  In analogy with radiation fields for asymptotically Euclidean manifolds,
introduced by F.G. Friedlander, we define radiation fields for asymptotically
hyperbolic manifolds. We use them to give a translation representation of the
wave group and to obtain the scattering matrix for such manifolds. Furthermore,
we prove a support theorem for the radiation fields which generalizes to this
setting the well known support theorem of Helgason and Lax and Phillips for the
horocyclic Radon transform. This is used to show that the manifold and the
metric, up to invariants, are determined by the scattering matrix at all
energies.
