The equation for evolution of the four-component Stokes vector in weakly anisotropic and smoothly inhomogeneous media is derived on the basis of a quasi-isotropic approximation of the geometrical optics method, which provides the consequent asymptotic solution of Maxwell’s equations. Our equation generalizes previous results obtained for the normal propagation of electromagnetic waves in stratified media. It is valid for curvilinear rays with torsion and is capable of describing normal mode conversion in inhomogeneous media. Remarkably, evolution of the four-component Stokes vector is described by the Bargmann–Michel–Telegdi equation for relativistic spin precession, whereas the equation for the three-component Stokes vector resembles the Landau–Lifshitz equation describing spin precession in ferromagnetic systems. The general theory is applied for analysis of polarization evolution in a magnetized plasma. We also emphasize fundamental features of the non-Abelian polarization evolution in anisotropic inhomogeneous media and illustrate them by simple examples.
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