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From what I understand, when you have linearly-polarized light, the angular momentum vector is perpendicular to the poynting vector. Does this mean that the angular momentum vector is always in the same direction as the electric field? If not, what is the relationship between the respective directions of the angular momentum vector, the electric field, and the poynting vector?

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  • $\begingroup$ the title of your question refers to linear momentum but the body to angular momentum. Which is which? $\endgroup$ – ZeroTheHero Oct 26 '17 at 21:35
  • $\begingroup$ My apologies. I've fixed the title. $\endgroup$ – user172785 Oct 26 '17 at 21:37
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    $\begingroup$ If you are referring to OAM (as a comment of yours below indicate), then please edit your question to reflect this. $\endgroup$ – flippiefanus Oct 27 '17 at 4:51
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I will assume you mean spin angular momentum when you say "angular momentum". In which case, no. The spin of a photon points along the direction of travel, whereas the magnetic field vector of an electromagnetic wave is perpendicular to the direction of propagation.

I am also unsure of where you heard that spin is perpendicular to the Poynting vector. Both would point along the direction of propagation.

In summary, the Poynting vector is proportional to $\vec{E} \times \vec{B}$ when you are considering an EM wave. If you are considering a photon, the spin points along the direction of travel.

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  • $\begingroup$ I believe the OP means orbital angular momentum. $\endgroup$ – ZeroTheHero Oct 26 '17 at 22:52
  • $\begingroup$ Yes, I was referring to orbital angular momentum, not spin. Sorry for the lack of specification. $\endgroup$ – user172785 Oct 26 '17 at 22:58
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This plot clarifies how the two spin orientations of the photon build up the polarization of the classical beam

photang

The Left and Right circular polarization and their associate angular momenta .

The photons as with zero mass and spin 1 have the only possibilities of having the spin +1 or -1 to their direction of motion.

The article on angular momentum of light :

The angular momentum of light is a vector quantity that expresses the amount of dynamical rotation present in the electromagnetic field of the light. While traveling approximately in a straight line, a beam of light can also be rotating (or “spinning”, or “twisting”) around its own axis. This rotation, while not visible to the naked eye, can be revealed by the interaction of the light beam with matter.

There are two distinct forms of rotation of a light beam, one involving its polarization and the other its wavefront shape. These two forms of rotation are therefore associated with two distinct forms of angular momentum, respectively named light spin angular momentum (SAM) and light orbital angular momentum (OAM).

The total angular momentum of light (or, more generally, of the electromagnetic field and the other force fields) and matter is conserved in time.

Going to the orbital angular momentum link:

The orbital angular momentum of light (OAM) is the component of angular momentum of a light beam that is dependent on the field spatial distribution, and not on the polarization. It can be further split into an internal and an external OAM. The internal OAM is an origin-independent angular momentum of a light beam that can be associated with a helical or twisted wavefront. The external OAM is the origin-dependent angular momentum that can be obtained as cross product of the light beam position (center of the beam) and its total linear momentum.

The title asks:

Is the angular momentum vector of a photon in the same direction as the magnetic field?

As a photon is a tiny building block of the classical wave, whose orbital momentum depends on initial and boundary conditions of the beam, there cannot be an individual photon definition of angular momentum as each photon contributes with its wavefunction differently so as to build up the classical E and B. So the angular momentum of each photon will generally be different with respect to the axis of E or B because of the way the quantum fields build up the classical fields .

The classical beam emerges from the photons that build it up by a superposition of the wave functions of the photons. A QFT derivation can be found here .

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  • $\begingroup$ Actually, a single photon can carry a quantum of $\hbar$ of angular momentum. In fact, for OAM one photon can carry an amount of $\ell\hbar$, where $\ell$ is any integer. However, this is only valid if the spatial degrees of freedom of the photon is an OAM eigenstate. $\endgroup$ – flippiefanus Oct 27 '17 at 4:46

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