斐波那契序列与准晶态

本文从兔子繁殖的数学问题谈起,引入Fibonacci数列.研究了晶体的准周期结构,表明它与Fibonacci数列有密切的关系.     

自相位调制及群速色散对超短脉冲在准周期LiNbO3 Fibonacci超晶格中传输的影响

从LiNbO₃ Fibonacci超晶格的结构特点出发,数值模拟了超短脉冲在LiNbO₃ Fibonacci超晶格内传输过程中,自相位调制及高阶群速色散效应对脉冲形状和频谱的影响．结果表明,超短脉冲在Fibonacci超晶格中传输时,由于自相位调制(SPM)与群速色散(GVD)耦合效应的影响,脉冲形状畸变和频谱展宽均是不对称的,随着晶格长度的增加,脉冲将会发生分裂,以至成为两个独立的子脉冲,同时也会出现脉冲频谱上的分裂. 关键词：     

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     

二维周期结构基本方程及其数值算例

在矢量衍射理论基础上导出了任意倾斜入射下二维周期结构的衍射方程和求解(m,n)级衍射波方向即衍射角和衍射方位角的公式,理论分析了这些表达式中包含的二维周期结构衍射级次(m,n)的限制条件,并给出了相应的数值算例结果表明,矢量衍射理论在光栅基本表达式的推导方面有独特优势.     

一维压电Fibonacci类准周期声子晶体传输特性

基于传输矩阵法研究了一维压电Fibonacci类准周期声子晶体的传输特性, 比较了一维Fibonacci序列压电准周期声子晶体与非压电准周期声子晶体以及压电周期性声子晶体的透射性. 计算结果表明:弹性波通过一维准周期结构压电声子晶体时与周期性声子晶体一样会有带隙的出现, 且发现具有压电性的Fibonacci序列准周期声子晶体禁带宽度发生了展宽. 进一步讨论了入射角度对固定频率下声子透射系数的影响,结果表明一维压电Fibonacci序列准周期结构声子透射性依赖于入射角度的选取.     

二维光栅光调制器阵列的光学分析与实验

基于标量衍射理论分析了二维光栅光调制器的衍射特性,提出了投影系统的光学处理方法,利用Matlab软件进行了仿真分析.分析结果表明,二维光栅光调制器的衍射光强分布是单个像素衍射光强的干涉叠加,其分布趋势与单个光调制器的衍射光强分布类似;通过反傅里叶变换可将各个调制器的衍射光重新分开而成像.如果用±1级衍射光的成像,相位为2kπ的调制器在投影面得到一个明亮的像,而相位为(2k-1)π的调制器在投影像面上得到一个黑暗的像.通过一个基于静态微光电系统光栅光调制器的投影光学系统得到了一幅明暗调制的像,证明了光栅光调制器用于投影显示的可行性.     

一种适用于非周期结构高分辨象模拟计算的新方法

通常的FFT多片层法(FFTMS)动力学衍射计算中,由于采用了边界采样点周期性延伸的假设,从而导致非周期结构高分辨象模拟的严重失真。在仔细研究这种误差成因的基础上,本文提出了一种适用于非周期结构的高分辨象模拟计算新方法,它基于实空间多片层(RSMS)象模拟计算方法,但在势投影及传播因数计算中充分考虑了非周期结构的特点,从而得到与实验符合较好的结果。 关键词：     

基于超晶格结构衍射图的倒易矢量分布

根据超晶格结构的激光衍射图,提出了一种定量确定倒易矢量分布的实验方法.首先,将正方形周期超晶格结构作为参考光栅,得到其衍射图.根据傅里叶光学理论,计算出基本倒易矢量的大小,与衍射图上的几何长度建立标尺关系.通过引入矩形超晶格结构,证明了该方法在周期超晶格结构中的可行性.其次,将H型和谢尔宾斯基分形超晶格结构作为光栅,获得的衍射图与正方形结构衍射图进行对比.由衍射点间的几何长度比值,推算出分形衍射图中的倒易矢量分布.根据倒易矢量和准相位匹配谐频的基频波长之间的定量关系,理论计算出能够进行的谐频波长.最后,实验制备分形结构LiNbO3非线性光子晶体,探测准相位匹配倍频,所实现的倍频波长与理论计算值相吻合.谢尔宾斯基分形结构光栅在理论与实验上均可实现1.352μm的有效倍频输出.     

带电粒子束的等时周期场聚焦

在质子直线加速器中经常利用等时周期场对粒子束进行聚焦. 这种周期场的特点是周期长度不等而粒子经过每一周期的时间为常数,本文讨论等时周期场聚焦的基本理论,并将它推广到周期长度缓慢变化的周期场.     

