Electron Singularities, Matter Wave Catastrophes, and Vortex Lattice Singularimetry

Singularities in wave fields, such as phase vortices, are of substantial interest for light optics, matter waves and x-ray optics. New theoretical insights [1] and cutting edge nanofabrication techniques have recently created a wide variety of electron vortex beams [2, 3] for the transmission electron microscope (TEM), which can provide spectroscopic information pertaining to the magnetic properties of nanoscale specimens [2]. The rich diffraction physics of singular optics is vast and many concepts can be directly translated to electron microscopy. Interesting physics has been discovered by highlighting differences between electron and optical vortex beams, such as a remarkable interplay between Zeeman coupling, Landau levels and Gouy phases in the TEM [4] or the Faraday effect for electron vortex beams propagating in a magnetic field, which interestingly occurs in vacuum [5].