The propagation of a polarized Gaussian beam in a smoothly inhomogeneous isotropic medium

We present a description of the evolution of a polarized Gaussian beam in a smoothly inhomogeneous isotropic medium in frame of the eikonal-based complex geometrical optics which describes the phase front and the cross section of the Gaussian beam using the quadratic expansion of the complex-valued eikonal. The linear complex-valued eikonal components are introduced to describe the influence of the spin-orbit interaction and the deformation of a polarized Gaussian beam on the propagation firstly in this paper. In an inhomogeneous medium, the interaction between the polarization and the rotation deformation of the light beam is presented besides the spin-orbit interaction, it corresponds to the spin-intrinsic orbital angular momentum interaction and makes the correction for the spin Hall effect of a polarized Gaussian light beam.