Imagine an electromagnetic wave (a monochromatic one for example). The electric field amplitude and its variations travel in the propagation direction.
So, if there really exists a propagation direction, what happens in other directions? I mean, is there an oscillation in those other directions? Does something (electric or magnetic field) move in those directions? Does it's speed in those direction depends on frequency,or is this wave infinitely thin? Is it not covering any space in other directions?
I have seen many graphs showing that the field variation is not in the direction of propagation, that "means", based on polarization experiments that it's not a Longitudinal wave, It's a transverse wave.
If I accept that the field is not varying in the propagation direction (it just goes forward in that direction), then I could think it's varying in other directions, but in what direction?
Perhaps we can't say it's varying in any direction, it's not a spatial variable. I just can't imagine how the field variation is distributed in space.
Electromagnetic waves just move in one single spatial propagation direction.. then all spatial concepts that take account other directions are wrong, like "polarization" and "transverse wave" definition
Electromagnetic waves moves in others directions too, then speed of propagation in those other directions could depend on frequency, and thats weird, but who knows!
EDIT 2 (Add my comment as part of the question)
If there are infinite wave planes, then imagine a light that is turned OFF and then is turned ON, comparing the EM, first it is covering nothing, and then suddenly reach "infinity" (or at least very far..in fact any distance is enough), what is the speed of THAT propagation? because it is NOT a wave propagation, because is not in the direction of propagation, that infinite or very large field extends itself at infinite speed?