Quantum theory of light What's the scattering matrix for a PBS (polarization beam splitter)?
Is it just unitary?
If one polarization never couples into another polarization (then there's a lot of zeroes in that 4x4 matrix) - is that impossible somehow?
 A: I think it's simplest just to propagate S and P separately, Then use the ABCD matrix for a mirror for the reflected polarization and the matrix for transmission (or no matrix at all :-) ) for the transmitted polarization.
A couple possibly useful references here.
One of a series of powerpoint lectures -- I haven't looked at the contents of the other 37.
Wikipedia's pages for Jones calculus  and ABCD ray tracing
A: 
quantum theory of light

Yes, there exists a quantum theory of light which turns into an  operator form  Maxwell's equations and  gives a wave function to a photon. The classical electromagnetic wave emerges from a confluence of individual photons with energy E=h*nu , the frequency of the classical wave. It is not a simple formulation, as one can see in this blog entry here. .
Once one deals with beams and polarizations and beam splitters it is a lot simpler/elegant  to use the classical formulations as given in the answer by Carl, since there exists a rigorous correspondence in the mathematical description between the quantum states and the classical ones for the case of light.
