Not sure if you are pointing towards the actual phase plug patents or the foam plug. However, I do not find any of these patents useful. It looks to me like trying to fix a problem without actually fixing it. When you pressurize a horn via a dome, through an annular phase plug with multiple slits, and both the dome and the exit diameter are larger than a quarter og a wavelength, there is no way we can fully remove HOM just by altering the phase plug. The foam plug only act as a brake. Having a taller profile in the centre, it flattens the wave front slightly, but it does not actually resolve the issue with pressure differences as the brake is isotropic.