1. A horn antenna, comprising:a double-ridged waveguide input, having dimensions of width, a, and height, b, where the width and height comprise waveguide outer dimensions, and internal ridges having ridge width, w, with a gap dimension, g, between the ridges; and
a radiating aperture;
wherein the waveguide outer dimensions, a and b, and ridge width, w, increase smoothly and monotonically over a length of the horn from the double-ridged waveguide input to the radiating aperture; and
wherein the gap dimension, g, is given mathematically by one or more of the other waveguide dimensions (a, b, or w) raised to a power, p, over a majority of the length of the horn.