Radiation pattern of a corrugated conical horn in terms of Laguerre-Gaussian functions

Many papers can be found on radiation properties of corrugated feeds. The radiated field is described either by means of the Kirchhoff-Huyghens formula, or with a spherical mode expansion. In both cases, especially where the horn is long, the computation may be important. In this letter we present a third method founded on a Laguerre-Gaussian expansion in cylindrical coordinates.