一维Fibonacci系列的X射线衍射峰轮廓的计算

用简单原子层的Fibonacci系列模型,根据振幅-相位关系,计算了其X射线衍射图谱,衍射峰位置在k=2π((m+nτ)/(1+2τ))d^-1,d为平均面间距。衍射峰角宽度β与原子层总厚度D仍满足Scherrer公式:β=0.88λ/Dcosθ。并用振幅-相位图解释了弱衍射峰的强度随原子层数增大时产生起伏的现象。 关键词：     

Average unit cell approach to diffraction analysis of some aperiodic structures — decorated fibonacci chain

The average unit cell approach has been successfully used to construct the probability distributions of atomic distances from the reference lattice points and to calculate the diffraction patterns for decorated Fibonacci chains with non-Fibonacci type of decoration. General method able to distinguish between various quasilattice decorations has been elaborated and tested for decorated Fibonacci chains. Financial support from the Polish Committee for Sci. Research under grant No. 2 P03B 041 16 is acknowledged. Presented at the DI-CRM Workshop held in Prague, 18–21 June 2000.     

Diffraction properties of one-dimensional finite size fibonacci quasilattice

The diffraction patterns from Fibonacci quasilattices have been calculated. Finite-size effects are evaluated for weak and strong peaks. For a smaller number of scatterers (<100) there are fluctuations in the intensities of weak and strong peaks. The fluctuations in weak peaks are greater than that in strong peaks. The fluctuations in intensities of weak and strong peaks near the origin are larger than in the corresponding cases of weak and strong peaks far away from the origin. Small shifts in peak-positions are unexpectedly found, the shifts being proportional toN ^−3/2 for a large number of scatterers. The diffraction pattern of a one-dimensional crystal and random structure is compared with that of the Fibonacci quasilattice. The strong peaks observed in the diffraction pattern of 1-d crystal show negligible peak-shifts, they being comparable with computational errors even when the number of scatterers is as small as 5. The implications for analysing the experiments are briefly indicated.     

Grating light modulator for projection display

A novel grating light modulator for projection display is introduced. It consists of an upper moveable grating, a bottom mirror, and four supporting posts between them. The moveable grating and the bottom mirror compose a phase grating whose phase difference is controlled by the actuating voltage. When the phase difference is 2kπ, the grating light modulator will switch the incident light to zero-order diffraction; when the phase difference is （2k - 1）π, the grating light modulator will diffract light to first-order diffraction. A 16 × 16 modulator array is fabricated by the surface micromachining technology. The device works well when it is actuated by a voltage with 1-kHz frequency and 10-V amplitude. The fabricated grating light modulator can show blackness and brightness when controlled by the voltage. This modulator has potential applications in projection display system.     

Bandgap structure of optical Fibonacci lattices after light diffraction

The modification of the bandgap structure of optical Fibonacci lattices that arises from an increase in the system size is analyzed. It is found that there is a minimum critical size of the Fibonacci lattice necessary to form a photonic bandgap. The analysis of localized photonic modes of Fibonacci lattices shows that the removal of two layers of a lattice makes the lattice mirror-symmetric. The “method of oblique bands” is developed to analyze the bandgap structure of quasi-crystals. This method can also be applied to study two-and three-dimensional photonic and atomic quasi-crystals.     

二维Fibonacci准晶电子能谱

基于重整化群技术,我们用分解-消元方法研究二维Fibonacci准晶电子能谱性质,得到了具有多种分支结构的能谱,这与一维Fibonacci的单一分支结构完全不同。同时,利用晶格的四重旋转对称性将哈密顿量化简,然后进行数值模拟计算,计算结果与分析结果完全一致。 关键词：     

Omnidirectional Single-negative Gap and in Fibonacci Sequences Composed of Single-negative Materials

The band structures of Fibonacci sequence composed of single-negative materials are studied with a transfer matrix method. A new type of omnidirectional single-negative gaps is found in the Fibonacci sequence. In contrast to the Bragg gaps, such an omnidirectional single-negative gap is insensitive to the incident angles and polarization, and is invariant upon the change of the ratio of the thicknesses of two media. It is found that omnidirectional single-negative gap exists in the other Fibonacci sequence, and it is rather stable and independence of the structure sequence.     

Spectral analysis of a family of binary inflation rules

The family of primitive binary substitutions defined by \(1 \mapsto 0 \mapsto 0 1^m\) with \(m\in \mathbb {N}\) is investigated. The spectral type of the corresponding diffraction measure is analysed for its geometric realisation with prototiles (intervals) of natural length. Apart from the well-known Fibonacci inflation (\(m=1\)), the inflation rules either have integer inflation factors, but non-constant length, or are of non-Pisot type. We show that all of them have singular diffraction, either of pure point type or essentially singular continuous.     

Fibonacci quasi-periodic superstructure fiber Bragg gratings

Superstructure fiber Bragg gratings constructed following the Fibonacci sequence are proposed and simulated by using the transfer matrix method. The reflection spectrum has a multi-fractal structure as a function of the wavelength and is symmetric to the center. The reflectivity has self-similarity and scaling with respect to the Fibonacci sequence order at the central wavelength. For the transmission spectrum, the interaction of the core-cladding mode is investigated and the particular wavelengths for which the resonance condition is satisfied are located by varying the grating parameters. The potential application of the quasi-periodic structure as fiber sensors is also proposed.