Radiation pattern of electric and magnetic currents located near a smooth convex conductive surface of large electrical size

Using the parabolic equation method, approximate asymptotic expressions are obtained for the radiation patterns of electric and magnetic dipoles located near a smooth, convex conducting surface of large electrical size. These expressions are expressed in terms of the Fock function in the light, penumbra, and shadow regions relative to the field source. In the penumbra and shadow regions, they supplement known solutions based on the parabolic equation method with the following asymptotic term, which takes into account the torsion of geodesic lines (surface rays). It is shown that for surface sources, the obtained expressions agree with the corresponding expressions based on the uniform geometric theory of diffraction. The radiation patterns of arbitrary sources are found by integrating the products of the dipole radiation patterns with the current density over the source coordinates. General expressions are specified for resonant “half-wave” radiators: slots on the surface and vibrators elevated above the surface, as well as for conducting spheres and a circular cone. The numerical results for calculating the radiation patterns of half-wave slots and dipoles on a sphere, cylinder, and cone are in good agreement with the results of calculations by other authors and with calculations using the rigorous eigenfunction method. A simplified version of the formulas is proposed that does not require constructing geodesic lines on the surface and is suitable for calculating the radiation pattern in the light and penumbra regions.