光腔模式及光束传输的特征向量算法

发展了一种新颖的适用于光腔模式及光束传输模拟计算的特征向量法.该方法的核心是基于菲涅耳-基尔霍夫衍射积分理论构造了一种新的光腔传输矩阵,通过求解激光谐振腔的本征积分方程,即可一次求解得到表征腔镜上多个光场模式振幅及相位分布的特征向量组;而谐振腔内或腔外任意地方的光场分布,也可采用该方法进行光束传输模拟而求得.对与该方法有关的单元划分、形函数选取、误差及稳定性分析等问题进行了论述,分析表明:合适的单元划分和形函数选取有利于提高计算速度、精度和稳定性.     

用傅里叶分析法研究艾里光束远场传播特性

为了从理论上深入分析新型无衍射光束艾里光束在有限能量条件下的远场传播特性,首先,从决定光波在自由空间传播的一维旁轴波动方程入手,采用傅里叶分析法,结合艾里函数的特殊性质,并利用经过指数衰减的有限能量初始条件,完整给出了有限能量条件下用于精确描述一维艾里光束在自由空间传播特性的波动方程解析解.然后,利用所得到解析解分别对一维和二维艾里光束在自由空间的传播特性进行了研究,重点分析了不同参量条件对艾里光束进行无衍射传播和横向自加速的影响.研究表明:当任意横向尺度为100μm,衰减系数为0.03、0.05、0.07、0.1、0.2时,二维艾里光束无衍射传播距离分别为1 014、624、455、338、193mm;当横向尺度保持不变时,衰减系数越小,艾里光束保持无衍射传播的距离越大;当衰减系数保持不变时,横向尺度越小,艾里光束横向自加速越大.所采用的研究方法也可用于研究艾里光束在介质中的传播特性.     

多动型变焦距物镜设计

变焦距光学系统在校正像差的同时还必须满足像面稳定的要求,补偿或消除由于光学系统中各组元的运动所造成的像相对接收器的偏移。利用动态光学稳像原理,推导变焦距光学系统的稳像方程,建立变焦距光学系统的数学模型,设计光学系统的凸轮曲线。给出了变焦距物镜的动态分析过程,利用光学设计软件CODE V最终得到了一个变倍倍率为8.15×,焦距范围为27 mm~220 mm的变焦距物镜,光学系统F#数为固定值4.2,视场为4.12°~33.56°。给出了凸轮曲线的计算方法及CODE V成像质量分析结果和MTF等。     

顶端ZnO纳米结构对GaN基LED光提取效率的影响

为了提高GaN基蓝光LED的光提取效率,本文建立了LED顶面分别铺设ZnO纳米柱和纳米锥结构的两种模型,利用时域有限差分法对两种模型进行仿真并对结果进行了比较.仿真结果表明,ZnO纳米结构的各项几何结构参量(包括排列周期P、高度L、宽度W以及斜率k等),对LED顶端光提取效率影响显著.仿真分别得到了两种结构的最佳模型,通过比较,LED顶面纳米柱和纳米锥结构对光提取效率的提高效果相近,其最佳提取效率分别增强至无任何结构时的2.5倍和2.3倍.同时,通过对各项参量扫描获得的对光提取效率的变化曲线进行了分析,并给出了相应相应的理论解释.这些模型优化和理论分析对实际的高性能GaN基LED的设计制造有着指导意义.     

The Fifth Order Peregrine Breather and Its Eight-Parameter Deformations Solutions of the NLS Equation

We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real parameters. This gives new families of quasi-rational solutions of the NLS equation and thus one can describe in a more precise way the phenomena of appearance of multi rogue waves. With this method, we construct new patterns of different types of rogue waves. We get at the same time, the triangular configurations as well as rings isolated. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.     

Derivation of baroclinic Ertel–Rossby invariant-based thermally-coupled vorticity equation in moist flow

For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant （ERI）, is there a corresponding vorticity tendency equation？ Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors＇ influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.     

Relativistic symmetries of Deng Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interactions

Relativistic symmetries of the Dirac equation under spin and pseudo-spin symmetries are investigated and a combina- tion of Deng-Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interaction terms are considered. The energy equation is obtained by using the Nikiforov-Uvarov method and the corresponding wave functions are expressed in terms of the hypergeometric functions. The effects of the Coulomb and Yukawa tensor interactions are numerically discussed as well.     

Polarization and Angular Distribution of Ll X-Ray Following Inner-Shell 2p3/2 Photoionization of Magnesium-Like Ions

The inner-shell 2pa/2 photoionization and the subsequent decay of Mg-like Fe^14＋, Cd^36＋, W^62＋ and U^80＋ ions are studied theoretically within the multiconfiguration Dirac-Fock method and the density matrix theory. Special attention is paid to exploring the influence of the non-dipole terms which arise from the multipole expansion of the electron-photon interaction in the photoionization process. The results show that the non-dipole contribution to the total cross section, the magnetic sublevels cross section of the photoionization process, the degree of linear polarization and angular distribution of the subsequent characteristic x-ray radiation become more important with the increase of photons energy and atomic nuclear Z. Especially for the cross section and the degree of linear polarization, the non-dipole contribution arrives at 50% for U^80＋ at four time energy threshold units. However, for the angular distribution, the maximum contribution does not exceed 4%, even for U^80＋ ions.     

核类似铜酸盐超导模型的su_s(1,1)su_d(1,1)代数结构

由Iachello提出的核类似铜酸盐超导模型具有su(3)代数结构,其平均场近似下的Hamilton量可以写成su(3)生成元的线性组合.通过代数生成元的实现,该模型约化的Hamilton量具有Su_s(1,1)SU_d(1,1)代数结构,利用相干算子U(θ,φ)的幺正变换,可得到系统约化Hamilton量的能隙方程及本征值,发现应用不同代数结构求解会得到不同侧重点的分析结果.     

基于分数阶傅立叶变换的线性调频回波参数估计

本文提出了一种适用于宽带线性调频回波的分数阶傅立叶变换参数估计方法。它通过寻找合适的信号代替发射信号做模版,使得模版信号与接收信号的模糊函数匹配度高,峰值尖锐,失真率低。再利用分数阶傅立叶变换与模糊函数的关系,使用两次分数阶域的峰值搜索代替原有的一次二维搜索降低计算量。仿真实验结果表明,本文提出的方法在精确估计宽带回波的时延和频移的同时降低了计算复杂度。