由刻有周期性凹槽的刚性板构成,通过改变晶体中某一格点或某一排格点的几何参数可以构建点缺陷和线缺陷.利用有限元法与超胞法能够十分方便地计算出表面声子晶体的点缺陷和线缺陷对应的缺陷带结构以及特定频率声波局域在点缺陷与线缺陷的本征压力场.通过分析缺陷能带结构与本征压力场,可以直观地了解缺陷型表面声子晶体中的声限制和声波导.     

二维准分形结构声子晶体透射特性的数值研究

本文用时域有限差分方法研究了几种具有相似几何结构的准分形声子晶体的透射特性.计算了由水中钨柱组成的二维准分形结构声子晶体的ΓX和FM方向禁带,计算表明,对于钨柱分布在水背景中的情况,这种具有正方形点阵特点的准分形声子晶体存在多频带隙的特点,能带随级数的增大整体地趋向于低频部分.而且这种准分形声子晶体带隙的宽度及中心频率会随声子晶体单胞内结构单元几何形状的改变而改变.     

音叉型声子晶体能带结构研究

利用超元胞法研究音叉型散射体构成的声子晶体的声波带结构,分析音叉型散射体的几何参数(板的厚度,圆柱体的半径和高)对能带结构的影响.研究结果表明:这种新型的声子晶体比传统声子晶体具有更优的带隙,而且带隙的调节机制更为简单,结果还表明超元胞法是研究这一类声子晶体能带结构的一种有效方法.     

基于边界元法的三相声子晶体能带结构的计算

发展了计算二维三组元局域共振型声子晶体带隙结构的边界元法,该方法在一个单胞内分别对基体和含有包覆层的嵌入体(三相材料)建立边界积分方程,在基体边界上施加Bloch条件,并考虑不同相之间的界面条件后得到一个线性的特征值方程.该方法的计算结果和对应的二组元体系计算结果进行了比较,结果表明,在三相体系中声波发生局部共振,此时中间包覆层材料的作用类似于一个软弹簧;而且由于包覆层材料的密度很低且声速很小,所以对应的系统共振频率较低,使声带隙出现在较低频段.另外,本文还分析了“包覆层”材料的特性以及边界元法计算三组元声子晶体的特点.     

具有完全带隙的异质结构声子晶体的声波导特性

利用正方形和三角形结构声子晶体具有范围较大完全带隙的特性,设计了新型正方形晶格和三角形晶格构成的声子晶体异质结.采用平面波展开和超原胞相结合的方法研究了该异质结的能带结构特性.给出异质结的结构和相应的能带图,分析了异质结界面传导模,研究两侧结构作横向拉开和侧向滑移时对传导模的影响,讨论这些结构的实际可行性.计算结果表明,没有任何晶格移动,该结构异质结在完全带隙中就有传导模存在,界面两侧发生相对移动时,带隙内传导模的数量及位置都发生变化.     

Optical Properties of Cholesteric Liquid Crystals at Oblique Incidence

The optical properties of a periodic structure characterized by a uniform rotation of the dielectric tensor about a given axis are theoretically analyzed. The electromagnetic wave is described as a superposition of elementary modes having the form of Bloch waves. Each elementary mode is represented by a sum of plane waves elliptically polarized, whose wavevectors are the solutions of a characteristic equation. This equation, presented in a preceding paper, is furtherly analyzed, in order to obtain the wave vectors in terms of a power series of a small parameter δ, representing the anisotropy of the dielectric tensor. The coefficients of the series up to terms containing δ⁶ are explicitly given, and the corresponding truncation errors computed. The spectral composition and the polarization states of the Bloch waves are also analyzed and discussed for different values of the incidence angle in the frequency range containing the lower reflection bands. In particular it is shown that in the regions between the reflection bands both the wave functions and the wavevectors can be evaluated with very good approximation by simple analytic expressions, while for an accurate evaluation of the reflection properties of the structure more involved expressions are needed.     

Modeling of energy bands in ultra-thin layer quantum nanostructures for solar cell applications

In this paper we propose a simple calculation of the energy band in nano-structured meta-materials based on ultra-thin periodic Si/SiO₂ layers (quantum-well superlattice) for third-generation solar cell application. For this purpose, the Schrödinger equation (with periodic Bloch's conditions) is numerically solved considering the exact potential profiles of both the valence and conduction bands of the Si/SiO₂ system. This method allows us to analyze the carrier energy band structure and to extract the essential electronic properties (bandgaps, miniband widths) of such 1-D periodic nanostructures. The energy band structure and more particularly the meta-material bandgap is found to strongly depend on quantum well thickness and spacing.     

晶体结构控制晶体形态的理论及应用

本文对比分析了研究晶体宏观形貌与内部结构关系的3种主要理论,即布拉维法则、周期键链理论和负离子配位多面体生长基元理论.提出利用布拉维法则,结合晶胞形状及结构中螺旋轴、滑移面的影响,可以更准确地分析晶体的习性,并据此对晶体习性进行了分类.     

