Goos-H\"anchen and Imbert-Fedorov beam shifts: An overview

TL;DR

This paper provides a comprehensive overview of the Goos-H"anchen and Imbert-Fedorov beam shifts, unifying their description through geometric and polarization analysis, and exploring their relation to angular momentum and geometric phases.

Contribution

It introduces a unified, self-consistent framework for understanding beam shifts using geometric optics and Jones matrices, linking shifts to geometric phases and angular momentum conservation.

Findings

Unified description of beam shifts via geometric-optics and Jones matrices

Relation of Imbert-Fedorov shift to geometric phases and angular momentum

Extension of beam shift concepts to vortex beams with orbital angular momentum

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-H\"anchen and Imbert-Fedorov shifts (the latter being also known as spin-Hall effect of light). Our description reveals 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 the 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.