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.

• 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". Commented Dec 17, 2011 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
Commented Dec 17, 2011 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. Commented Dec 17, 2011 at 2:58

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.