Energy streamlines: a way of understanding how horns radiate backwards

A small fraction of the radiation emitted by an open-ended waveguide or a pyramidal horn antenna escapes backwards around the edges by diffraction. Sommerfeld's exact solution for diffraction at an infinite half-plane is used to calculate the energy streamlines, and hence to estimate the thickness of the boundary layers of flux that escape around the edges of the horn perpendicular to the electric field. The thickness of the corresponding boundary layers for the edges parallel to the field is obtained by differentiation of the Sommerfeld solution. For the pyramidal horn used in our experiments, each of the two boundary layers parallel to the electric field has a thickness of 0.0515[Lambda] and each of the two perpendicular to the electric field a thickness of 0.0146[Lambda]. From this information it is estimated that the fraction of the total energy radiated that is lost into the backward hemisphere is about 2.2%. Virtually all of this is lost around the two edges perpendicular to the electric field direction. Measurements very close to the aperture plane using the modulated scatterer technique show the edge-wave associated with the boundary layer very clearly.