论文标题
贝塞尔 - 高斯光束叠加的打结淋巴结线
Knotted nodal lines in superpositions of Bessel-Gaussian light beams
论文作者
论文摘要
提出了一种简单的分析方法，即提出了用打结的淋巴结线创建贝塞尔 - 高斯光束叠加的方法。它基于自由粒子的近距离波方程与二维Schrödinger方程之间的等效性。 $ 2D $Schrödinger的传播器以Bessel功能表示，该功能可以直接获得具有淋巴结线拓扑的光束叠加。以明确的方式构建了四种类型的结：Unkont，Hopf链接，硼曲线环和Trefoil。还以图形结的示例显示了更复杂的结构需要大量的组成梁以及数值和实验侧的高精度。光束强度的微小变化会导致打结“切换”。
A simple analytical way of creating superpositions of Bessel-Gaussian light beams with knotted nodal lines is proposed. It is based on the equivalence between the paraxial wave equation and the two-dimensional Schrödinger equation for a free particle. The $2D$ Schrödinger propagator is expressed in terms of Bessel functions, which allows to obtain directly superpositions of beams with a desired topology of nodal lines. Four types of knots are constructed in the explicit way: the unknot, the Hopf link, the Borromean rings and the trefoil. It is also shown, using the example of the figure-eight knot, that more complex structures require larger number of constituent beams as well as high precision both from the numerical and the experimental side. A tiny change of beam's intensity can lead to the knot "switching".
