Q: Elliptical polarization and waveguides It is known that a generic harmonic electric field which propagages in free space has an elliptical polarization (if you want to read the proof, look at this, slides 72 - 99).
My question is: what about the polarization of E and H fields in a waveguide or a transmission line? I have always read about elliptical, circular and linear polarization for electromagnetic waves in free space, but I have never heard/found something referred to guided waves. So, I'll say that waves in waveguides are simply linearly polarized. But:


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*I do not know if this is true. I have never read also the sentence "Waves in waveguides have linear polarization".

*I do not understand why we cannot have elliptical polarization in waveguides. As you may see from the slides is the consequence of the harmonic behaviour of E and H fields, which is described by the wave equations. In theory, it is true also for waveguides...

A: Let's directly answer your questions, first, then address your misconception:

So, I'll say that waves in waveguides are simply linearly polarized

That can't be the case. How would you, in a round waveguide, like a circular tube waveguide or, very prominently, a coax cable, satisfy any boundary conditions with a linearly polarized wave (in cartesian coordinates, at least). 
You can very well have a waveguide with e.g. a circular polarization; for example, when you open a satellite dish feed (satellite TV is circularly polarized), there's parts of the waveguide system that are linearly polarized (because that's easy to pick up with a monopole) and parts that are circularly polarized, and there's the transition between the two.
So, nothing to see here: wrong claim, can't be justified.

Polarization is something that you define from the direction of the E-field. 
In free-space propagation, that's easy: at any given time and point, a plane wavefront will have exactly one direction of the E-field.
It doesn't work if you have a mode propagating in your waveguide that has more than one half-wave width. Higher-order modes usually can't be assigned any polarization at all; not even an elliptical one. The concept polarization doesn't apply!
