  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.
