广义Fibonacci准周期结构声子晶体透射性质的研究

提出了一维广义Fibonacci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数值计算,并与周期结构和标准Fibonacci准周期结构声子晶体的透射系数进行比较. 结果表明,利用一维广义Fibonacci准周期结构的声子晶体可获得比周期结构和标准Fibonacci准周期结构声子晶体更大的带隙范围,同时在带隙内有更丰富的局域模式存在. 对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： 广义Fibonacci准周期结构 声子晶体 局域化     

弹性波通过一维复合材料系统的透射性质

提出了不同结构的一维弹性波复合材料系统模型,包括一维周期结构声子晶体、标准Fibonacci准周期结构声子晶体、广义Fibonacci准周期结构声子晶体以及完全无序结构的复合材料系统. 采用模式匹配理论法,数值计算了弹性波通过一维复合材料系统的透射系数. 计算结果表明,利用特殊的准周期结构声子晶体可获得比周期结构声子晶体更宽的带隙范围,准周期结构排列的复合材料系统相当于在周期结构中引入了缺陷体一样,带隙内出现了丰富的局域模式. 对弹性波/声波在复合材料系统中局域态性质的研究有助于弹性波/声波滤波器、导波器 关键词： 弹性波复合材料 局域化     

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     

太赫兹波在一维反铁磁/电介质准周期光子晶体的传输性质

本文利用传递矩阵方法研究了电磁波倾斜入射时,一维反铁磁/电介质准周期光子晶体的透射性质.反铁磁层和电介质层按Fibonacci数列排列构成准周期光子晶体.通过数值模拟发现光子禁带中有透射峰出现, 而且随着准周期光子晶体级数的增加透射峰的数目也在增加.此外,透射峰受电介质层的介电常数、入射角度和电磁波偏振影响明显. 关键词： 反铁磁层 准周期光子晶体 太赫兹波传输性质     

正方点阵上Fibonacci超元胞声子晶体的带结构

用平面波展开方法研究了水柱体作为填充物, 按照二维Fibonacci排列成超元胞填充在Hg基体中构成的声子晶体的声频带结构. 结果发现, 随着超元胞中准晶格常数的变化, 各个能带均出现三分裂. 对声场分布的研究发现了居间态的存在. 这些现象体现了准周期结构的特征. 关键词： Fibonacci排列 声子晶体 能带结构     

二维8重固-流型准周期声子晶体带隙特性研究

针对二维8重固-流型(钢-水)准周期声子晶体,通过实验方法测试得到了不同大小准周期系统的透射谱,并利用有限元方法计算了准周期体系的频散曲线和透射谱.结果显示,实验与有限元方法所得透射谱结果基本符合,但有限元方法得到的透射谱显示的带隙特性更为明显;二维固-流型8重准周期声子晶体选用包含其中心拼图在内的最小超元胞可以近似计算整个准周期结构的频带结构.     

新型二维压电声子晶体板带隙可调性研究

设计了一种由涂有硬质材料涂层的柱状压电散射体周期性连接在四个环氧树脂薄板上构成的具有大带宽的新型二维压电声子晶体板,并利用有限元方法计算了该声子晶体板的能带结构、传输损失谱和位移矢量场.研究表明：与二组元材料构成的传统声子晶体板相比,新设计的声子晶体板的第一完全带隙频率更低,并且带宽扩大了5倍;通过在压电体表面上施加不同的电边界条件,可以实现多条完全带隙的主动调控;压电效应对能带结构有很大的影响,并且有利于完全带隙的扩大与形成.基于带隙的可调谐性,分析了可切换路径的压电声子晶体板波导,结果表明可以通过改变电边界条件来限制弹性波能量流.     

Fibonacci序列的统计属性和电子输运系数

对按膨胀规律A→AB和B→A生成的Fibonacci序列,采用一维随机行走模型数值计算了序列的自相关函数以及自行定义的准标准偏差.利用Hurst分析法研究了序列的再标度范围函数及其Hurst指数,并将结果与一维随机二元序列进行了对比.发现这些统计量有奇特的准周期振荡行为以及小于05的Hurst指数,直接论证了Fibonacci序列具有关联、标度不变及自相似等性质.从Anderson紧束缚模型出发,采用传输矩阵方法研究了Fibonacci序列的电子输运特性,讨论了输运系数对能量及其序列长度的依赖关系.研究 关键词： Fibonacci序列 统计属性 电子输运系数     

广义Fibonacci时间准周期量子行走波包扩散的动力学特性

本文通过数值计算的方法研究了一维离散时间准周期量子行走的动力学特性,主要研究了两个自旋空间C算符按照广义Fibonacci准周期排列的量子行走,发现对两类广义Fibonacci准周期序列,波包扩散都是超扩散(即标准方差σ约为t~γ,0.5γ1),而且在给定的两个C算符下,第二类广义Fibonacci准周期序列的幂指数γ大于第一类广义Fibonacci准周期序列.通过对波包扩散的概率分布情形和标准方差的研究发现,第一类广义Fibonacci准周期序列的波包扩散更接近于经典随机行走(γ=0.5),而第二类广义Fibonacci准周期序列的波包扩散更接近于均匀量子行走(γ=1),这与两类广义Fibonacci准周期量子自旋链中量子相变时的特性相反.     

