A model of an annular flat-topped vortex beam based on multi-Gaussian superimposition is proposed. We experimentally produce this beam with a computer-generated hologram (CGH) displayed on a spatial light modulator (SLM). The power of the beam is concentrated on a single-ring structure and has an extremely strong radial intensity gradient. This beam facilitates various applications ranging from Sisyphus atom cooling to micro-particle trapping.

在束腰不在物镜入瞳位置的一般情况下，利用理查德〖CD*2〗沃尔夫矢量衍射积分公式获得了径向偏振高阶矢量贝塞尔-高斯光束通过有初级球差和受孔径限制的物镜聚焦的三维光场的径向，方位角和纵向分量表达式。数值模拟了入射光束受圆孔径和环形孔径限制情况下初级球差对光场分布的影响。结果表明：球差对焦平面光场分布的影响是非常小的，尤其是环形孔径限制情况下球差的影响可以完全忽略；在受圆形孔径限制情况下，光束经有球差物镜聚焦后，焦平面前后的光场分布不再对称。球差导致在焦平面各点的强度分布变化并不总是一致变大，或一致变小；使用环形孔径时光束聚焦后的光斑尺寸要远小于使用圆形孔径时光束聚焦后的光斑尺寸。

新型特殊模式激光束的传播是激光应用研究的基础和重要课题。利用柯林(Collins)积分公式研究了广义超几何光束在ABCD近轴光学系统中的传播行为, 得到了光束在输出平面复振幅的解析表达式。结果表明,其传播后的复振幅分布与库默尔(Kummer)函数成正比。通过将Kummer函数展开成级数, 获得了光束在输出平面复振幅的模的级数形式, 从该级数可以看出, 广义超几何光束在ABCD近轴光学系统中传播时的模式结构一般是要发生变化的。作为特殊光学系统, 讨论了自由空间传播时近场和远场衍射近似表达式, 它们均为一系列同心圆环, 空间频率随径向坐标增加而增加, 近场衍射时横向模式结构保持不变, 而远场衍射时则发生变化。给出了光束的归一化系数, 分析了该光束一些简化模式与高斯光束的关系。

By using the closed orbit theory, the photodetachment cross section of H- near a metal surface is derived and calculated. The results show that the metal surface has great influence on the photodetachment process. As the ion-surface distance is very large, the influence of the electrostatic image potential caused by the metal surface becomes small and can be neglected. The period, action, and length of the detached electron’s closed orbit are nearly the same as the case of the photodetachment of H- near an elastic interface. However, with the decrease of the ion-surface distance, the influence of the metal surface becomes significant. The amplitude of the oscillation in the photodetachment cross section becomes complicated. Each resonance peak in the Fourier transformed cross section is associated with one electron’s closed orbit. Unlike the case of the photodetachment of H- near an elastic interface, the length of the closed orbit does not equal the twice distance between the ion and the surface. But with the increase of the ion-surface distance, the length of the closed orbit approaches the case of the closed orbit near an elastic interface, which suggests the correctness of our method. This study provides a new understanding on the photodetachment process of H- in the presence of a metal surface.

The limitation of paraxial condition of paraboloid refracting system in performing fractional Fourier transform acts like an aperture, which makes the system different from ideal systems. With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of fractional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented. Complicated and practical fractional Fourier transform systems can be constructed by cascading several apertured paraboloid refracting systems which are the simplest and the most basic units for performing more precise transform.

Quantum billiards have attracted much interest in many fields. People have made a lot of researches on the two-dimensional (2D) billiard systems. Contrary to the 2D billiard, due to the complication of its classical periodic orbits, no one has studied the correspondence between the quantum spectra and the classical orbits of the three-dimensional (3D) billiards. Taking the cubic billiard as an example, using the periodic orbit theory, we find the periodic orbit of the cubic billiard and study the correspondence between the quantum spectra and the length of the classical orbits in 3D system. The Fourier transformed spectrum of this system has allowed direct comparison between peaks in such plot and the length of the periodic orbits, which verifies the correctness of the periodic orbit theory. This is another example showing that semiclassical method provides a bridge between quantum and classical mechanics.