title: Tying knots in light fields.
abstract: We construct analytically, 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 shear free, preserves the topology of the knots and links. Our approach combines the construction of null fields with complex polynomials on S3. We examine and illustrate the geometry and evolution of the solutions, making manifest the structure of nested knotted tori filled by the field lines.
authors.affiliation: Physics Department and the James Franck Institute, University of Chicago, 929 East 57th Street, Chicago, Illinois 60605, USA.
authors.forename: Hridesh
authors.initials: H
authors.lastname: Kedia
authors.forename: Iwo
authors.initials: I
authors.lastname: Bialynicki-Birula
authors.forename: Daniel
authors.initials: D
authors.lastname: Peralta-Salas
authors.forename: William T M
authors.initials: WT
authors.lastname: Irvine