Electron Tomography of Optical Phase Singularities

Phase singularities are a universal concept ubiquitous to many wave systems. Exploration of electromagnetic wave singularities intersects advanced optics, materials science, and wave physics. These singularities, where the phase of the wave is undefined and its amplitude is zero, play a crucial role in the development of technologies ranging from optical manipulation tools [1] to high-resolution microscopy [2] and optical communications [3]. In 2D systems, various types of singularities have been demonstrated, from polariton vortices [4] and Möbius rings [5] to skyrmions [6], carrying a conserved topological charge. The measurement of these 2D singularities has been advanced in the far-field [5] and near-field [4], [6]. Extending the concept to 3D introduces increased complexity. 3D singularities such as optical vortex knots [7] and hopfions [8] represent just a small subset of the intricate topological structures that can occur in light fields. These singularities are harder to measure and analyse. Progress in this field calls for new imaging techniques that will capture the full spatial information.