一种可用于分析任意介电常数张量的各向异性波导导模的二维时域有限差分模型

为分析具有任意介电常数张量的各向异性波导的导模，本文通过把简化的二维时域有限差分（２－ＤＦＤＴＤ）法扩展至任意各向异性介质，提出了一种以Ｄ、Ｅ和Ｈ场为基础的统一的简化２－ＤＦＤＴＤ模型．利用该模型，研究了简化的复数２－ＤＦＤＴＤ方法与实变数２－ＤＦＤＴＤ方法之间的关系．文中还讨论了复变数方法和实变数方法的激励技术．     

应变Ge/Si1-xGex 价带色散模型

基于k·p微扰理论, 通过引入应变哈密顿量作为微扰, 建立了双轴应变Ge/Si_1-xGe_x价带色散关系模型. 模型适于任意晶向弛豫Si_1-xGe_x虚衬底上的应变Ge价带结构, 通过该模型可获得任意k方向应变Ge的价带结构和空穴有效质量. 模型的Matlab模拟结果显示, 应变Ge/Si_1-xGe_x价带带边空穴有效质量随Ge组分的增加而减小, 其各向异性比弛豫Ge更加显著. 本文研究成果对Si基应变Ge MOS器件及集成电路的沟道应力与晶向的设计有参考价值.     

双模腔场中具有不同耦合常数的两原子多光子辐射谱

研究了与双模腔场具有不同耦合常数的两个二能级原子的多光子辐射谱,给出了双模多光子辐射谱的一般表达式.结果表明,当双模腔场分别处于不同数态时,虽然两原子与双模腔场之间具有不同的耦合常数,但对于任意的N₁和N₂(N_i(i＝1,2,)为模i腔场被每个原子吸收或发射的光子数),辐射谱总是关于共振频率ω₀对称分布;并且,当N₁＝N₂时,对于任意的数态光子数n₁和n₂交换,辐射谱不变.上述特点用解析方法给予了解释.计算了非简并双光子情况下的辐射谱,并得到了一些新结果.双模腔场中单原子及具有相同耦合常数的两原子辐射谱可从本文结果分别做为特例而得到.     

垂直场下磁性薄膜中的铁磁共振现象

将铁磁共振频率看成外磁场的函数, 讨论了垂直场下磁性膜中的铁磁共振现象. 结果显示: 当外磁场平行于膜面, 并考虑磁膜具有垂直磁晶各向异性情形时, 其磁共振频率随外磁场的变化分为高频支和低频支两种情况, 具体的依赖关系取决于磁膜内磁晶的各向异性; 当外磁场垂直于膜面, 其磁共振频率随外磁场的关系仅存在一支, 一般地, 磁共振频率随外磁场的增加单调地非线性减小, 但当立方磁晶各向异性场H_k1 与单轴磁晶各向异性场H_a之比值介于2/3 < H_k1/H_a <1时, 其磁共振频率随外磁场的增加单调增加, 这与相关的实验结果一致. 研究结果表明: 磁薄膜中有无垂直于膜面的磁各向异性可以通过其磁共振谱的测量进行辨析.     

多模虚共轭相干态与多模真空态的叠加态光场的等阶N次方Y压缩

利用多模压缩态理论,研究了多模虚共轭相干态|{iZ_j^*}〉q与多模真空态|{O_j}〉q的叠加态|{Ψ_p⁽²⁾}〉q的广义非线性等阶N次方Y压缩特性.结果发现态|{Ψ_p⁽²⁾}〉q是一种典型的多模非经典光场,它在一定的条件下,可呈现出周期性变化的、任意奇数阶和任意偶数阶的等阶N次方Y压缩效应,而在另外的条件下,则可呈现出等阶N次方Y相似压缩现象.     

