Gravitational waves with distinct wavefronts

Exact solutions of Einstein's vacuum equations are considered which describe gravitational waves with distinct wavefronts. A family of such solutions presented recently, in which the wavefronts have various geometries and which propagate into a number of physically significant backgrounds, is here related to an integral representation which is a generalization of the Rosen pulse solution for cylindrical waves. A non-diagonal solution is also constructed which is a generalization of the Rosen pulse, being a cylindrical pulse wave with two states of polarization propagating into a Minkowski background. The solution is given in a complete and explicit form. A further generalization to include electromagnetic waves with a distinct wavefront of the same type is also discussed.