# Light's orbital angular momentum

## Main Question or Discussion Point

http://scitation.aip.org/content/aip/magazine/physicstoday/article/57/5/10.1063/1.1768672 [Broken]

Apparently, light can have orbital angular momentum as well as spin. But I don't see how this is possible, at least in vacuum. Is this in vacuum or a waveguide? (It wasn't too clear in the article or first reference) To have orbital momentum, one has to orbit around something. What is light orbiting around? The article says the center of the beam, but there's nothing there, right?

I see there are various modes for Gaussian beams called Laguerre-Gaussian modes. Do these exist in free space or only in some kind of laser resonator?

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mfb
Mentor
It can have "orbital" angular momentum in vacuum. You don't need an orbit, in a similar way a massive object can have angular momentum without rotating or orbiting, if its flight direction does not point towards/away from the origin of the coordinate system.

I thought of that, but that would mean that the light beam must be diverging/converging quite rapidly. Is this the case for this kind of beam?

mfb
Mentor
I don't have access to the article here. Orbital angular momentum is a common thing in nuclear transitions, for example.

vanhees71
Gold Member
2019 Award
I've to read the article first, to say anything about it, but for sure it's highly misleading to talk about orbital and spin angular momentum for a relativistic (classical or quantum) field and particularly for the electromagnetic field, which is a massless vector field, because there is no gauge invariant way to define this split of the total angular momentum (which is of course well defined) for the electromagnetic field.

The correct mathematical treatment is well known as "multipole expansion" in classical electrodynamics. For QED the corresponding mode decomposition of the electromagnetic field operator is the use of simultaneous single-photon eigenstates for energy, and total angular momentum (quantum numbers $\ell$ and $m$ as in the multipole expansion). For a very thorough treatment of this, see

Landau/Lifshitz Vol. 4 (Quantum Electrodynamics).

anorlunda
Mentor
Just a layman here, but let me take a stab.

A collapsing star gravitates and has angular momentum. If it becomes a black hole, it still gravitates and has the same angular momentum. But we do not know (and can not know) if the stuff inside the BH has rest mass or if it has all been converted to radiation. But we need not know, because it has the same gravity and angular momentum either way.

By that reasoning, I say light must have angular momentum. Whether that qualifies as "orbital angular momentum" is a different question.

vanhees71