Corner Cube Polarization
I won't say that this is mission-critical, but this is an opportunistic exploration of the properties of corner-cubes that is not well represented in the literature. The particular issue is: if you send polarized light at a retroreflector, what is the polarization state of the returning light? It isn't linear. In general, it will be elliptical. I found one paper in the literature that treated the problem via polarization Jones matrices, but the paper actually got the problem wrong in the way it handled coordinate systems. When I did the calculations from scratch, I got wholly different Jones matrices that predicted wildly different output polarizations. My answer was validated by a paper with actual measurements of the polarization.
Now I want to extend the work to allow variation of the incident angle to the corner-cube: not just restricted to normal-incidence. This could be a nice piece of work to put into the optics literature.
In the context of APOLLO, we care about this because our laser is polarized, and is routed by the T/R switch via a dielectric coating with vastly different reflection/transmission coefficients for P-polarized or S-polarized light. The laser output hits the mirror in the P-polarization orientation, getting about 10-5 transmission. S-polarization is 1.5 orders-of-magnitude more transmissive. When the light comes back from the corner cube, it has a tweaked polarization state, and the amount transmitted by the reflective coating and intended for the receiver depends crucially on this polarization state. Since we want roughly 1010 attenuation, we will use two such coatings. P-polarization would indeed get 1010 attneuation, but S-polarization might get only 107 attneuation, which is a huge difference.
My calculations indicated that the return light is very nearly in the P-state, with only about a 7° rotation, and slight ellipticity (for perfect normal-incidence). So we should get fairly good attenuation. But it would be nice to carry out the full calculation correctly so we could know exactly what size corner cubes and what coating specifications to aim for.