Optical ray theory is used to design a phase-corrected microwave horn antenna of shortlength which produces a tapered aperture amplitude distribution in the E-plane. The basis of the design is the creation of a region where the effective refractive index varies with hyperbolic secant (HYSEC) form in a direction normal to the horn axis. In a practical realisation this effective refractive index distribution is achieved in both smooth and stepped form by varying the plate separation of the planar waveguide supporting a TE01mode. Good agreement is found between predicted and experimentally determined aperture and far-field distributions. Finally, the study is extended to the design of a novel antenna incorporating dielectric loading which, in theory, allows for operation at even shorter horn lengths.