Spheroidal wave functions of large frequency parametersc = kfand the radiation fields of a metallic prolate spheroid excited by any circumferential slot

Stratton, Chu, Flammer, and others have dealt with spheroidal wave functions and expanded them into series of Legendre or spherical Hankel functions for frequency parameters
c = kf
less than about ten, where
k
is the wavenumber in free space and
f
is the focal length of the spheroid. However, when
c
is greater than ten, the series converges very slowly and even diverges. A method is devised by the present authors to calculate the spheroidal wave functions asymptotically for any value of
c
greater than ten using Wentzel-Kramer-Brillouin (WKB) and Langer transformations and the asymptotic characteristics of Airy functions. By means of the functions thus obtained, we calculated the radiation fields and input admittance of a metallic prolate spheroid of any length uniformly excited by any circumferential slot on the spheroid. The radiation patterns and input admittance obtained for some special cases conform very closely with known results.