# does photon travels in a helical path in an optical vortex?

The wave front of the optical vortex beam is helical. Does it mean that the photon travels in a helical path? When the optical vortex beam is focused on a screen, an annular ring with dark center is observed. If I take a small arc of this ring only, block rest of the ring and let it propagate, would I see the light beam actually following a helical path? How would this happen? Of course, Optical vortex beam has orbital angular momentum but still it's not making sense to me. How the photon should be travelling in a helical path?

• Photons don't travel, at all. A photon is simply a quantum number that belongs to an excitation of the quantum field. Commented Jun 8, 2015 at 0:13

No, the photons do not travel in a helix, they travel in a straight line but with a phase delay that is dependent on position. Looking across the beam's wavefront there is a phase delay that is dependant on the polar angle $\theta$ around the beam axis.
If we take a simple helical mode's complex amplitude as $\zeta(r,\theta,z) = u(r,z) e^{-ikz} e^{il \theta}$ where $u(r,z)$ is the amplitude at radius $r$, $z$ is the distance traveled by the beam, $k$ is the wavenumber and $l$ is a fixed integer. The $e^{il \theta}$ part shows that the only thing special about the beam is this fixed phase delay that is dependent on $\theta$.
Of course when we propagate the whole beam the phase changes with $z$ as with any other beam. If we plot the line when the modulo phase shift equals zero, this would trace out a helix, hence the name.