Dual-band feed horn with common beam widths

A dual-band feed horn having a connection surface configured for connection to a waveguide and a first surface coupled to the connection surface. The first surface has a cylindrical surface with a length and a first diameter chosen to propagate TE11 modes for both a low frequency band and a high frequency band. The horn has a bandwidth ratio of the high-frequency band to the low frequency band in the range of 1.6-4.0. The horn also has a substantially conical surface coupled to the first surface at a first slope discontinuity. The conical surface includes multiple surfaces each having a respective slope and coupled to adjacent surfaces by a respective plurality of slope discontinuities each having a respective diameter. The slopes and diameters are chosen to generate primarily TM1,m modes (m=1, 2, 3, etc.) in the high-frequency band and primarily higher order TE1,n modes (n=2, 3, etc.) in the low-frequency band such that the low frequency band and the high frequency band have approximately equal beam widths.