2.2.3.   Polarizing Cube Beam Splitter

The beam splitter can also take the form of a glass cube. It can be a non-polarizing
beam splitter or a polarizing beam splitter. The second option has many advantages
that we will describe in Section 2.8.1, as pointed out by Bruning and Herriott (1970)
and Bruning et al. (1974).

Two important properties of the cube beam splitter are that the interferometer
is automatically compensated and that most beam splitter faces are all dielectric
with no absorption. If polarized light is used, some other important characteristics
are present. Figure 2.9 shows an interferometer using a polarizing cube
beam splitter, where all the P polarized component of the light beam is transmitted
while the S polarized component of the light beam is reflected. If the

incident light beam is linearly polarized in a plane at 45^o with respect to the
square cube edges the reflected intensity is equal to the transmitted intensity.
However, as mentioned before, if the mirrors M₁ and M₂ have different reflectivities,
a half wave phase plate can be inserted before the cube beam splitter to
maximize the fringe contrast. If the angle between the slow or fast axis of the
phase plate forms an angle θ/2 with respect to the plane of polarization of the
incident beam, this plane of polarization will rotate an angle θ. If the fast and
slow axes of the phase plate are interchanged by rotating the phase plate 90^o, the
phase or the output beam whose plane of polarization is rotated changes 180^o.
The S and the P components will have different intensity as desired depending on
this angle.

When the transmitted and the reflected light go to mirrors M₁ and M₂, both
beams pass twice through quarter wave phase plates with their axes at 45^o
before returning to the beam splitter. Thus, both planes of polarization will
rotate by 90^o. This allows the returning beams to go to the observing screen
instead of returning to the light beam. So, there is no returning complementary
interference pattern when using a nonpolarizing beam splitter. Both interference
patterns go to the observing screen, but we can separate them later, as we will
next describe. Figure 2.10 illustrates the polarization states at different points
along the light trajectories. We can see that after recombining and exiting the
beam splitter, the two beams are orthogonally polarized. So, interference cannot
take place. Let us assume that these two beams with S and P polarizations have
the amplitudes

where OPD is the optical path difference between the two beams. A λ/4 phase plate
with its axis at 45^o is placed after the beam splitter to transform these two beams into.

two circularly polarized beams with opposite sense. The total electric field due to the
superposition of the two fields along the slow axis can be shown to be

and along the fast axis

If we place a linear polarizer (analyzer) in front of these circularly polarized
beams, only the components along the axis of the polarizer forming an angle α with
the slow axis of the phase plate will pass through. Thus, the amplitude along this axis
of the polarizer is

which can be transformed into

or equivalently into

Hence, the interferogram irradiance can be shown to be

The conclusion is that the orientation α of the axis of the analyzer will change the
phase difference between the two interfering beams without modifying the contrast.
The phase difference between the two interfering beams changes linearly with the
angle. By turning the analyzer by an angle α, the phase difference will change by 2α.
This effect is frequently used in phase shifting interferometers.