Angular-momentum transformation and IF shift of refracted beams at axial-symmetric interfaces

We have shown that the optical angular momentum is conserved on both sides of the interface for a Gaussian beam with circular polarization incident on an axially symmetric interface. In particular, the difference between reflected and incident spin angular momentums (SAMs) in the axial direction is transformed into the orbit angular momentum (OAM) of the reflected beam. Under this conclusion, one can easily evaluate the Imbert-Fedorov (IF) shift of reflected and refracted beams, including the case of birefringence where the transmitted beams can be ordinary refracted beams or evanescent beams. Using this approach, the IF shift of refracted beams at the surface of hexagonal boron nitride is calculated.