Tying knots in light fields
arXiv:1302.0342 · doi:10.1103/PhysRevLett.111.150404
Abstract
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 . We examine and illustrate the geometry and evolution of the solutions, making manifest the structure of nested knotted tori filled by the field lines.
5 pages, 3 figures
References in corpus (4)
Cited by in corpus (80)
- The role of the Riemann-Silberstein vector in classical and quantum theories of electromagnetism
- Topological Semimetals carrying Arbitrary Hopf Numbers: Hopf-Link, Solomon's-Knot, Trefoil-Knot and Other Semimetals
- Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
- Knotting fractional-order knots with the polarization state of light
- Helicity conservation by flow across scales in reconnecting vortex links and knots
- High capacity topological coding based on nested vortex knots and links
- Singular knot bundle in light
- Knotted Defects in Nematic Liquid Crystals
- Photonic Dirac monopoles and skyrmions: spin-1 quantization
- Knotted solutions, from electromagnetism to fluid dynamics
- Weaving knotted vector fields with tunable helicity
- Classification of Electromagnetic and Gravitational Hopfions by Algebraic Type
- Optical excitations of Skyrmions, knotted solitons, and defects in atoms
- Untying links through anti-parity-time-symmetric coupling
- New knotted solutions of Maxwell's equations
- Helicity, Topology and Kelvin Waves in reconnecting quantum knots
- Knotted Polarizations and Spin in 3D Polychromatic Waves
- Energy backflow in unidirectional spatiotemporally localized wavepackets
- Bunch Shaping in Electron Linear Accelerators
- Topological near fields generated by topological structures
- Gravitational waves carrying orbital angular momentum
- Knotted solutions for linear and nonlinear theories: electromagnetism and fluid dynamics
- Linked and knotted chimera filaments in oscillatory systems
- Maxwell's Theory of Solid Angle and the Construction of Knotted Fields
- Relativistic helicity and link in Minkowski space-time
- Topological quantum quench dynamics carrying arbitrary Hopf and second-Chern numbers
- Linked and Knotted Gravitational Radiation
- Unsupervised Learning of Topological Non-Abelian Braiding in Non-Hermitian Bands
- Helicity Conservation, and Twisted Seifert Surfaces for Superfluid Vortices
- Non-Abelian Braiding of Topological Edge Bands
- Knotted optical vortices in exact solutions to Maxwell's equations
- Spacetimes dressed with stealth electromagnetic fields
- Constructing a polynomial whose nodal set is the three-twist knot
- Constructing a class of topological solitons in magnetohydrodynamics
- Lattice topology dictates photon statistics
- When do knots in light stay knotted?
- Discharging dynamics of topological batteries
- Broken mirror symmetry of tracer's trajectories in turbulence
- Some exact solutions for light beams
- New solutions of the Dirac, Maxwell and Weyl equations from the fractional Fourier transform
- Quantum numbers and spectra of structured light
- Spin-Orbital momentum decomposition and helicity exchange in a set of non-null knotted electromagnetic fields
- Nonlinear electrodynamics is skilled with knots
- Discrete-Gauss states and the generation of focussing dark beams
- Linked and knotted synthetic magnetic fields
- Braiding topology of symmetry-protected degeneracy points in non-Hermitian systems
- Electrodynamics of dual superconducting chiral medium
- A Knotted Meta-molecule with 2-D Isotropic Optical Activity Rotating the Incident Polarization by 90°
- Zitterbewegung structure in electrons and photons
- Observing the nodal-line conversion determined by the relative homotopy
- Stable knots and links in electromagnetic fields
- Topological atom optics and beyond with knotted quantum wavefunctions
- Optical polarization skyrmionic fields in free space
- Photon traps in nonlinear electrodynamics
- On spacetime foliations and electromagnetic knots
- On the existence of the field line solutions of the Einstein-Maxwell equations
- Numerical simulation of knotted solutions for Maxwell equations
- Knotted trajectories of neutral and charged particles in Gaussian light beams
- Fluid-electromagnetic helicities and knotted solutions of the fluid-electromagnetic equations
- Contactless generation and trapping of hydrodynamic knots in sessile droplets by acoustic screw dislocations
- Knotted nodal lines in superpositions of Bessel-Gaussian light beams
- Hopfion solutions in gravity and a null fluid/gravity conjecture
- Exact vacuum solution with Hopf structure in general relativity
- Nonlinear dynamics of a charged particle in a strong non-null knot wave background
- Efficient sampling of knotting-unknotting pathways for semiflexible Gaussian chains
- Particle on a Torus Knot: Anholonomy and Hannay Angle
- Biot-Savart helicity versus physical helicity: A topological description of ideal flows
- Lagrangian formulation, generalizations and quantization of null Maxwell's knots
- Gravitoelectromagnetic knot fields
- Helicity, Spin, and Infra-zilch of Light: a Lorentz Covariant Formulation
- Entanglement manifestation of knot topology in a non-Hermitian lattice
- Harmonic field in knotted space
- Knots and the Maxwell Equations
- Knotted surfaces as vanishing sets of polynomials
- Topological monopoles and currents in electromagnetic waves
- Chiral Balls: Knotted Structures with Both Chirality and Three-dimensional Rotational Symmetry
- Noise-driven Topological Changes in Chaotic Dynamics
- Emergence of Nodal-Knot Transitions by Disorder
- Force-Free Fields are Conformally Geodesic
- Residual gauge theory for quanta of surface plasmons