基于Fibonacci序列准周期结构的小角度低通空间滤波器

利用常规材料构造了Fibonacci序列准周期结构,运用传输矩阵法研究了该结构的空间传输特性,并基于该结构优良的空间传输特性设计了小角度低通空间滤波器.数值模拟结果表明,该小角度空间滤波器的角域带宽可通过改变序列的结构类型和序列数来调谐,其调谐规律为:随着Fibonacci序列F(m,1)中m值的增加,对应空间滤波器的角域带宽减小;随着序列数的增大,对应角域带宽也减小.在调谐的基础上,还可通过改变构成准周期结构的介质折射率参量来精确调节其角域带宽.相比于基于超材料的小角度空间滤波器而言,基于Fibonacci序列的小角度空间滤波器制备更简单,且有望应用于新一代的高功率激光系统中.     

弹性波斜入射声子晶体的缺陷模及其转型

推导出弹性波斜入射固-固掺杂结构声子晶体的转移矩阵和透射系数公式.计算固-固掺杂结构声子晶体中弹性波的透射系数.得到当横波斜入射时,透射波中横波的缺陷模随着入射角的增大而减弱,横波向纵波的转型随着入射角的增大而增强.当纵波斜入射时,透射波中纵波的缺陷模随着入射角的增大而减弱,纵波向横波的转型随着入射角的增大而增强.     

Transmission properties of Fibonacci quasi-periodic one-dimensional photonic crystals containing indefinite metamaterials

The transmission properties of Fibonacci quasi-periodic one-dimensional photonic crystals (1DPCs) containing indefinite metamaterials are theoretically studied. It is found that 1DPCs can possess an omnidirectional zero average index (zero-n?) gap which exists in all Fibonacci sequences. In contrast to Bragg gaps, such zero-n? gap is less sensitive to the incidence angle, the scale length and the polarizations of electromagnetic waves. When an impurity is introduced, a defect mode appears inside the zero-n? gap with a very weak dependence on the incidence angle and scaling.     

Edge apodization of crystal-like structures

It is suggested that the selectivity of crystal-like structures (semiconductor superlattices, photonic crystals, and phononic crystals) be raised by apodization of their edges. The transmission and reflection coefficients illustrating the efficiency of this approach are presented.     

Band structures of Fibonacci phononic quasicrystals

The paper studies the band structures of a two-component Fibonacci phononic quasicrystal which is considered as a phononic crystal disordered in a special way. Oblique propagation in an arbitrary direction of the in-plane elastic waves with coupling of longitudinal and transverse modes is considered. The transfer matrix method is used and the well-defined localization factors which are used to study the ordered and disordered phononic crystals are introduced to describe the band gaps of the phononic quasicrystals. The transmission coefficients are also calculated and the results show the same behaviours as the localization factor does. The results show the merits of using the localization factors. The band gaps of the phononic quasicrystal and crystals with translational and/or mirror symmetries are presented and compared to the perfect phononic crystals. More band structures are exhibited when symmetries are introduced to the phononic quasicrystals.     

Elastic wave localization in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity

The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor, which is calculated by the plane-wave-based transfer-matrix method. By treating the random disorder and aperiodicity as the deviation from the periodicity in a special way, three kinds of aperiodic phononic crystals that have normally distributed random disorder, Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered and the band structures are characterized using localization factors. Besides, as a special case, we analyze the band gap properties of a periodic planar layered composite containing a periodic array of square inclusions. The transmission coefficients based on eigen-mode matching theory are also calculated and the results show the same behaviors as the localization factor does. In the case of random disorders, the localization degree of the normally distributed random disorder is larger than that of the uniformly distributed random disorder although the eigenstates are both localized no matter what types of random disorders, whereas, for the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with the quasi-periodic (Fibonacci) sequence not present in the results of the Rudin-Shapiro sequence.     

Wave localization in two-dimensional porous phononic crystals with one-dimensional aperiodicity

The localization properties of in-plane elastic waves propagating in two-dimensional porous phononic crystals with one-dimensional aperiodicity are initially analyzed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method in this paper. The band structures characterized by using localization factors are calculated for different phononic crystals by altering matrix material properties and geometric structure parameters. Numerical results show that the effect of matrix material properties on wave localization can be ignored, while the effect of geometric structure parameters is obvious. For comparison, the periodic porous system and Fibonacci system with rigid inclusion are also analyzed. It is found that the band gaps are easily formed in aperiodic porous system, but hard for periodic porous system. Moreover, compared with aperiodic system with rigid inclusion, the wider low-frequency band gaps appear in the aperiodic porous system.