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Vortex generation and inhomogeneous Faraday rotation of a nonparaxial Gaussian beam in isotropic magneto-optic crystals.

We study the propagation of a nonparaxial Gaussian beam in the isotropic Bi₄Ge₃O₁₂ crystal under an external magnetic field. The analytical solutions in the paraxial limit are derived, which show that a vortex with topological charge m=2 (m=1) generates in the E_ (E(z)) component. Numerical calculations in the nonparaxial regime confirm that, with the assistance of an external magnetic field, the spin-to-orbital angular momentum coupling effect can occur even in the isotropic crystal. We also study the Faraday rotation of the nonparaxial Gaussian beam. At the center of the transverse plane, the rotation of the plane of polarization is linearly proportional to the magnetic field. However, the rotation is not uniform on the whole transverse plane, manifesting the nonparaxial effect.