Topologies of light in electric-magnetic space

In nonparaxial, monochromatic light the electric and magnetic fields generally have different energy densities, different singularities and different polarisation structures. A topological picture of the electric field or magnetic field in isolation cannot capture the elusive topology of nonparaxial light that exists in the spatially dependent relationship between the two fields: the degree to which light breaks fundamental symmetries (parity, duality, time-reversal). With this work a new ellipse is introduced that resides not in real space, but in electric-magnetic (EM) space, and whose geometry depends on these broken symmetries. The EM ellipse has circular and linear polarisation singularities and may be organised into particle-like textures. These thus-far hidden topologies are present even in rudimentary structured waves, for a second-order EM-space meron is shown to be present in a focussed linearly polarised vortex beam.