Knotted trajectories of neutral and charged particles in Gaussian light beams

Abstract

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.

REVTEX, 8 pages, 4 figures

References in corpus (4)

• Nonparaxial Mathieu and Weber accelerating beams
• Hypergeometric-Gaussian Modes
• Motion of charged particles in an electromagnetic knot
• Manipulating neutral particles in Bessel beams: from rings, through fixed helices to 3D traps

Cited by in corpus (4)

• A concise and universal method for deriving arbitrary paraxial and non-paraxial cylindrical Gaussian-type light modes
• Properties of "special'' hyperbolic Bessel-Gaussian optical beams
• Knotted nodal lines in superpositions of Bessel-Gaussian light beams
• Guiding polarizable particles in multi-hole Gaussian beams