Transverse waves are characterized by the fact that the particles of the medium vibrate perpendicular to the direction of propagation of the wave. This means that the wave has two possible directions of vibration, perpendicular to each other and to the direction of propagation.

On the other hand, plane polarization occurs when the vibration of the particles of the medium is restricted to a single plane. This means that the wave has only one possible direction of vibration, and it is said to be plane polarized.

Therefore, plane polarization does not occur in transverse waves, because transverse waves have two possible directions of vibration.