On small beams with large topological charge: II. Photons, electrons and gravitational waves

Abstract

Beams of light with a large topological charge significantly change their spatial structure when they are focused strongly. Physically, it can be explained by an emerging electromagnetic field component in the direction of propagation, which is neglected in the simplified scalar wave picture in optics. Here we ask: is this a specific photonic behavior, or can similar phenomena also be predicted for other species of particles? We show that the same modification of the spatial structure exists for relativistic electrons as well as for focused gravitational waves. However, this is for different physical reasons: for electrons, which are described by the Dirac equation, the spatial structure changes due to a spin–orbit coupling in the relativistic regime. In gravitational waves described with linearized general relativity, the curvature of space–time between the transverse and propagation direction leads to the modification of the spatial structure. Thus, this universal phenomenon exists for both massive and massless elementary particles with spin 1/2, 1 and 2. It would be very interesting whether other types of particles such as composite systems (neutrons or C _60 ) or neutrinos show a similar behavior and how this phenomenon can be explained in a unified physical way.

Keywords

• non-paraxial effect
• Maxwell equation
• Dirac equation
• linearized gravity
• tight focusing
• transverse spatial modes