Transverse, longitude shift and deflected angle from the spin Hall effect of a Gaussian wave packet

Replacing the saddle-point approximation extensively adopted in previous literature, an exact expression for the Fourier transformation of electric field distributions of reflected and refracted polarised Gaussian beams is derived to investigate the spin Hall effect of light. A general method based upon the partial differential of the light intensity distributions of the reflected and refracted propagating beams is presented to determine the beam shifts from the spin Hall effect of light. Compared with the previous integration method along one direction reported in the literature, our method not only is much more explicit, but also enables us simultaneously to obtain the transverse and longitude shifts of the reflected and refracted wave packets. Furthermore, at any propagation distance away from the interface between two optical media, the shifts of the propagating beams and their split ones can be analytically expressed by means of transverse- and longitude-deflected angles.