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Circular polarization: https://en.wikipedia.org/wiki/Circular_polarization

Orbital angular momentum of light: https://en.wikipedia.org/wiki/Orbital_angular_momentum_of_light

From point of view, twisted light (Orbital angular momentum of light) basically is a quantum effect involved quantization, where circular polarization is also a quantum effect but was much described by the idea of plane wave from the classical electromagnetics.

However, when looking at the wave front of the circular polarization and twisted light(of $m\neq 0$), the graph looked almost exactly same. Further, twisted light seemed to be dependent on the coordinate system, while circular polarization is more light an intrinsic property of photons.

What's the difference between twisted light and light of circular polarization?

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Short answer: twisted light (i.e., light with well defined OAM) has an azimuthal dependence given by $\exp(i\ell\phi)$, where $\phi$ is the azimuthal coordinate of a cylindrical coordinate system, and $\ell$ is an integer. So OAM is determined by the spatial profile of an optical beam and not by its polarization properties.

The "twisted" property comes from the local Poynting vectors. On either side of the centre of the beam the direction of propagation of the light (given by these local Poynting vectors) are twisted: the one on the left goes slightly upward (downward) while the one on the right goes slightly downward (upward). Depending on the handedness of the twist.

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