A PCS works by taking the beam of focused light and splitting the light into two different polarizations, S and P. The P vector is denoted as an arrow and stands for light incident with its electric field vector parallel to the plane of incidence. The plane of incidence is defined as the plane which contains the surface normal vector and the incident ray propagation vector at the point where the ray hits the surface. In Figure 1 below, this is the plane of the paper or screen.

In the figure below, the S vector is shown as a letter O denoting the tip of the vector out of or into the page or screen. S stands for the German word for perpendicular which is senkrecht. In a PCS array there are two rhombs with a polarizing beamsplitter coating between them. The entry and exit faces of both rhombs are coated with broadband antireflection coatings.

The polarizing beamsplitter coating has a high reflectivity for S polarization and a high transmission for P polarization. In the above figure we can see that the unpolarized light is incident on this pair of rhombs and when it hits the interface of the two rhombs it encounters the PBS coating on the interface between the rhombs. This coating reflects the S polarization downward and transmits the P polarization straight through the interface. This means that the two beams exiting the upper and lower rhombs have linearly polarized light but it is oriented at 90 degrees from each other.

Now, a half-wave plate is introduced to one of the beams, in this case the lower one:

The half wave plate's function is to rotate the S polarization that transmits through the rhomb interface into P polarization. With the addition of the half-wave plate to the rhombs with S polarization we now have all light exiting the PCS array as P polarization, which is what we need for operation with the LCD and LCoS panels. Note of course the waveplate could have been introduced into the upper channel instead, so that the output would be S polarized