If memory serves me right, the beam dispersion in degrees is equal to 90 / (opening size / wavelength). So, for zero dispersion, you would need an infinitely wide opening. Also, note that one of the implications of this formula is that to get low dispersion numbers you have a wide opening which means that the power density starts out lower.
A pipe the diameter of the wavelength is a waveguide, not a horn, and will emit microwaves in all directions from the opening of the pipe.


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