Elliptically Polarized Waves and Antennas

Various properties of elliptically polarized waves and antennas are investigated by utilizing a complex vector method. Well-known relations derived for linear polarization appear as special cases of more general relations for elliptical polarization. A geometrical representation of complex vectors provides a corresponding geometrical interpretation of many of the results obtained. Elliptically polarized fields are resolved into "orthogonal' elliptically polarized components, of which linear and circular components are special cases. Formulas are obtained relating to the polarization ellipse, the polarization pattern, ellipticity, phase, and sense of polarization. A unit complex polarization vector and complex transmission and reception vectors are introduced to represent respectively the state of polarization of a given field, the field transmitted, and the voltage received. With the aid of these vectors, the transmitting and receiving properties of antennas are obtained. The notions of radiation pattern, gain, beamwidth, and phase are examined. Measuring techniques involving linearly polarized and circularly polarized field components are discussed and compared for accuracy. A power transfer equation between two elliptically polarized antennas is obtained in terms of the gains and polarization characteristics of the two antennas, and is applied to special cases.