Spatio-temporal vortex beams and angular momentum

TL;DR

This paper introduces a new class of spatio-temporal vortex beams that carry intrinsic orbital angular momentum at arbitrary angles, extending the concept of traditional monochromatic vortex beams to polychromatic, exact solutions of the Klein-Gordon equation.

Contribution

It develops a space-time generalization of vortex beams, constructing exact non-diffracting solutions with arbitrary OAM orientation via wave-vector shifts or Lorentz boosts.

Findings

Constructed time-diffracting and non-diffracting spatio-temporal Bessel beams.

Demonstrated these beams can describe relativistic and nonrelativistic vortex states.

Potential applications in quantum physics and astrophysics.

Abstract

We present a space-time generalization of the known spatial (monochromatic) wave vortex beams carrying intrinsic orbital angular momentum (OAM) along the propagation direction. Generic spatio-temporal vortex beams are polychromatic and can carry intrinsic OAM at an arbitrary angle to the mean momentum. Applying either (i) a transverse wave-vector shift or (ii) a Lorentz boost to a monochromatic Bessel beam, we construct a family of either (i) time-diffracting or (ii) non-diffracting spatio-temporal Bessel beams, which are exact solutions of the Klein-Gordon wave equations. The proposed spatio-temporal OAM states are able to describe either photon or electron vortex states (both relativistic and nonrelativistic), and can find applications in particle collisions, optics of moving media, quantum communications, and astrophysics.