Opt Lett. 2018 Jul 1;43(13):3084-3087. doi: 10.1364/OL.43.003084.
Here we theoretically study Gaussian beams with arbitrarily located polarization singularities (PSs). Under PSs, we mean here an isolated intensity null with radial, azimuthal, or radial-azimuthal polarization around it. An expression is obtained for the complex amplitude of such beams. We study in detail cases in which there is one off-axis PS, two opposite PSs, or more than two PSs located in the vertices of a regular polygon. If such a beam has one or two opposite PSs, these PSs are the centers of radial polarization. If there are three PSs, then one of them has radial polarization, and the other two have mixed radial-azimuthal polarization. If the beam has four PSs, then there are two PSs with radial polarization and two PSs with azimuthal polarization. When propagating in space, PSs are shown to appear in a discrete set of planes, in contrast to the phase singularities existing in any plane. If the beam has two PSs, their polarization is shown to transform from the radial in the initial plane to the azimuthal in the far field. The results can find application in optical communications by using non-uniform polarization.
我们从理论上研究了具有任意位置偏振奇点（PS）的高斯光束。这里的 PS 是指其周围存在径向、角向或径向-角向偏振的孤立强度零点。我们得到了这种光束的复振幅表达式。我们详细研究了具有一个离轴 PS、两个相对 PS 或多个 PS 位于正多边形顶点的情况。如果这样的光束有一个或两个相对的 PS，那么这些 PS 就是径向偏振的中心。如果有三个 PS，则其中一个具有径向偏振，另外两个具有混合的径向-角向偏振。如果光束有四个 PS，则有两个具有径向偏振的 PS 和两个具有角向偏振的 PS。在空间中传播时，PS 被显示出出现在离散的一系列平面中，与存在于任何平面中的相位奇点形成对比。如果光束有两个 PS，则它们的偏振会从初始平面中的径向转变为远场中的角向。这些结果可以通过使用非均匀偏振在光通信中得到应用。
