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

TLDR

Beam reflection and refraction obey total angular momentum conservation, but individual photons do not due to missing path information. The study proposes a solution for the reflection and refraction of a polarized Gaussian beam at a transparent interface. The authors compute transverse shifts of the beam centers of gravity and analyze the field structure of the reflected and refracted beams. The scattering of a linearly polarized beam produces a spin Hall effect, with opposite helicity photons accumulating at opposite beam edges, observable in the cross‑polarized component.

Abstract

We present a solution to the problem of reflection and 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, but, in general, do not satisfy the conservation laws for individual photons as a consequence of the lack of the "which path" information in a two-channel wave scattering. The field structure for the reflected and refracted beams 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.