Asymptotic approximation and experimental study of electromagnetic fields excited by an electric dipole located over a conducting concave spherical surface

The dome antenna has been proposed for scanning an antenna beam at a high speed in a wide angular range. For the design of a dome antenna, an electromagnetic analysis in the concave side of the conducting sphere is required. In connection with this problem, the electromagnetic field by an electric dipole placed on the concave surface of an open conducting sphere has been reported and analyzed in terms of the sum of the whispering gallery (WG) modes, continuous spectrum and ν = 0 (ν: wavenumber in the θ direction) by the authors. However, it has been pointed out that this expression has a problem for an arbitrary ka, although it provides a valid result for ka = nπ/2 (k: wavenumber, a: sphere radius, n: integer). It is also unattractive numerically since Legendre functions must be calculated by numerical integration. In this paper, an engineering application is attempted by using a high‐frequency approximation. By means of the approximate asymptotic solution and the previous expression, actual numerical calculations have been carried out. By way of comparison with experimental results, the validity of each expression is confirmed and its range of applicability is studied.