I polarize the slits (one H, the other V) of a Young's double-slit. If my source is H or V, do I see fringes? What about if my source is D or AD? In my journey to understand light better, I build a "polarized Young's interferometer".  Imagine the following polarizations: horizontal, vertical, diagonal, and anti-diagonal (H, V, D, and AD).  I place an H sheet polarizer over one slit, and V over the other.  I use a polarized laser source.  Finally, I place a D sheet polarizer "mixer" between the polarzied Young's and the observation screen.  I orient the source to explore the output of the four inputs above (H, V, D, and AD).  What are the results of my journey?  Do I see fringes for H?, for V?, for D?, for AD?  If I see fringes, are they always the same phase?  (Note that D input means colinear with the mixer, and AD input means perpendicular to the mixer.  Also, the lines on the polarizers refer to the transmitted electric field axis of sheet polarizers and do not denote wire polarizers.  Assume I conduct this experiment at a visible laser line with slits ~1.5 mm center-to-center, and each ~0.5 mm wide.  I find it safe to assume that the bare slits have a negligible effect on polarization, and that the sheet polarizers are very efficient.)
 A: Since light must travel through both slits for an interference pattern to be seen, when the source light is H or V, no interference will occur since the incident light will only be able to pass through one slit.
When the incident light is D or AD, an interesting situation occurs.  Depending on how narrow the slit widths are, the slit itself has a tendency to polarize the light (which we can define as the V orientation).  These means that very little light will get through the slit with the H polarizer placed over it regardless of the polarization of the incident light.
Therefore, even in the case of D and AD essentially no interference pattern will be seen. You have basically designed an experiment that for all practical purposes prevents the incident light from going through both slits.  And, this is the case for any and all polarizations of the incident light.
A: In your setup you cannot get two slit interference if the photon source is all vertical or all horizontal but keep in mind you will still have single slit interference. If the photon source is all diagonal or all anti-diagonal then your setup will get two slit interference.
