在光场中打结
Tying knots in light fields
摘要：
我们构造了一个新的家庭零解麦克斯韦方程组在自由空间中的场线编码所有环面结和链接。这些零场的演化，类似于沿坡印廷矢量的可压缩流，既测地线又无剪切，保持了节点和链接的拓扑结构。我们的方法结合了贝特曼和旋量形式主义的零字段的建设与复杂的多项式$\mathbb{S}^3$。我们研究和说明的几何形状和演化的解决方案，使体现的结构嵌套打结环面填充的场线。
英文摘要：
We construct a new family of null solutions to Maxwell's equations in free space whose field lines encode all torus knots and links. The evolution of these null fields, analogous to a compressible flow along the Poynting vector that is both geodesic and shear-free, preserves the topology of the knots and links. Our approach combines the Bateman and spinor formalisms for the construction of null fields with complex polynomials on $\mathbb{S}^3$. We examine and illustrate the geometry and evolution of the solutions, making manifest the structure of nested knotted tori filled by the field lines.
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