How Can I Mathematically Represent the Polarization of a Laser Beam?

[Asierro]

Hi, I'm new to this forum, and I need some help with this.
I want to determine the polarization of a laser beam, that is, the type of polarization (linear, elliptical), the angle of polarization (if it is linear). Then, I want to represent this mathematically.
I used some linear polarizers to find the polarization of the laser, passing the laser beam through the polarizer to a wall. I found the angle in which the laser light was more intense (bright) on the wall, and then started spinning it slowly, wanting to find the angle in which the intensity after the polarizer was zero (90º from the brightest angle). However, there was no point in which there was no light behind the polarizer. So I thought the polarization had to be elliptical.
I also tried to find Brewster's angle, but there was no angle without reflection, so I confirmed the laser beam is not linearly polarized.

Getting to the point, I have a photometer so I can determine the intensity of the laser beam at certain angles, but how, with that information, can I represent the polarization that I have? Is this method OK, or, what method should I follow so as to get relevant information? Some webpages (such as this one: http://en.wikipedia.org/wiki/Elliptical_polarization) say how this is done, but I sometimes don't know what each letter means since it is not always clarified?
Please someone help me, I'll really appreciate it. Thanks in advance.

(Please if you quote any webpage please let me know the source, and excuse my writing, English is not my native language)

 

[UltrafastPED]

I would first check the technical specifications provided by the manufacturer for that model; the most common polarization is horizontal, though they may have installed a wave plate (or two) so that it outputs vertical or circular. Some lasers make it easy for you to adjust the polarization.

The generation of linearly polarized light is most often done via a Brewster window (slope cut at the Brewster angle) as the exit from the lasing cavity; this will have a fixed orientation, but the following wave plates will adjust the final output polarization.

What kind of laser are you working with?

BTW, your technique of "watching the wall" is unreliable because the human eye is a very poor "brightness" measurement tool - this helps you to see well in dim light as well as bright light, but the photometer is a much better tool for this.

You should then mount your polarization analyzer so that it can be slowly rotated (with the major axis marked as reference); then you can record angle vs intensity for a 180 degree rotation, and when you plot the points you will know the polarization axis.Forget the Wikipedia article; this "optics lab" project will provide much better guidance:
http://www.colorado.edu/physics/phys3340/phys3340_sp14/CourseInformation/Optics/Polarization%20Lab%202012%20v6.pdf