Quantum theory of photonic vortices and quantum statistics of twisted photons

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