  We study the head-on collision of linearly polarized, high frequency plane
gravitational waves and their electromagnetic counterparts in the
Einstein-Maxwell theory. The post-collision space-times are obtained by solving
the vacuum Einstein-Maxwell field equations in the geometrical optics
approximation. The head-on collisions of all possible pairs of these systems of
waves is described and the results are then generalised to non-linearly
polarized waves which exhibit the maximum two degrees of freedom of
polarization.
