The Faraday effect has been investigated in various fields of study since 1845. In this paper, we provide a unified formulation of the effect for several media. In the classical case, the direction of propagation is parallel to the magnetic field. Here we generalize to any direction of propagation. When describing the state of wave polarization, we find it convenient to use the complex polarization ratio R plane. On the complex R plane, the change of polarization as the wave propagates follows a circle. The resulting polarization loci are illustrated for three different lossless media: a biaxial medium, a chiral medium, and a magnetoionic medium. Through the analysis of the patterns of these loci, we can visualize the generalized Faraday effect on the polarization state diagram and also gain some physical insights into these media in terms of their wave polarization characteristics.
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