约束力学系统的联络及其运动方程的测地性质

用现代整体微分几何方法研究非定常约束力学系统运动方程的测地性质，得到非定常力学系统的动力学流关于１＿射丛上的联络具有测地性质的充分必要条件·非定常情形下的动力学流关于无挠率的联络总具有测地性质，因此任何非定常约束力学系统在外力作用下的运动总可以表示为关于１＿射丛上无挠率的动力学联络的测地运动，这与定常力学的情形有所区别·     

On the Bergman representative coordinates

We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the Bergman metric contained in this set. By concrete examples we show that these estimates are the best possible.     

复空间形式中常数量曲率的完备全实伪脐子流形

设CNnc是具有常全纯截面曲率c(≤O)的复n维的复空间形式,Mn是CNnc中常数量曲率的完备全实伪脐子流形,R,‖h‖2分别表示Mn的标准数量曲率和第二基本形式模长的平方.假设R≥c/4.利用丘成桐的广义极大值原理和自伴随算子研究了关于‖h‖2的pinching问题,得到了两个Mn成为全测地或全脐的刚性定理.     

Large‐acceptance diamond planar refractive lenses manufactured by laser cutting

For the first time, single‐crystal diamond planar refractive lenses have been fabricated by laser micromachining in 300 µm‐thick diamond plates which were grown by chemical vapour deposition. Linear lenses with apertures up to 1 mm and parabola apex radii up to 500 µm were manufactured and tested at the ESRF ID06 beamline. The large acceptance of these lenses allows them to be used as beam‐conditioning elements. Owing to the unsurpassed thermal properties of single‐crystal diamond, these lenses should be suitable to withstand the extreme flux densities expected at the planned fourth‐generation X‐ray sources.     

Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

     

Efficient coupling and relaxed alignment tolerances in pigtailing of a laser diode using dual ball lenses

In this paper, we report an efficient coupling scheme with relaxed misalignment tolerances. The proposed coupling scheme consists of two ball lenses of same diameter (1 mm) and different refractive indices. The second ball lens which is facing the fiber tip has a higher refractive index (1.833), whereas the first one which faces the laser diode has a refractive index of 1.5. Employing Gaussian and ABCD ray tracing optics, the theoretically obtained coupling efficiency can reach a unity with relaxed working distance (separation of the coupling system from the fiber tip) in the range between 1 and 4 mm at some optimum positions of the coupling lenses with regard to each other and to the facet of the laser diode. It has been found that if the distance between the first ball lens and the laser diode (d₁) is fixed at 1.1 mm, which is twice its focal length, the coupling efficiency and the working distance as well as the misalignment tolerances are greatly affected by variation of the separation between the two ball lenses (s), and for this proposed coupling scheme the highest coupling efficiency and largest working distance are obtained when s is in the range of 0.3-0.35 mm. Above and below this range there is a significant reduction in the values of the above-mentioned parameters. Experimentally, the Nd:YAG laser welding system has been used for the alignment and welding of the coupling components in a butterfly configuration; the experimentally obtained coupling efficiency of the proposed coupling system was around 75% with relaxed working distance. From the effect of lateral and angular offsets on coupling efficiency, it is clearly noticed that the mode field of laser diode is transformed from elliptical into circular and hence effectively matched with that of the single-mode fiber.     

温度变化对谐衍射透镜性能的影响

分析了温度变化对谐衍射透镜的焦距、谐振波长、衍射效率等性能的影响,建立了相应的数学表达式,并对其进行了数值模拟.提出了漂移函数的概念,以表征焦距和谐振波长随温度的变化程度.另外,还给出了各谐振级次的衍射效率随温度变化的相关规律.最后比较了在相位匹配数不同、但设计波长相同时,温度变化对衍射效率的影响,发现相位匹配数越大,衍射效率对温度变化越敏感.     

用于半导体激光器的等共轭距双曲柱面镜系统

论述用于把窗口尺寸为０－１２８５ｍ ｍ ×３ ．２３９０ ｍ ｍ 的半导体激光器发出４４°×１３°的发散光束压缩成在±０－００２５ｒａｄ 内出射光的柱面镜系统。该系统的核心是用两组互相垂直、且共轭距相等的双曲柱面镜,把激光器的条形窗口的像变粗变短;然后,再用透镜组把此像“准直”到“无限远”