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cepheid

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You'll notice that the x- and y-components of the E field have the same phase. As a result, they'll vary with time together, and the ratio of their magnitudes will never change. Therefore, the overall direction of the E-vector won't change. That's how you can tell just by looking at it that the vector is linearly polarized and that it will always point along the same line.

If the x- and y-components did not have the same phase, then they would vary out of step with each other. The ratio of the x- and y-components would therefore vary with time, and as a result, the vector would change direction with time. This would correspond to a rotation in the plane of polarization. The vector is not linearly polarized in this case.

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You'll notice that the x- and y-components of the E field have the same phase. As a result, they'll vary with time together, and the ratio of their magnitudes will never change. Therefore, the overall direction of the E-vector won't change. That's how you can tell just by looking at it that the vector is linearly polarized and that it will always point along the same line.

If the x- and y-components did not have the same phase, then they would vary out of step with each other. The ratio of the x- and y-components would therefore vary with time, and as a result, the vector would change direction with time. This would correspond to a rotation in the plane of polarization. The vector is not linearly polarized in this case.

ok so if i had an equation like E=iE0sin(wt-kz)+ jE0sin(wt-kz-pi/4), i should be dividing one by the other to get the ratio of x to y and that will tell me if it is circular, elliptical or linearly polarized? so in that case it varies by a pi/4 component which would make it, elliptical? is there a graphical way to look at this, so i get what the waves look like from wikipedia and such but i dont understand how that translates to linear, versus circular since none of the pics look down the propagation axis.

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cepheid

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ok so if i had an equation like E=iE0sin(wt-kz)+ jE0sin(wt-kz-pi/4), i should be dividing one by the other to get the ratio of x to y and that will tell me if it is circular, elliptical or linearly polarized?

No, I wasn't saying that you explicitly had to divide them. I was just saying that you could tell at a glance whether or not it was linearly polarized based on whether the ratio of the magnitudes of the components was varying with time or not.

so in that case it varies by a pi/4 component which would make it, elliptical? is there a graphical way to look at this, so i get what the waves look like from wikipedia and such but i dont understand how that translates to linear, versus circular since none of the pics look down the propagation axis.

A quick Google image search of "light polarization" revealed many potentially helpful images. For circular polarization, it's clear that the two vector components have to have the same magnitude and be out of phase with each other by pi/2, since one would then be described by a cosine wave, and the other by a sine wave, and hence the total E-vector would clearly trace out a circle in the plane of polarization. For a more rigorous treatment of polarization that explains how you can tell the difference polarization states apart from each other mathematically I also find this set of optics lecture notes helpful:

http://atomoptics.uoregon.edu/~dsteck/teaching/optics/

Click on the link to the full PDF on that page and go to Chapter 8. Note: the author is making this freely available. He explains how elliptical polarization is the most general type, and all of the others are special cases of it.

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