Diffraction by a conical horn

Abstract

The geometrical theory of diffraction is used to investigate the gain and radiation pattern of a conical horn excited by a circular waveguide operating in the TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> mode. A simple expression for evaluating the eigenvalues in the horn is derived and a systematic procedure is given for converting the field of the dominant mode into a geometrical-optics ray form. It is shown that the dominant contribution due to these rays may be attributed, in the principal planes of diffraction, to a pair of Brillouin rays emanating from a spheroidal mode-caustic generator. The edge rays excited at the aperture plane are also taken into account and their contribution is obtained as an asymptotic series in terms of the horn dimensions. Finally, it is shown that the ray-optical technique gives a physical insight into the diffraction mechanisms of a conical horn and leads to an excellent agreement with experiment.