Helical wavefronts of vortex beams

Question

Vortex beams are characterized by an azimuthal angle phase dependence, basically $e^{i lphi}$. Why is this azimuthal angle phase dependence crucial and will I get a helix if I were to plot the surface of constant phase for Laguerre Gaussian beams?
NB: I have edited the question because of a confusion.

mike stone · Accepted Answer

If the wave propagates in the $z$ direction and $Phi(z,r, phi,t)$ is the phase of the wave
$$
A(r)e^{iPhi(z,r, phi,t)}= 
A(r)e^{ikz -iomega t+ilphi},
$$
then the surfaces of constant $Phi$, are indeed helical.

Helical wavefronts of vortex beams

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