几何光学传递函数及其计算方法

本文借助Bessel函数、数值积分和样条函数插值给出几何光学传递函数的数值计算方法,这种方法有益于保证精度和节省计算量。     

修正的莫比乌斯反演公式在晶体对势计算中的应用

将陈-莫比乌斯公式作了进一步推广。用修正的莫比乌斯反演公式解决了Ewald求和的反问题——由晶体中原子所受的总势求得原子间的对势。对几种典型晶体结构,提出了基于迭代法的算法及相应的存储结构。分析了算法的稳定性及误差,并进行了试算。 关键词：     

计算凹面闪耀光栅衍射效率的通用方法

为使凹面光栅的衍射能量更多地集中在所需要的级次上,提出了利用机械刻划的方法在凹面基底上制作变刻槽角度的凹面闪耀光栅,并利用菲涅耳-基尔霍夫衍射公式推导了同时在主截面和非主截面内计算凹面闪耀光栅衍射效率的理论方法,弥补了以往只在主截面内考虑衍射效率的不足,最后利用Matlab仿真软件模拟了衍射效率随波长的变化曲线,并对比了在不同制作和使用参数下衍射效率峰值的变化规律,为今后凹面光栅的设计和制作提供了参考价值。     

New approach to Q-P （P-Q） ordering of quantum mechanical operators and its applications

In this paper, we introduce a new way to obtain the Q-P （P-Q） ordering of quantum mechanical operators, i.e., from the classical correspondence of Q-P （P-Q） ordered operators by replacing q and p with coordinate and momentum operators, respectively. Some operator identities are derived concisely. As for its applications, the single （two-） mode squeezed operators and Fresnel operator are examined. It is shown that the classical correspondence of Fresnel operator’s Q-P （P-Q） ordering is just the integration kernel of Fresnel transformation. In addition, a new photo-counting formula is constructed by the Q-P ordering of operators.     

Cubature Kalman filters: Derivation and extension

This paper focuses on the cubature Kalman filters （CKFs） for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.     

色散光学模型中色散积分的解析和数值计算

利用解析和数值计算的方法计算了色散光学模型中色散积分的数值,并与Quesada等人的解析计算作了比较,结果显示两者结果基本一致。     

平面偏振光的布儒斯特入射

菲涅耳公式给出了两种透明介质界面处,平行入射面的光矢量(P矢量)和垂直入射面的光矢量(S矢量),在分界面上的振动状态[1].     

不倒翁的力学分析

从力学上对不倒翁进行了分析，得出了对其配重位置的限定条件及其微振动的周期公式。     

渐变折射率波导传播特性微扰计算的代数递推公式

应用量子力学的超位力定理（HVT）和赫尔曼－费恩曼（Hellmann-Feynman）定理（HFT），导出了用微扰法计算渐变折射率平面波导传播常数各级近似值的代数递推公式，并给出了由传播常数近似值计算模场近似表达式的代数式。计算了几个典型实例，此法的特点是便于直接计算任意级近似的传播常数及模场分布，且可推广到二维波导的计算。     

周期轨道的量子化与量子能谱中的长程关联

用二维可积系统的半经典量子化方案和二维无关联振子系统的量子能级与周期轨道之间的对应关系,讨论了一组量子能级之间具有长程关联的内在机制,在二维无关联振子系统中,发现了具有相同拓扑M(M1,M2)的周期轨道相对应的量子能级之间存在着长程关联,并以二维4次无关联振子系统为例做了具体说明.