4D topological textures in light

Abstract

We present 4D topological textures in (quasi)monochromatic nonparaxial optical lattices that contain all possible polarization ellipses with every combination of ellipticity and orientation in 3D space. These fields span the nonparaxial polarization space (a complex projective plane) and a 4-sphere within specific spatiotemporal regions, forming 4D skyrmionic structures. Constructed from five plane waves with adiabatically varying relative amplitudes, they are experimentally realizable in free space by focusing a temporally variant beam with a high numerical aperture lens.