  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
behaviour and how this phenomenon can be explained in a unified physical way.
