A wide variety of desirable antenna beam patterns can be synthesized by optimal excitation and phasing of the HE11 and HE12 modes in scalar corrugated feedhorns. However, the bandwidth of such twomode horns is often limited by modal dispersion. In this paper we introduce a class of low dispersion, twomode feedhorns that can operate, in some cases, over operating bandwidths of 40-50%. We provide example designs that include horns with high coupling efficiency to: 1) a pure HE11 mode for single-mode excitation of corrugated pipe transmission lines; 2) a LG00 and LG02 combination for radiometry, with narrow beams; 3) a pure Laguerre Gaussian LG00 mode for quasi-optical instrumentation with constant phase centers; 4) a constant gain antenna for uniform illumination with frequency; 5) Airy patterns or "top hat" patterns for radar or communications applications, designed to maximize aperture efficiencies when used with larger reflect or lens antennas. More generally, we show methods to generate and phase multiple HE1n modes, to synthesize symmetric output beams at any desired frequency or gain.INDEX TERMS Aperture antennas, antenna feeds, corrugated horns, horn antennas, quasi-optics, ultrawideband antennas.