Analysis of thermal property in hollow-core polarization maintaining photonic crystal fibers

We study the thermal-induced variance of effective refractive indices (ERIs) and birefringence in several kinds of polarization maintaining fibers (PMF) and carry out numerical simulations by utilizing the finite element method (FEM). Responses under varying temperatures in these fibers are analyzed thoroughly. According to our computational results, hollow-core photonic crystal fibers (HC-PCFs) exhibit much more stable temperature-dependent ERIs and birefringence among these PMFs.     

Exploring an unknown graph

We wish to explore all edges of an unknown directed, strongly connected graph. At each point, we have a map of all nodes and edges we have visited, we can recognize these nodes and edges if we see them again, and we know how many unexplored edges emanate from each node we have visited, but we cannot tell where each leads until we traverse it. We wish to minimize the ratio of the total number of edges traversed divided by the optimum number of traversals, had we known the graph. For Eulerian graphs, this ratio cannot be better than two, and two is achievable by a simple algorithm. In contrast, the ratio is unbounded when the deficiency of the graph (the number of edges that have to be added to make it Eulerian) is unbounded. Our main result is an algorithm that achieves a bounded ratio when the deficiency is bounded. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 265–297, 1999     

Further generalization of Fermat’s principle

From Maxwell’ s equations for electromagnetic fields, time-averaged energy flow density vector of stable monochromatic linearly polarized light in an isotropic insulative nonmagnetic medium is deduced. By the introduction of time-averaged energy flow density rays and the definition of new generalized refractive indexn _G1, Fermat’s principle of geometric optics is further generalized and its application conditions are discussed. The generalized Fermat' s principle can be used to describe stable transmission of light in a medium with variable refractive index. The necessary and sufficient conditions of a nondivergent and nonfocusing light beam are derived from this Fermat’s principle. Project supported by the National Natural Science Foundation of China (Grant No. 69789801) and Guangdong Provincial Natural Science Foundation of China.     

基于Rydberg原子天线的太赫兹测量

Rydberg原子在微波和太赫兹频段具有极大的电偶极矩,利用量子干涉效应可实现对该频段电磁波场强的高灵敏探测,理论上灵敏度可达到远高于现有探测技术的水平.基于Rydberg原子量子效应的电磁场探测及精密测量技术在太赫兹的场强和功率计量、太赫兹通信和太赫兹成像等方面有着巨大的应用前景.本文回顾了基于Rydberg原子量子干涉效应实现电磁波电场自校准和可溯源测量的基本理论和实验技术,详细介绍了基于Rydberg原子的高灵敏太赫兹场强测量、太赫兹近场高速成像和太赫兹数字通信的基本原理和技术方案.最后简单介绍了本研究团队正在开展的基于Rydberg原子的太赫兹探测工作.     

具有自由边界的二维渗流问题

渗流的自由边界问题是工程上很受关注的问题．现有的数值分析方法需事先估计边界形态，逐次逼近．本文采用“变分不等式”的模式，结合有限元方法研究有自由边界的渗流问题，在整个结构区域内作有限元剖分，避免了传统的有限元分析中估计自由边界、反复修正计算区域的迭代过程．本文方法为简单而快速地分析渗流自由边界问题提供了一条有效的途径．     

可获得高衬比干涉条纹的实时全息记录方法

本文提出了一种可以获得高衬比的实时全息记录方法,它通过分析所记录的第一张实时全息图来获得拍摄最佳衬比实时全息图的拍摄参数,文中指出了拍摄最佳衬比实时全息图需要满足的条件,给出了理论分析和实验验证,实验结果与理论相符甚好,对于透明物体的实时法全息图.条纹衬比可接近最佳值1.     

Femtosecond fiber laser based methane optical clock

An optical clock based on an Er³⁺ fiber femtosecond laser and a two-mode He–Ne/CH₄ optical frequency standard (λ=3.39 μm) is realized. Difference-frequency generation is used to down convert the 1.5-μm frequency comb of the Er³⁺ femtosecond laser to the 3.4-μm range. The generated infrared comb overlaps with the He–Ne/CH₄ laser wavelength and does not depend on the carrier–envelope offset frequency of the 1.5-μm comb. In this way a direct phase-coherent connection between the optical frequency of the He–Ne/CH₄ standard and the radio frequency pulse repetition rate of the fiber laser is established. The stability of the optical clock is measured against a commercial hydrogen maser. The measured relative instability is 1×10⁻¹² at 1 s and for averaging times less than 50 s it is determined by the microwave standard, while for longer times a drift of the He–Ne/CH₄ optical standard is dominant.     

矩形柱群非均匀湍尾流中的层次相似律

对绕3个矩形柱的非均匀湍尾流流场速度脉动时间序列进行了系统的测量与细致的统计分析，发现从近场到远场的每个测量点上，She-Leveque(SL)湍流层次相似律都很好地成立．应用层次相似律分析的γ检验和检验方法对层次结构参数随下游距离的变化进行了计算，并对其物理特性进行了讨论，为系统地研究非均匀湍流中流动的统计结构打下了基础。     

A polynomial algorithm for finding (g,f)-colorings orthogonal to stars in bipartite graphs

Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two nonnegative integer-valued functions defined on V(G) such that g(x)≤ f(x) for every vertex x of V(G). A (g. f)-coloring of G is a generalized edge-coloring in which each color appears at each vertex x at least g(x) and at most f(x) times. In this paper a polynomial algorithm to find a (g. f)-coloring of a bipartite graph with some constraints using the minimum number of colors is given. Furthermore, we show that the results in this paper are best possible.     

Condition number based complexity estimate for computing local extrema

In this paper, we present a new algorithm for computing local extrema by modifying and combining algorithms in symbolic and numerical computation. This new algorithm improves the classical steepest descent method that may not terminate, by combining a Sturm’s theorem based separation method and a sufficient condition on infeasibility. In addition, we incorporate a grid subdivision method into our algorithm to approximate all local extrema. The complexity of our algorithm is polynomial in a newly defined condition number, and singly exponential in the number of variables.