Descriptions and images of right or left circular polarization do differ based on a viewpoint being either behind or in front of the wave source. Furthermore, I see pictorial representations that do not seem to match the stated polarisation. For example, the Wikipedia article on the spin angular momentum of light has a diagram that gives left and right polarization stated as looking towards the wave source, but I think the red vectors are incorrect:


I want an easy-to-remember starting point to check all the polarization representations I see. Is it correct to remember that the field vector rotates clockwise ↻ for right circular polarization when viewed from behind the wave source and counterclockwise ↺ when looking at the wave source?


1 Answer 1


Ok, Wikipedia has by far the best answers.

There are two conventions.

My preferred convention follows the right hand rule. If I point my thumb along the $k$-vector for the beam my figures curl in a certain direction. The the $E$-field vector rotations in time at a fixed position in the same direction as my finger curl I call that right circularly polarized. In this case the $E$-field vector rotations in time in the clockwise direction when viewed from behind (from the source), or the counterclockwise direction when viewed from in front (from the target). Left hand circular is the opposite.

There is a second convention which defines right circularly polarized light as light that rotates clockwise when viewed from the target. I'm not sure when or why this convention is preferred.

Note that here I'm talking about beams of light, But, multiple beams that are all crossing in a single plane, and also with polarization in plane, can generate circular polarized light with respect to an axis out of the plane. More generally we define a reference axis $\hat{n}$ and circular polarization is defined with respect to that axis. My preference is that $E$-field rotating around this axis in a right hand rule sense is called right hand circularly polarized with respect to that axis. For beams of light we typically choose $\hat{n} = \hat{k}$, but in some cases that is not appropriate. Note that under this convention the magnitude of the right circularly polarized component of light at a given point in space is proportional to the projection of spin angular momentum of light onto the reference axis at that point in space.


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