We have the following equation.s for the E field of a wave : $$ \dot{E} = \left[ \hat{x} + 0.75 \hat{y} + \left( 2 + j \ 5 \right) \hat{z} \ \right] \ e^{-j \ 2.3 \ \left(-0.6 \ x \ + \ 0.8 \ y \right)} $$
I know that in order to determine the polarization I need to look at the phase difference between the electric field components but I'm having trouble here as I usually have only two components.
The electric field is in the plane orthogonal to the wavevector, the latter being proportional to $\vec{k}\propto -0.6\hat{x}+0.8\hat{y}$ (Check this assertion).
So, all you need to do is find an orthonormal basis - any such basis for this plane orthogonal to $\vec{k}$ and resolve the electric field components onto this basis - the complex quantities so gotten are the components of the Jones vector relative to that basis (and polarization is always defined relative to a basis of the plane transverse to $\vec{k}$ that must be chosen for a full specification).
I would suggest that the vectors $e_1 = \hat{x} + 0.75\hat{y}$ and $e_1 = \hat{x} + 0.75\hat{y} + \hat{z}$ are linearly independent and both orthogonal to $\vec{k}$, thus they span the plane you need. They're not orthogonal, though.
So make an orthonormal basis out of these two, using the Gramm-Schmidt procedure to do so - then calculate your Jones vector.
