Conservation of Angular Momentum, Transverse Shift, and Spin Hall Effect in Reflection and Refraction of Electromagnetic Wave Packet

Abstract

We present a solution to the problem of reflection/refraction of a polarized Gaussian beam on the interface between two transparent media. The transverse shifts of the beams' centers of gravity are calculated. They always satisfy the total angular momentum conservation law for beams, however, in general, do not satisfy the conservation laws for individual photons in consequence of the lack of the ``which path'' information in a two-channel wave scattering. The field structure for the reflected/refracted beam is analyzed. In the scattering of a linearly-polarized beam, photons of opposite helicities are accumulated at the opposite edges of the beam: this is the spin Hall effect for photons, which can be registered in the cross-polarized component of the scattered beam.