Electromagnetic symmetry dislocations

TL;DR

This paper introduces basis-independent topological features in monochromatic electromagnetic fields, linking them to symmetries like parity, duality, and time-reversal, advancing the understanding of electromagnetic singularities beyond scalar vortex concepts.

Contribution

It proposes a new framework for topological features in electromagnetic fields that are basis-independent and connected to fundamental symmetries, unlike traditional scalar vortex or polarization singularities.

Findings

Defines basis-independent topological structures in electromagnetic fields.

Links topological features to local symmetries such as parity, duality, and time-reversal.

Provides a new perspective on electromagnetic singularities beyond scalar vortex models.

Abstract

Singular optics aims to understand and manipulate light's topological defects, pioneered by the discovery that phase vortex lines, strands of destructive interference, naturally occur in scalar wave fields. Monochromatic electromagnetic fields, however, are described by complex three-dimensional vectors that make individual scalar phase vortices in their vector components, which depend on the choice of co-ordinate basis, less meaningful. Instead, polarisation singularities can capture the vector texture of complicated, even non-paraxial light, with separate spatial descriptions for the electric $\mathbf{E}$ and magnetic $\mathbf{H}$ fields. But polarisation textures, too, are basis-dependent, because the laws of electromagnetism can be expressed not only by separate $\mathbf{E}$ and $\mathbf{H}$ fields, but by linear combinations of the two. We instead propose fundamental, basis-independent topological features generic in monochromatic electromagnetic fields: one- and two-dimensional structures that relate to time-averaged symmetries, including parity, duality and time-reversal, held locally by the combined electric and magnetic field polarisation geometry.