Spin Hall effect of Airy beam in inhomogeneous medium

The spin Hall effect of Airy beam in the quadratic-index inhomogeneous medium is investigated based on the matrix optics method. It is known that Airy beam possesses an asymmetrical field distribution and some intriguing propagation properties, such as it is a non-diffracting, self-healing, and self-accelerating beam. We find that the spin Hall effect of an Airy beam in the quadratic-index inhomogeneous medium displays some distinctive polarization-dependent phenomena which are completely different from the traditional spin Hall effect of light. First, there is a polarization-dependent rotation of Airy beam induced by the spin-orbit coupling; second, there is a polarization-dependent phase front deformation of Airy beam induced by the spin-orbit coupling, besides the polarization-dependent shift of the entire phase front of the beam; third, transverse deflection of the center of gravity of the beam in the phase transition locations is determined not just by the polarization of the beam, but also by the position. These results mean that the symmetry of the field distribution of the beam also plays an important role in the spin Hall effect of light.