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Is there any sense in saying that circularly polarized EM waves have angular momentum?

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Yes. Electromagnetic waves carry energy and momentum, and can carry angular momentum.

A linearly polarized wave packet doesn't carry any angular momentum (measured about an axis through its center -- a linearly polarized wave packet moving past you off to one side has angular momentum about an axis located where you are, just as a baseball flying past you does.)

A circularly polarized wave packet does carry angular momentum about its center ("spin" as opposed to "orbital" angular momentum, roughly).

Griffiths's book Introduction to Electrodynamics is a good place to learn about this at the advanced-undergraduate level.

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A linearly polarized light can carry angular momentum. For light you have both spin angular momentum (i.e. circular polarization) and orbital angular momentum (the spatial shape of the beam), see e.g. physics.gla.ac.uk/Optics/play/photonOAM. – Piotr Migdal Mar 11 '11 at 18:20
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I'm pretty sure that's what I said! Linearly polarized light carries orbital but not spin; circularly polarized carries both. Am I misunderstanding you? – Ted Bunn Mar 11 '11 at 18:59
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Hi @Igor, the best way to count the angular momentum is in terms of photons. A photon carries the energy $E=hf=\hbar \omega$ and if it is circularly polarized, the angular momentum in the direction of motion (around this axis) is $\pm\hbar =\pm h/2\pi$. So the ratio of energy and angular momentum of the photon - and the same for a big electromagnetic wave - is $\omega=2\pi f$. – Luboš Motl Mar 11 '11 at 19:32
@Luboš Motl: What about elliptically polarized wave then? I am asking because I want to analyze nonlinear conversion of potential (l) waves in magnetized plasma into conventional E/M wave (t). In magnetic field, all those waves are elliptically polarized. Following quantum analogy, conservation of energy and momentum in the process l_1 + l_2 -> t leads to the eqs: \omega_1+\omega_2 = \omega_3, k_1+k_2=k_3. I would expect, that conservation of angular momentum gives one more equation. But there is noting regarding angular momentum in existing theory of 3-waves interaction . – Igor Mar 15 '11 at 7:56

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