Propagation of electromagnetic waves is considered for a medium with (x, y)-dependent locally isotropic dielectric and magnetic susceptibilities ∊ik = ∊(x, y)δik and μik = μ(x, y)δik, i.e., for a waveguide. In the paraxial approximation the polarization is disconnected from the propagation. We have developed a self-consistent theory of the postparaxial corrections. It allows, in particular, for the description of intrafiber geometrical rotation of polarization and its inverse phenomenon, the optical Magnus effect, which are both determined by the profile of refractive index only and constitute spin–orbit interaction of a photon. The birefringence splitting of linearly polarized modes or meridional rays on the other hand, turns out to be dependent on the gradients of impedance , the quadrupole part of spin–orbit interaction. An important point of the theory is a transformation of field variables such that the z-propagation operator becomes Hermitian, in analogy with the transitions from a full relativistic Dirac equation to the Schrödinger–Pauli equation with spin–orbital corrections. A theoretical explanation is given for the phenomenon previously observed in experiment: preservation of circular polarization by an axially symmetric step-profile multimode fiber and depolarization of an input linearly polarized wave by the same fiber.
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