Goos–Hänchen and Imbert–Fedorov beam shifts: an overview

TLDR

The paper reviews extensions and generalizations of basic beam‑shift phenomena and related effects. The authors examine reflection and transmission of polarized paraxial light beams at a plane dielectric interface. They model field transformations using plane‑wave representation and geometric rotations, construct an effective Jones matrix for spatial‑dispersion properties, and analyze spatial and angular shifts—including analogues for higher‑order vortex beams with orbital angular momentum. This yields a unified, self‑consistent description of the Goos–Hänchen and Imbert–Fedorov shifts, showing that the transverse Imbert–Fedorov shift is linked to geometric phases between constituent waves and to angular‑momentum conservation.

Abstract

We consider reflection and transmission of polarized paraxial light beams at a plane dielectric interface. The field transformations taking into account a finite beam width are described based on the plane-wave representation and geometric rotations. Using geometrical-optics coordinate frames accompanying the beams, we construct an effective Jones matrix characterizing spatial-dispersion properties of the interface. This results in a unified self-consistent description of the Goos–Hänchen and Imbert–Fedorov shifts (the latter being also known as the spin Hall effect of light). Our description reveals the intimate relation of the transverse Imbert–Fedorov shift to the geometric phases between constituent waves in the beam spectrum and to the angular momentum conservation for the whole beam. Both spatial and angular shifts are considered as well as their analogues for higher-order vortex beams carrying intrinsic orbital angular momentum. We also give a brief overview of various extensions and generalizations of the basic beam-shift phenomena and related effects.