Pure helicity vortex and spinstatedependent quantum coherence in twisted light
Abstract
The topological charge of a photonic vortex is the essential quantity in singular optics and the critical parameter to characterize the vorticity of twisted light. However, the definition of the photonic topological charge remains elusive. Here, we put forth a theoretical formalism to provide a comprehensive treatment of photonic vortices. We introduce quantum operators for the photon current density and helicity current density based on the continuity equations from the paraxial Helmholtz equation. Our formalism allows us to introduce flow velocity and circulation for photonic currents in parallel to their counterparts in superfluids. The quantized circulation of the photonic currents conserves on propagation and it gives an explicit definition of the photonic topological charge as the winding number of a photonic vortex. In particular, we predict helicity current generated pure helicity vortices, in which the photon current vanishes. Finally, we show an interesting effect that the quantum statistics of twisted photon pairs are essentially determined by their spin states.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.04705
 Bibcode:
 2021arXiv211004705Y
 Keywords:

 Quantum Physics;
 Physics  Atomic Physics;
 Physics  Optics
 EPrint:
 15 pages and 7 figures