Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium

TL;DR

This paper reviews how the geometry of polarized light in gradient-index media leads to phenomena like Berry phase and spin Hall effect, revealing their underlying physical and mathematical structures.

Contribution

It introduces a unified geometrical framework explaining spin-orbit coupling, Berry phase, and spin Hall effect in electromagnetic wave propagation.

Findings

Berry phase causes polarization variations depending on the trajectory

Spin Hall effect results in polarization-dependent trajectory shifts

Unified geometrical structures underpin the phenomena

Abstract

We review the geometrical-optics evolution of an electromagnetic wave propagating along a curved ray trajectory in a gradient-index dielectric medium. A Coriolis-type term appears in Maxwell equations under transition to the rotating coordinate system accompanying the ray. This term describes the spin-orbit coupling of light which consists of (i) the Berry phase responsible for a trajectory-dependent polarization variations and (ii) the spin Hall effect representing polarization-dependent trajectory perturbations. These mutual phenomena are described within universal geometrical structures underlying the problem and are explained by the dynamics of the intrinsic angular momentum carried by the wave. Such close geometro-dynamical interrelations illuminate a dual physical nature of the phenomena.