中性粒子和带电粒子在高斯光束中的扭结轨迹
Knotted trajectories of neutral and charged particles in Gaussian light beams
摘要：
利用傍轴波动方程与二维薛定谔方程的等价性，解析地得到了具有纽结构的单色光高斯光束。这些光束属于被称为超几何-高斯光束的傍轴光束[E。Karimi，G.齐托湾皮奇里洛湖Marrucci和E. Santamato，Opt. Lett. { \bf 32}，3053（2007）]。四个拓扑处理：unknot，霍普夫链，Borromean环和三叶。它示出的数值方式，中性的可极化粒子放置在这样的光场，在精确的初始条件的调整，可以被迫遵循相同的打结的轨迹。类似的结果也适用于受有质动力势支配的带电粒子。这种效应可以用来精确地引导粒子沿着选择的复杂路径，表现出非平凡的拓扑特征，引导它们绕过障碍物，似乎有助于工程更复杂的纳米粒子。
英文摘要：
Making use of the equivalence between paraxial wave equation and two-dimensional Schrödinger equation, Gaussian beams of monochromatic light, possessing knotted nodal structures are obtained in an analytical way. These beams belong to the wide class of paraxial beams called the Hypergeometric-Gaussian beams [E. Karimi, G. Zito, B. Piccirillo, L. Marrucci and E. Santamato, Opt. Lett. {\bf 32}, 3053(2007)]. Four topologies are dealt with: the unknot, the Hopf link, the Borromean rings and the trefoil. It is shown in the numerical way that neutral polarizable particles placed in such light fields, upon precise tuning of the initial conditions, can be forced to follow the identical knotted trajectories. A similar outcome is also valid for charged particles that are subject to a ponderomotive potential. This effect can serve to precisely steer particles along chosen complicated pathways exhibiting non-trivial topological character, guide them around obstacles and seems to be helpful in engineering more complex nanoparticles.
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