Knotted optical vortices in exact solutions to Maxwell's equations

Abstract

We construct a family of exact solutions to Maxwell's equations in which the points of zero intensity form knotted lines topologically equivalent to a given but arbitrary algebraic link. These lines of zero intensity, more commonly referred to as optical vortices, and their topology are preserved as time evolves and the fields have finite energy. To derive explicit expressions for these new electromagnetic fields that satisfy the nullness property, we make use of the Bateman variables for the Hopf field as well as complex polynomials in two variables whose zero sets give rise to algebraic links. The class of algebraic links includes not only all torus knots and links thereof, but also more intricate cable knots. While the unknot has been considered before, the solutions presented here show that more general knotted structures can also arise as optical vortices in exact solutions to Maxwell's equations.

arXiv comment5 pages, 3 figures; revised abstract, introduction, and conclusion; results unchanged

References in corpus (13)

• Vortex knots in light
• Tying knots in light fields
• Knots in a Spinor Bose-Einstein Condensate
• Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes I. General Theory and Weak-Gravity Applications
• Weaving knotted vector fields with tunable helicity
• Linked and knotted beams of light, conservation of helicity and the flow of null electromagnetic fields
• New knotted solutions of Maxwell's equations
• Electromagnetic vortex lines riding atop null solutions of the Maxwell equations
• Electromagnetic Torus Knots
• Linked and Knotted Gravitational Radiation
• The covariant description of electric and magnetic field lines of null fields: application to Hopf-Ranada solutions
• Constructing a class of topological solitons in magnetohydrodynamics
• Nonlinear electrodynamics is skilled with knots

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• Knotted trajectories of neutral and charged particles in Gaussian light beams
• On the existence of the field line solutions of the Einstein-Maxwell equations
• Knotted nodal lines in superpositions of Bessel-Gaussian light beams
• Finsler Geometries from Topological Electromagnetism
• Nonlinear dynamics of a charged particle in a strong non-null knot wave background
• Knots and the Maxwell Equations