A formal, exact solution is obtained for the electromagnetic field radiated by a dipole antenna of electric or magnetic type oriented normal to the striations of a periodically stratified dielectric medium of fairly arbitrary profile. The scalar potential functions appropriate to each excitation are evaluated asymptotically by the saddle-point technique. The case of magnetic dipole excitation of a sinusoidally varying medium is studied as an example. It is found that, for frequencies greater than some minimum value, the emitted radiation is characterized by the presence of caustic surfaces which confine most of the radiated power in the broadside direction. The caustics increase in number and colatitude angle with increasing frequency.