How do horn antenna work? When looking at horn antenna simulations the strength of the propagated wave is directionally dependent.(this is the entire reason they exist)
I am wondering how this is able to be done?
Basic beamformers use a collection of dipole or monopole antenna and use linearity to create directions where the waves add in phase to amplify signals.
The mechanism by which horn antennas work is not at all clear to me. How can you eject an EM wave in only one direction? Shouldn't a radiative element eject EM wave in all directions?
 A: *

*Imagine an ideal dipole radiator.

*cut in half and place in the middle an ideal mirror, this is a grounded monopole. At RF the mirror is just a metal plate. The radiation from the monopole goes in all direction but the mirror also reflects so only in one half plane where you find radiation.

*now "slowly" fold and stretch the mirror around the radiator to form a tube in a perpendicular direction to the monopole. The tube is a waveguide in which the monopole radiates. While you are folding you must make sure that the monopole is still matched to its feed line otherwise there is no radiation. In practice, this means that the natural bandwidth of a monopole is reduced at the cost of being able to radiate in to the tube. To help with matching you let the tube have a flare going  away from the source. The broader the flare the easier is the match. Also, the waveguide should support a single mode only so the phase and amplitude of the field inside be easy to control.

*cut the tube somewhere to end it, and keep matching for there is a reflection at the end of tube; now you have a horn antenna that matches the free space impedance $120\pi \Omega = 377 \Omega$ to the feed line of the monopole, usually $50\Omega$.
Every point of the horn aperture is a source of an elementary Huygens spherical wavelets that because of the way you formed the tube/flare and the proper impedance matching is approximately in phase with each other, hence, the radiation is essentially axial and confined by the horn.

Usually, one has a waveguide with one end shorted by a metal wall and the monopole "launcher"  is placed about a quarter wavelength from that wall so when the wave reflects in the opposite phase at the metal mirror and also travels two quarter wavelengths to catch up with the other half of the wave it will be in phase with the other wave propagating already in the desired direction. By adjusting the wall distance, the thickness and depth of the probe you can match the impedance of the launcher as it loads its feed line. This will not be enough though, you also need to make sure that while the waveguide has only a single mode propagating when it hits the flare the reflections are minimized and not allow multiple uncontrollable modes to arise. Instead, you shape the flare (grooves, ridges, teeth, etc.) so that the modes launched at the transition between the single-mode homogeneous guide and the flare are controlled. In fact, the best horns use in addition to the fundamental mode from the waveguide several higher order modes to "flatten" the phase distribution at the end of the flare, i.e., the aperture, and also to control the amplitude distribution for that determines the radiation sidelobes.
