Connection between Polarization and Coherence in optics

Question

It is not completely clear to me how the notions of polarization and coherence, in optics, work together! I quite understand both of them but it's still hard to grasp their deep connection.
I'm quite familiar with the mathematical description of polarization for both perfectly polarized waves (Jones calculus) and non-perfectly polarized ones (Stokes parameters), so you can give me example in terms of them if you like. I'd say that if you have a non-coherent wave, for instance of the kind $\mathbf{E_0}e^{i(kx-\omega t+\phi(t))}$, you'd just average over the phase too to take into account non coherence.. how does this effect polarization practically? Can anyone give me some insight or specific example?

Thanks!

Answer 1

Polarization and (temporal) coherence/phase of a light wave are two different, yet completely unrelated concepts. So there is no deep connection.

• Polarization has to do with the fact that the electric field is a vector and hence has a direction. This applies to static fields as well, although one does not speak of polarization here, but merely just "direction" (but the meaning almost the same).

• Phase of a light wave, or the (temporal) coherence, is a property that all waves have, e.g. radio waves, digitally generated waveforms in a computer, sound waves, etc. (where the latter are scalar waves, so there is no equivalent of polarization).

To put it mathematically: The polarization is encoded in the angle of the vector $\mathbf{E}_0$ (and poteltially the wave vector $\mathbf k$) and the temporal coherence in $\phi(t)$.