Dual-band feed horn

A radio frequency (RF) horn can include an interior surface with an inner geometry comprising irregular, aperiodic corrugations and/or undulations. The pattern of the inner geometry can excite higher order modes simultaneously in two RF signals each at a different frequency that combine with fundamental modes of the signals to produce substantially Gaussian profiles of the two signals at the output aperture of the horn. Even though the signals are at different frequencies, the illumination pattern of both signals on a reflector antenna at which the horn is directed can be substantially the same.