Shaping the skeleton of structured light in 3D space: From self-imaging singularity networks to optical skyrmionic Hopfions

Meandering throughout three-dimensional (3D) space, optical singularities form the structurally stable skeleton of structured light fields and define its topology. Although structured singular light fields have already allowed for advanced applications in, e.g., optical manipulation by custom angular momentum, their diverse fundamental properties are not yet fully understood. Due to experimental constraints, the study of tailored vectorial light and singularities in 3D space, in particular, has been limited to only a few examples. Pushing the limits, we present the customization of complex polarization singularity networks in self-imaging vectorial fields and their all-digital adaptability by our holographic modulation approach. Furthermore, we demonstrate control of the full electric field and its singularities in 3D space by forming linked constructs of polarization singularities sculpting the first optical skymionic Hopfion.