A numerical parametric study is presented, of a circularly polarised square hard horn realised by dielectric-filled longitudinal corrugations. The horn is analysed as an open waveguide. The attenuation introduced by losses in the dielectric material is calculated from the characteristic equation of the modifiedTE10mode. The far field, including radiation from the walls, is found from the electric vector potential. The attenuation, aperture efficiency and crosspolar sidelobe level are presented for different dielectric linings and waveguide sizes, and are compared with the performance of the smooth-walled horn.