Kotlyar Victor V, Kovalev Alexey A
Opt Express. 2020 Jul 6;28(14):20449-20460. doi: 10.1364/OE.394273.
We obtain theoretical relationships to define topological charge (TC) of vortex laser beams devoid of radial symmetry, namely asymmetric Laguerre-Gaussian (LG), asymmetric Bessel-Gaussian (BG), and asymmetric Kummer beams, as well as Hermite-Gaussian (HG) vortex beams. Although they are obtained as superposition of respective conventional LG, BG, and HG beams, these beams have the same TC equal to that of a single mode, n. At the same time, the normalized orbital angular momentum (OAM) that the beams carry is different, differently responding to the variation of the beam's asymmetry degree. However, whatever the asymmetry degree, TC of the beams remains unchanged and equals n. Although separate HG beam does not have OAM and TC, superposition of only two HG modes with adjacent numbers (n, n + 1) and a π/2-phase shift produces a modal beam whose TC is -(2n + 1). Theoretical findings are validated via numerical simulation.
我们得到了一些理论关系，用于定义无径向对称性的涡旋激光束的拓扑电荷（TC），即非对称拉盖尔 - 高斯（LG）光束、非对称贝塞尔 - 高斯（BG）光束和非对称库默尔光束，以及厄米 - 高斯（HG）涡旋光束。尽管这些光束是由各自传统的LG、BG和HG光束叠加而成，但它们具有与单模相同的拓扑电荷，即n。同时，这些光束携带的归一化轨道角动量（OAM）不同，对光束不对称程度的变化有不同的响应。然而，无论不对称程度如何，光束的拓扑电荷保持不变且等于n。虽然单独的HG光束不具有轨道角动量和拓扑电荷，但仅两个相邻数（n，n + 1）且有π/2相移的HG模式叠加会产生一个模态光束，其拓扑电荷为 -（2n + 1）。理论结果通过数值模拟得到验证。
