The invention relates to an antenna device having a printed circuit board and at least one antenna radiator which is arranged on the printed circuit board and can be excited by the printed circuit board or a coupling window arranged thereupon, which radiator is designed in such a manner that it comprises at least two polarisations, which are preferably orthogonal to each other, and at least two resonance frequency ranges which are continuous or different to one another and at an interval from one another, wherein the antenna radiator comprises: at least one first dielectric body mounted on the printed circuit board and designed as a resonator, having a first relative permittivity, at least one second dielectric body designed as, having a second relative permittivity, wherein the first relative permittivity is greater than the second relative permittivity and wherein the second dielectric body is formed in such a manner that it is arranged over the at least one first dielectric body in such a manner that it bundles or scatters the electrical field in a plane orthogonal to the main beam direction at least in one of the resonance frequency ranges. The invention also relates to an antenna array.