Physical Interpretation of Poynting Vector

Question

I'm looking for a physical interpretation of the Poynting Vector. I understand that it should be thought of as an energy flow due to the electromagnetic field, but would I be correct in saying that in some sense it's equivalent to a photon flow/packet? After all, for an electromagnetic wave, the poyntig vector yields the direction of propogation, or the direction in which the photon is moving. Does this analogy apply in general?

Answer 1

Yes, you are basicaly right.

The Poynting vector gives you the momentum of the the EM wave. At the quantum level, it is an operator of the form (see page 7 of http://www.physics.usu.edu/torre/3700_Spring_2013/What_is_a_photon.pdf) : $$\hat{\mathbf{P}} =\sum_\mathbf{k} \mathbf{k}\, \hat a^\dagger_\mathbf{k} \hat a_\mathbf{k}$$ for a given polarisation (here $\hbar=1$).

This, if the system has just one photon with momentum $\mathbf{q}$, the average value $\mathbf{P}$ of the Poynting vector will be $\mathbf{P}=\mathbf{q}$ has you would expect.