Horns
We may use an aperture method to determine the parameters of waveguide fed horns.  This is a reasonable approximation provided the gain is greater than about 15 dB.  Small gain horns have significant current flowing on their outsides whose contribution to the pattern needs to be included in the analysis and synthesis.
Below the aperture approach is used to design and analyze horns. We could use a mode match technique for rapid analysis or use a slower method of moments or time domain code to analyze horns.  Even the mode-matching approach requires the addition of external currents when the gain is low.  A series of programs can be downloaded and run in a DOS window for the design and analysis of horns.  Remember these programs are internally consistent, but all rely on an aperture approach. The programs produce designs within about 0.1 dB gain which was verified using the slow analysis methods.
          RHOPTG (Linux version) - Pyramidal horn designed to gain
          REBWDN (Linux version) – Pyramidal horn designed for given beamwidths
          HORNPY (Linux version) – Pyramidal horn parameters from dimensions
          CIRHDN (Linux version) – Circular TE11 mode design to gain
          CIRBWD (Linux version) – Circular TE11 mode design to beamwidth
          HORNCI (Linux version) – Circular TE11 mode parameters given dimensions
          CORHDN (Linux version) – Balanced hybrid mode corrugated horn designed to gain
          CORBWD (Linux version) – Balanced hybrid mode corrugated horn designed to beamwidth
          HORNCO (Linux version) – Balanced hybrid mode corrugated horn parameters from dimensions