Knotted trajectories of neutral and charged particles in Gaussian light beams

TL;DR

This paper analytically constructs Gaussian light beams with knotted nodal structures and demonstrates that neutral and charged particles can be guided along these complex topological trajectories using such light fields.

Contribution

It introduces a method to generate knotted Gaussian beams and shows how they can steer particles along intricate topological paths.

Findings

Particles can be guided along knotted trajectories in these beams.

Neutral and charged particles respond similarly to the light's topology.

The method enables precise control of particle pathways for nanotechnology applications.

Abstract

Making use of the equivalence between paraxial wave equation and two-dimensional Schr\"odinger 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.