Why is Polarization of a wave important, and what happens when a wave is polarized in all three dimensions?

I don't quite understand this, I understand that given a wave traveling in a certain direction, it will be polarized in the direction its not travelling in, so if its travelling in the Z direction, k will be in x,y direction (polarization)

Now what i don't understand is that, if the wave is polarized in all 3 directions, x,y,z. which way will it travel?

also, for Tranverse magnetic, why is there no electric field normal to the plane of incidence?

i know this might be stupid, but what is the purpouse or use of polarization of a wave, in class we were just taught that a wave can be polarized, they never indicated why is the use of it.

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Hi Rave, and welcome to Physics Stack Exchange! By "transverse magnetic" are you referring to the TM mode of propagation in a waveguide? If not, perhaps you can explain what you mean by that to make your question more clear. Also, while you're at it, it would improve your question a lot if you phrase the title as a question, rather than "Waves and Polarization". – David Z Dec 17 '11 at 2:43
Hello, Zaslavsky Yes i am refering to the TM [transverse magnetic] mode of propagation in a waveguide. I have refined my title, thank you – Rave Dec 17 '11 at 2:48
OK, well in that case that will entail enough of an explanation that you might be better off asking it as a separate question. I'd suggest just removing the paragraph about the TM mode from this post and posting it as a separate question. – David Z Dec 17 '11 at 2:58

Generally an EM field contains three time dependent components, especially next to the source. Far from the localized source it is reduced to a transversal propagating wave with polarization perpendicular to the propagation direction.

An EMW determines the force acting on a probe charge. The force is a vector quantity, so the force direction is important. This direction is determined with polarization, not with propagation vector.

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1) We need polarization to define the state of the wave. Just "monochromatic wave traveling in $\vec{n}$ direction" is not enough. If you add polarization, it is enough.

2) Wave can not be polarized along its propagation direction. I did not completely understood what you mean by "f the wave is polarized in all 3 directions...". Probably you mean that you may construct non-monochromatic wave which has all components of a field in some region? Polarization is perfectly defined for monochromatic waves. In other cases it is better not use this word. However, if you could write explicit form of the wave you consider, discussion would be more constructive.

3) For the TM I thought it is a definition.

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