Polarization of photon emitted after absorption If a vertically polarized photon is absorbed by an atom (bringing an electron to a higher orbital), and then later a photon is emitted as the electron returns to the lower orbital, will the photon still be linearly polarized?  Is there a function that describes the angle of the photon's polarization as a function of the direction the photon is emitted?
 A: The photon can have any polarization that is allowed by the angular momentum of the excited state and the open electron orbitals that the excited electron can fall back into.  It is naturally the case that it is always permitted for the emitted photon to have the same momentum and polarization as the initial one.  However, the emitted photon is not restricted to be moving along the same direction as the original photon, which means that the allowed polarization states are generally quite different; both linear and circular polarization states are generally allowed.  The final polarization vector $\hat{\epsilon}'$ must satisfy $\hat{\epsilon}'\cdot\vec{k}'=0$, where $\vec{k}'$ is the wave vector for the outgoing photon.  Generally $\vec{k}'$ and the incoming wave vector $\vec{k}$ are not parallel or antiparallel.  This means there is a different space of polarization vectors for the outgoing photon, than for the incoming one, for which the polarization needed to satisfy $\hat{\epsilon}\cdot\vec{k}=0$
There are, of course, correlations between the polarization that is initially absorbed and what polarizations can be emitted, since the angular momentum taken up in the absorption process determines the initial angular momentum state of the emission process, as well as which lower-energy orbitals are unoccupied.  However, the correlations are complicated to express and not at all universal; they depend in detail on the identity and initial electron configuration of the atom.
