For a PM component the ER is defined as:
are the intensities on the slow and fast axes respectively and phase is not considered.
The complete description requires reference to more general elliptical polarization such as Stokes Parameters and the Poincare Sphere. Google will bring up many excellent references, two of which have been summarized here for comparison with ER.
Figure 2 illustrates the polarization ellipse within a rectangle of sides
are the amplitudes of the slow and fast axis, and having major and minor axes a and b with phase difference
between the slow and fast axis beams.
Figure 3 shows the Poincare sphere and the related Stokes Parameters
It can be shown that
So the departure from linear or plane polarization is
which can be regarded as a modified Stokes parameter and taken as
for comparison with ER.
approaches zero the output is plane polarized at angle theta to the slow axis.