Bastiaans Martin J, Alieva Tatiana
Eindhoven University of Technology, Department of Electrical Engineering, P.O. Box 513,5600 MB Eindhoven, Netherlands.
J Opt Soc Am A Opt Image Sci Vis. 2010 Apr 1;27(4):918-27. doi: 10.1364/JOSAA.27.000918.
Based on the analysis of second-order moments, a generalized canonical representation of a two-dimensional optical signal is proposed, which is associated with the angular Poincaré sphere. Vortex-free (or zero-twist) optical beams arise on the equator of this sphere, while beams with a maximum vorticity (or maximum twist) are located at the poles. An easy way is shown how the latitude on the sphere, which is a measure for the degree of vorticity, can be derived from the second-order moments. The latitude is invariant when the beam propagates through a first-order optical system between conjugate planes. To change the vorticity of a beam, a system that does not operate between conjugate planes is needed, with the gyrator as the prime representative of such a system. A direct way is derived to find an optical system (consisting of a lens, a magnifier, a rotator, and a gyrator) that transforms a beam with an arbitrary moment matrix into its canonical form.
基于二阶矩分析，提出了一种二维光信号的广义规范表示，它与角庞加莱球相关联。无涡旋（或零扭曲）光束出现在该球的赤道上，而具有最大涡度（或最大扭曲）的光束位于极点。展示了一种简便方法，可从二阶矩推导出球面上作为涡度程度度量的纬度。当光束在共轭平面之间通过一阶光学系统传播时，该纬度不变。要改变光束的涡度，需要一个不在共轭平面之间工作的系统，其中回转器是此类系统的主要代表。推导了一种直接方法来找到一个光学系统（由透镜、放大镜、旋转器和回转器组成），该系统可将具有任意矩矩阵的光束转换为其规范形式。
