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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. – Piotr Migdal Mar 11 '11 at 18:20
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
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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