Source Current Polarization Impact on the Cross-Polarization Definition of Practical Antenna Elements: Theory and Applications

With the growing interest in polarization diversity in communications and radar systems, the use of Ludwig’s second and third definitions has become controversial among scientists and antenna engineers. Therefore, this paper is an attempt to clarify some of the ambiguity and confusion caused by these definitions. A detailed comparison of Ludwig’s second and thirrd definitions of cross polarization, as applied to linearly polarized antennas, was performed. The results show that, in the diagonal plane, Ludwig’s second definition leads to a lower cross-polarization level than the third definition for <inline-formula> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula>- or <inline-formula> <tex-math notation="LaTeX">$y$ </tex-math></inline-formula>-polarized current sources. For a Huygens source, by Ludwig’s third definition, the radiation pattern has a lower cross-polarization level than that obtained by Ludwig’s second definition. For some applications, the antenna is usually placed in the <inline-formula> <tex-math notation="LaTeX">$y{z}$ </tex-math></inline-formula> plane. Therefore, new polarization bases are proposed according to which the source is used as a reference, and also on how this source is oriented in the <inline-formula> <tex-math notation="LaTeX">$y{z}$ </tex-math></inline-formula> plane. To complement the theoretical framework demonstrated in this contribution and to provide readers with a better and simpler understanding of the cross-polarization definition, the analysis of several practical antennas for diverse applications was presented. Numerical and measured radiation patterns of wire and printed dipoles, rectangular patch, pyramidal horn, and open-ended rectangular waveguide (OEWG) antennas were investigated according to the polarization formulations presented in this paper. In addition, a dual-polarized element and a dual-polarized active phased array at broadside were utilized to generalize the application.