Assume having a laser beam which is horizontal linear polarized. As one measure the sqrt(intensity) transmitted through a rotatable linear polarizer its pattern corresponds to a cosine. Plotting this in a polar coordinate system results in the so called "polarization ellipse". But the result is far away from being a (more or less) horizontal line.
But what does the polarization ellipse tell me?
My problem is that from the polar plot one may interpret that the original beam has E-Field components also in non-horizontal direction. But this is (ideally) not true. But only the polarizator has (excepted for the vertical position) components in horizontal direction leading to a transmitted field.