A theorem on the polarization of null-free antennas

This paper presents an extension of previous works by Mathis and Saunders, who showed that one will always find both linear polarization and polarization other than linear on the far-field sphere of a null-free antenna. It is shown in this paper that a null-free radiation pattern must contain all axial ratios (ratio of semiminor to semimajor axes) of elliptical polarization ranging from -1 (circular polarization of one sense), through zero (linear polarization), to +1 (circular polarization of the opposite sense). It is also demonstrated that the results of Mathis and Saunders are easily recaptured by this proof.