The properties of the polarization ellipse are deduced in terms of the ratio of the Cartesian components of the complex electric vector of a beam of radiation by utilizing the Argand representation of a real two-dimensional vector as a complex number.
The two components of a beam that are accepted and rejected by a polarizer or a radio antenna are considered as orthogonal components in the directions of two complex orthonormal vectors. The intensities of the corresponding components of a polarized beam are derived and represented on the Poincare sphere. The methods are then applied to the important radio case of the Faraday effect in a uniform magneto-ionic medium. Finally, the measurable quantities characterizing a beam of partially polarized radiation are obtained from a diagonalization of the complex polarization tensor that specifies the beam.
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