Thanks.
I was thinking that since the E field is always in the plane orthogonal to the progagation direction, that the orientation of the E field must depend on (x,y,z). i.e Different locations would have different progagation directions, so the E field would be oriented differently.
Suppose we have a fixed coordinatre system (x,y,z). Suppose an antenna is horizonally polarized. Is the orientation of the E field fixed as a function of (x,y,z). Or does it change?