Hall Effect of Light

TL;DR

This paper derives a semiclassical model for light that incorporates Berry curvature, revealing a polarization-dependent Hall effect and proposing enhancement in photonic crystals, advancing understanding of light's angular momentum and its transverse shifts.

Contribution

It introduces a semiclassical equation of motion for light wave-packets that includes Berry curvature, explaining the polarization-dependent Hall effect and its enhancement in photonic crystals.

Findings

Identifies a polarization-dependent transverse shift of light.

Derives a semiclassical equation incorporating Berry curvature.

Proposes enhancement of the effect in photonic crystals.

Abstract

We derive the semiclassical equation of motion for the wave-packet of light taking into account the Berry curvature in the momentum space. This equation naturally describes the interplay between the orbital and spin angular momenta, i.e., the conservation of the total angular momentum of light. This leads to the shift of the wave-packet motion perpendicular to the gradient of the dielectric constant, i.e., the polarization-dependent Hall effect of light. An enhancement of this effect in the photonic crystal is also proposed.