Generation of the structures of molecular crystals with two molecules related by the center of inversion in a primitive unit cell

An algorithm for the generation of possible crystal structures with two inversion-related molecules of known shape in a primitive unit cell is proposed within the method of discrete packing modeling in molecular crystals. The algorithm is based on the replacement of molecules by polycubes (geometric figures composed of identical cubes) and looking through a finite number of all the possible periodic packings of these polycubes with a given coefficient of packing. A program package for personal computers is developed on the basis of the proposed algorithm and is approved by the example of several crystal structures that were determined earlier by X-ray diffraction.     

Study on transmission characteristics in photonic crystals with negative effective index of refraction

Transmission spectra from equivalent negative refractive photonic crystals (PCs) composed of a triangular array of air cylinders in a GaAs matrix are studied by finite‐difference time‐domain method in the paper. Mechanism of wave resonance is probed and propagation of optical waves in the PCs is described in terms of effective refraction index and Bloch waves. Our numerical results show that probability of spontaneous radiation would be enhanced extremely under the influence of Bloch resonance waves, stimulated emission and photon tunnel effect, resulting in the optical waves localized greatly in the PCs at particular frequencies. In addition, we find out that the position of transmission peaks, with values far greater than unit, can be controlled by tuning the central frequency of waveguide source. It means that photon current in the PCs also can be controlled to optimize transmission properties of PCs, so as to meet the requirements of novel optical devices based on PCs. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generation of structures of molecular crystals with two molecules related by a twofold axis or a plane of symmetry in a primitive unit cell

Within the method of discrete modeling of packings, an algorithm of generation of possible structures of molecular crystals with two molecules of known shape in the primitive unit cell, related by a twofold (screw or rotary) axis or a plane of mirror or glide reflection symmetry, is proposed. The algorithm is based on the approximation of molecules by polycubes (geometric figures composed of identical cubes) and calculation of all possible periodic packings of these polycubes with a specified packing factor. On the basis of this algorithm, a software package for personal computers is developed. Examples of approval of this package for several crystal structures, identified previously by X-ray diffraction analysis, are reported.     

Classification of proton configurations of gas hydrate frameworks

All molecular configurations differing in the position of hydrogen atoms (protons) in hydrogen bonds and satisfying periodic boundary conditions have been calculated for the unit cells of CS-I, HS-III, and TS-IV gas hydrate frameworks. The configurations obtained are ranged according to the number of stronger trans-configurations of hydrogen-bound molecular pairs and according to the type of spatial symmetry. The configuration symmetry was analyzed taking into account the additional antisymmetry operation, which is related to the change in the direction of all hydrogen bonds. The strong dependence of the framework properties on the specific position of protons in H bonds is established.     

Selective optical properties of a multilayered periodic gyrotropic structure at an arbitrary angle of incidence of waves

A multilayered periodic gyrotropic structure consisting of an arbitrary number of unit cells is considered. The gyrotropic properties of this multilayered structure are due to the external magnetic field. A matrix is calculated on the basis of the boundary conditions for waves in each layer, which relates a wave incident at an arbitrary angle with the transmitted and reflected waves. The complex amplitude transmittance and reflectance are found for the entire multilayered structure from the calculated matrix elements. The optimal parameters of a structure consisting of layers of potassium dihydrogen phosphate and europium-doped glass are calculated. The dependences of the intensity, ellipticity, and the angle of rotation of the major axis of the polarization ellipse of reflected and transmitted waves on the number of cells, light frequency, and magnetic field at an arbitrary angle of incidence of waves are obtained in graphical form. The structure considered is characterized by selective reflection of electromagnetic waves and can be used as a polarization converter controlled by a magnetic field.     

A thermal model of periodic crystallization

A model of periodic crystallization is constructed on the basis of the wave equation of heat transfer with two energy sources exponentially dependent on temperature. In the problem of metal crystallization in a mold, these sources are competing. In the problem of explosive crystallization of amorphous films, the sources have the same sign. Both problems are analytically solved using the generalized separation of variables and the construction of finite-mode Galerkin approximations. The amplitude and period of oscillations of the phase boundary velocity are analyzed. Spatially periodic structures of the one-and two-dimensional thermal fields are constructed. It is found that the isotherm chains are arranged in a staggered manner. Other important regularities are revealed.     

On the effect of sublattice displacement in visualization of crystal structures

Electron-microscopy images of 〈001〉-GeNb₉O₂₅ obtained at the atomic resolution have been studied at the electron energy E = 80 keV. It is established that one of the sublattices on the image is displaced with respect to the other sublattices. The nature of this displacement is interpreted in terms of physics. The effect was studied in the formalism of Bloch waves. The important role of the valence Bloch state is also considered.