# Polarization Measurement

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.

-
And how is the plot called one obtains by means of the measurement ("transmitted intensity of a linear polarized laser beam through a step-wise rotated linear polarizator") described above? –  user21079 Feb 17 '13 at 17:58

The polarization ellipse is not defined as the plot in polar coordinates. The polarization ellipse has $E_x$ and $E_y$ (if $z$ is the axis of propagation) as abscissa and ordinate.

-
This is correct, but needs more explanation. Fred indeed had a wrong interpretation of an elliptical polarization. The cosine transmission from the polarizer is not the ellipse when we refer to elliptical polarization. In fact, I have never seen plotted that cosine in a polar plot; it is quite misleading. A cosine that goes from 0 to 1, for example, is a linear polarization. That's clear because the extinction proves there is no component in one axis. For different contrasts of the cosine, you get a non-linear polarization, for example elliptical. –  fffred Jun 18 '13 at 4:16

I'm not sure, if I understand your question. Please elaborate a bit further. For starters, this demonstration at wolfram.com may be of help http://demonstrations.wolfram.com/VariableStatesOfPolarizationIncidentOnAWavePlate/.

If you're actually making polarization measurements and are confused by what it all means, check this out: Rotating Quarter-Wave-Plate Stokes Polarimeter.

possibly you may also want to look up the stokes parameters of polarization on Wikipedia,

-
Usually, your are measuring the intensity of the laser beam that is modulated (altered) by the wave plate with a photo diode. therefore in your plot you would have the intensity of the laser beam in volts as a function of the rotation angle of the wave plate. –  lomppi Feb 17 '13 at 19:58
The difference between linear horizontal polarized and linear vertical polarized is that you either have a sine or cosine intensity profile. which one you get depends on how you define the angles of the axes of your wave plate in the actual set-up –  lomppi Feb 17 '13 at 20:00
So which information actually contains the "intensity over polarizator angle" polar plot? –  user21089 Feb 17 '13 at 20:52
Did you actually visit any of the links I posted earlier? There are some examples of measurements in the Rotating Quarter Wave Plate Stokes Polarimeter link. The information in that is contained in this plot is the very polarization of your laser beam, i.e. the quantity you wanted to measure in the first place, if i understood correctly. –  lomppi Feb 17 '13 at 21:20