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

8 pages, 3 figures

References in corpus (7)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Divergence of an orbital-angular-momentum-carrying beam upon propagation
• Quantum entanglement of angular momentum states with quantum numbers up to 10010
• Holographic generation of highly twisted electron beams
• Relativistic electron wave packets carrying angular momentum
• Equivalence between focussed paraxial beams and the quantum harmonic oscillator

Cited by in corpus (6)

• Gravitational spin Hall effect of light
• Relativistic vortex electrons: paraxial versus non-paraxial regimes
• Non-linear quantum effects in electromagnetic radiation of a vortex electron
• Generation of electron vortex beams with over 1000 orbital angular momentum quanta using a tuneable electrostatic spiral phase plate
• Reinventing the Zel'Dovich Wheel
• OAM spatial demultiplexing by diffraction-based noiseless mode conversion with axicon