强场中NO分子回归谱的长程散射矩阵的理论研究

采用半经典散射矩阵方法研究外磁场中高里德伯态双原子分子在能量范围为77010—77050cm^-1的回归谱.通过引进模型势简化强磁场中NO分子的高里德伯电子的势函数,找出其在核转动量子数分别为N=1,3,5的三个通道中的闭合轨道,重点分析了强磁场中NO分子的长程散射矩阵元实部的傅里叶变换谱与闭合轨道之间的一一对应关系.     

Hulthén势散射态的解析解

在任意l波的离心项1/r²用λ²e^-λr/(1-e^-λr)²近似表达的条件下,对Hulthén势的径向Schrdinger方程作自变量指数变换,使此转化为超几何微分方程,获得了Hulthén势s波散射态的精确解和非s波散射态的近似解析解.给出了相移的解析表达式和按“k/2π标度”归一化的用超几何函数表示的径向波函数.讨论了解析解的意义.     

分子一阶超极化率溶剂效应的理论研究

基于一维谐振子模型建立了极性溶剂对光学二阶非线性分子一阶超极化率产生影响的简化理论模型,推导出了非线性分子的线性极化率α和一阶超极化率β的表达式. 以对硝基苯胺为例,所建立的理论模型计算结果较好地解释了实验获得的溶剂极性对其分子线性吸收峰波长（λ_p）和β值的影响.     

量子Generalized Reed-Solomon码

构造出了一族量子纠错码，这族码具有参数［［n，n-2k，k+1］］_q，是q维量子系统上的码，q是任意素数的幂.这族码的最小距离达到了理论上限，因此，以码距来说，它是最优的.证明了当2≤n≤q或者q²-q+2≤n≤q²时，码都是存在的.     

基于交叉增益调制效应全光波长变换中半导体光放大器增益与变换光脉冲啁啾分析

对于半导体放大器(SOA),由于连续光注入其有效增益降低,本文提出基于SOA交叉增益调制效应(XGM)全光波长变换(AOWC)简化的系统模型,应用此模型详细分析了信号光功率(P_s)、信号光脉宽(t_p)、泵浦电流和探测光功率(P_cw)对于变换光啁啾的影响.     

A Feynman-Kac formula for the quantum Heisenberg ferromagnet. I

The Hamiltonian of the (anisotropic) quantum Heisenberg (anti-) ferromagnet on an arbitrary finite lattice is lifted to a Hamiltonian acting on sections of the bundle obtained by twisting a certain line bundle over the classical spin configuration space (which is a Kähler manifold) with the Dolbeault complex. This procedure is extended fromSU(2) to arbitrary compact semi-simple Lie groups and arbitrary irreducible representations. The Bott-Borel-Weil theorem gives a heat kernel representation for the original partition function in an external magnetic field. TheU(1)-gauged local Hamiltonian is the sum of the free, supersymmetric, twisted Dolbeault Laplace operator (multiplied by the inverse of an arbitrary small mass parameter) plus the lifted Hamiltonian.The resulting (Euclidean) Lagrangian is nonlocal and describes bosons which do and fermions which do not propagate through the lattice. All fields couple to the external magnetic field. The Lagrangian contains Yukawa and Luttinger type interactions.     

Split-step finite-difference time-domain method with perfectly matched layers for efficient analysis of two-dimensional photonic crystals with anisotropic media

This Letter presents a split-step (SS) finite-difference time-domain (FDTD) method for the efficient analysis of two-dimensional (2-D) photonic crystals (PhCs) with anisotropic media. The proposed SS FDTD method is formulated with perfectly matched layer boundary conditions and caters for inhomogeneous anisotropic media. Furthermore, the proposed method is derived using the efficient SS1 splitting formulas with simpler right-hand sides that are more efficient and easier to implement. A 2-D PhC cavity with anisotropic media is used as an example to validate the efficiency of the proposed method.     

Upper Bound on the Density of Ruelle Resonances for Anosov Flows

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (−i)V, called Ruelle resonances, close to the real axis and for large real parts.     

