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Realization of high-efficiency rectangular horns is investigated by means of mode generation and profile optimization. Conditions required for maximum efficiency of an aperture array are derived and made specific to a rectangular aperture with twofold symmetry. It is shown that aperture coupling has a significant effect on aperture efficiency through mode coupling. Efficiencies in excess of 100% are predicted for aperture sizes that are slightly greater than an odd multiple of half-wavelengths. The method described here results in more compact horns than obtained by using conventional linear tapers or steps. Results are presented for horns suitable for array feeds or directly radiating array applications that achieve aperture efficiencies close to 100% with horns of aperture size ranging from 1.25 to 3 wavelengths and at the same time have a return loss 20 > dB and cross-polar isolation > 22 dB. Measured results are given for an experimental compact horn that has high efficiency over an 8% bandwidth. The agreement between computation and measurement is within the limits of experimental error and this is obtained without any special surface treatment on the inside surfaces.