In the following case, the light at the left hole is horizontally polarized, and the light at the right hole is vertically polarized:
What's going on here? Both the intensity and the phase patterns are different from the 2-hole scalar and same-polarization cases. In particular, there is no interference pattern in the intensity. Also, the phase shown here is the phase difference between the vertical and horizontal components of the polarization. Here is the same thing in the z-y plane:
And in the x-z plane:
In all views, the intensity interference pattern is gone, and the phase pattern has been simplified. But what about the 2d distribution of polarization? Here is the polarization in the x-y plane:
Rather than seeing a single linear polarization, we now see a wide variety of both linear and non-linear polarization of both chiral senses (green and red) that are confined to specific regions or bands on the screen. Overall, it is clear that the interference pattern has moved from the intensity domain into the polarization domain. Also, note that while the two light sources are linearly polarized, the resulting field is not just a gradation between the two linear orientations, but includes both elliptical and circular polarization states. In general, almost all 1-bit polarization states are now represented at different 3d points in the field. Here is the resulting pattern in the z-y plane:
And in the x-z plane:
This example shows how a wide range of polarizations can be created from a small number of simply-polarized sources. These variations in polarization with respect to spatial location --which go from linear polarization through elliptical polarization to circular polarization, and then through elliptical polarization back to linear and then into elliptical and circular of the opposite sense-- can be used to support computation by providing the encoding for 1-bit states (at discrete points) and for 2-bit states (an extended 2d pattern). Slightly more complicated source distributions produce other, more complicated diffraction patterns which can also be used for computation, and small variations in the location, polarization, and overall phase of each source can be used to "tune" the field as desired.