Prediction of photonic crystal fiber characteristics by Neuro–Fuzzy system

The most common methods applied in the analysis of photonic crystal fibers (PCFs) are finite difference time/frequency domain (FDTD/FDFD) method and finite element method (FEM). These methods are very general and reliable (well tested). They describe arbitrary structure but are numerically intensive and require detailed treatment of boundaries and complex definition of calculation mesh. So these conventional models that simulate the photonic response of PCFs are computationally expensive and time consuming. Therefore, a practical design process with trial and error cannot be done in a reasonable amount of time. In this article, an artificial intelligence method such as Neuro–Fuzzy system is used to establish a model that can predict the properties of PCFs. Simulation results show that this model is remarkably effective in predicting the properties of PCF such as dispersion, dispersion slope and loss over the C communication band.     

二维各向异性磁等离子体的无条件稳定ADE-CNAD-FDTD算法

针对二维各向异性磁等离子体提出一种有效的无条件稳定算法,新算法结合了辅助微分方程(ADE)方法与Crank-Nicolson approximate-decoupling(CNAD)时域有限差分算法仿真各向异性磁等离子体介质。传统的ADE-FDTD方法应用在一维各向异性色散介质具有较高的精度和效率,将提出的新算法ADE-CNAD-FDTD应用到二维各向异性磁等离子体介质中不仅解决了电磁波在具有各向异性和频率色散特性介质中传播的仿真难题,而且去除了CFL稳定性条件。该算法在保留了原有的精度情况下大幅度地提高了计算效率并成为无条件稳定的形式。给出一个算例证明该算法的有效性,通过模拟电磁波在磁等离子体中的传播,仿真结果与传统的ADE-FDTD算法对比,证实了该算法的高效率、无条件稳定性和高精度。     

Finite-Dimensional PT-Symmetric Hamiltonians

This paper investigates finite-dimensional PT-symmetric Hamiltonians. It is shown here that there are two ways to extend real symmetric Hamiltonians into the complex domain: (i) The usual approach is to generalize such Hamiltonians to include complex Hermitian Hamiltonians. (ii) Alternatively, one can generalize real symmetric Hamiltonians to include complex PT-symmetric Hamiltonians. In the first approach the spectrum remains real, while in the second approach the spectrum remains real if the PT symmetry is not broken. Both generalizations give a consistent theory of quantum mechanics, but if D>2, a D-dimensional Hermitian matrix Hamiltonian has more arbitrary parameters than a D-dimensional PT-symmetric matrix Hamiltonian.     

一种色散介质FDTD通用吸收边界

由单轴各向异性介质所满足的场方程出发,并根据相位匹配原理以得到介质中的色散关系和无反射条件.结合频域到时域的转换关系（即用/t代替jω）和移位算子时域有限差分（SO-FDTD）方法提出了一种适用于各向同性常见色散介质模型,包括德拜模型、洛伦兹模型、德鲁德模型等的通用UPML吸收边界.数值结果表明了该算法的通用性和高效性. 关键词： 时域有限差分 吸收边界 移位算子 色散介质     

An FDTD absorbing boundary condition for anisotropic media based on NPML

Based on the nearly perfectly matched layer (NPML) theory, a finite-difference time-domain (FDTD) absorbing boundary condition (ABC) is presented for truncating three-dimensional (3-D) anisotropic medium. In the proposed technique, the complex coordinate stretching in the NPML scheme and the spatial interpolation method are employed. The associated ABC formulations have the advantage of simplicity in the FDTD implementations. The radiation fields of an electric dipole in anisotropic media are calculated using the presented ABC. The results are numerically verified by the comparison with the reference solutions. Furthermore, in order to clearly show the effective absorbing performance of the proposed method, the reflection coefficient and time-dependent relative error for different layers NPML absorbing boundary are also simulated.     

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on Ġ may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.