Illustrate original/final polarizations with gnuplot

[zmitchell]

If you're running a simulation to see how some elements affect a beam, it's helpful to see a visual representation of the beam.

In general the polarization is an ellipse (linear and circular polarization are special cases), so this problem boils down to using the information in the polarization vector to plot an ellipse in Gnuplot. I want to use Gnuplot because it doesn't make sense to reinvent the wheel here.

To plot an ellipse you need to know the lengths of the major and minor axes, and the angle the ellipse makes with the +x-axis. Those equations can be found in the following (free) book:
Physics of Light and Optics - Section 6.3 (PDF)

In Gnuplot you plot an ellipse as a parametric equation. The parametric equations for a rotated ellipse can be found in this post.

The Gnuplot commands to plot a single ellipse would look something like this:

r_maj = ...
r_min = ...
angle = ...
fx(t) = ...
fy(t) = ...
set parametric
set trange [0:2*pi]
plot fx(t), fy(t) title "Ellipse"